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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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     "source": [
      "Designing Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import book_format\n",
      "book_format.load_style()"
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     "source": [
      "In this chapter we will work through the design of several Kalman filters to gain experience and confidence with the various equations and techniques.\n",
      "\n",
      "\n",
      "For our first multidimensional problem we will track a robot in a 2D space, such as a field. We will start with a simple noisy sensor that outputs noisy $(x,y)$ coordinates which we will need to filter to generate a 2D track. Once we have mastered this concept, we will extend the problem significantly with more sensors and then adding control inputs. \n",
      "blah blah"
     ]
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     "source": [
      "Tracking a Robot"
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     "source": [
      "This first attempt at tracking a robot will closely resemble the 1-D dog tracking problem of previous chapters. This will allow us to 'get our feet wet' with Kalman filtering. So, instead of a sensor that outputs position in a hallway, we now have a sensor that supplies a noisy measurement of position in a 2-D space, such as an open field. That is, at each time $T$ it will provide an $(x,y)$ coordinate pair specifying the measurement of the sensor's position in the field.\n",
      "\n",
      "Implementation of code to interact with real sensors is beyond the scope of this book, so as before we will program simple simulations in Python to represent the sensors. We will develop several of these sensors as we go, each with more complications, so as I program them I will just append a number to the function name. `pos_sensor1()` is the first sensor we write, and so on.\n",
      "\n",
      "So let's start with a very simple sensor, one that travels in a straight line. It takes as input the last position, velocity, and how much noise we want, and returns the new position. "
     ]
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      "import numpy.random as random\n",
      "import copy\n",
      "class PosSensor1(object):\n",
      "    def __init__(self, pos = [0,0], vel = (0,0), noise_scale = 1.):\n",
      "        self.vel = vel\n",
      "        self.noise_scale = noise_scale\n",
      "        self.pos = copy.deepcopy(pos)\n",
      "        \n",
      "    def read(self):\n",
      "        self.pos[0] += self.vel[0]\n",
      "        self.pos[1] += self.vel[1]\n",
      "        \n",
      "        return [self.pos[0] + random.randn() * self.noise_scale,\n",
      "                self.pos[1] + random.randn() * self.noise_scale]"
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     "source": [
      "A quick test to verify that it works as we expect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import book_plots as bp\n",
      "\n",
      "pos = [4,3]\n",
      "sensor = PosSensor1 (pos, (2,1), 1)\n",
      "\n",
      "for i in range (50):\n",
      "    pos = sensor.read() \n",
      "    bp.plot_measurements(pos[0], pos[1])\n",
      "\n",
      "plt.show()"
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       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c531d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That looks correct. The slope is 1/2, as we would expect with a velocity of (2,1), and the data seems to start at near (6,4).\n",
      "\n",
      "##### Step 1: Choose the State Variables\n",
      "\n",
      "As always, the first step is to choose our state variables. We are tracking in two dimensions and have a sensor that gives us a reading in each of those two dimensions, so we  know that we have the two *observed variables* $x$ and $y$. If we created our Kalman filter using only those two variables the performance would not be very good because we would be ignoring the information velocity can provide to us. We will want to incorporate velocity into our equations as well. I will represent this as\n",
      "\n",
      "$$\\mathbf{x} = \n",
      "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n",
      "\n",
      "There is nothing special about this organization. I could have listed the (xy) coordinates first followed by the velocities, and/or I could done this as a row matrix instead of a column matrix. For example, I could have chosen:\n",
      "\n",
      "$$\\mathbf{x} = \n",
      "\\begin{bmatrix}x&y&v_x&v_y\\end{bmatrix}$$\n",
      "\n",
      "All that matters is that the rest of my derivation uses this same scheme. However, it is typical to use column matrices for state variables, and I prefer it, so that is what we will use. \n",
      "\n",
      "It might be a good time to pause and address how you identify the unobserved variables. This particular example is somewhat obvious because we already worked through the 1D case in the previous chapters. Would it be so obvious if we were filtering market data, population data from a biology experiment, and so on? Probably not. There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n",
      "\n",
      "Beyond this you can start looking at how you might combine the data from two or more different sensors to produce more information. This opens up the field of *sensor fusion*, and we will be covering examples of this in later sections. For now, recognize that choosing the appropriate state variables is paramount to getting the best possible performance from your filter. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 2:** Design State Transition Function\n",
      "\n",
      "Our next step is to design the state transition function. Recall that the state transition function is implemented as a matrix $\\mathbf{F}$ that we multipy with the previous state of our system to get the next state, like so. \n",
      "\n",
      "$$\\mathbf{x}' = \\mathbf{Fx}$$\n",
      "\n",
      "I will not belabor this as it is very similar to the 1-D case we did in the previous chapter. Our state equations for position and velocity would be:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) \\\\\n",
      "v_x &= (0*x) +  (1*v_x) + (0*y) + (0 * v_y) \\\\\n",
      "y' &= (0*x) + (0* v_x)         + (1*y) + (\\Delta t * v_y) \\\\\n",
      "v_y &= (0*x) +  (0*v_x) + (0*y) + (1 * v_y)\n",
      "\\end{aligned}\n",
      "$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Laying it out that way shows us both the values and row-column organization required for $\\small\\mathbf{F}$. In linear algebra, we would write this as:\n",
      "\n",
      "$$\n",
      "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}' = \\begin{bmatrix}1& \\Delta t& 0& 0\\\\0& 1& 0& 0\\\\0& 0& 1& \\Delta t\\\\ 0& 0& 0& 1\\end{bmatrix}\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n",
      "\n",
      "So, let's do this in Python. It is very simple; the only thing new here is setting `dim_z` to 2. We will see why it is set to 2 in step 4."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import KalmanFilter\n",
      "import numpy as np\n",
      "\n",
      "tracker = KalmanFilter(dim_x=4, dim_z=2)\n",
      "dt = 1.   # time step\n",
      "\n",
      "tracker.F = np.array ([[1, dt, 0,  0],\n",
      "                      [0,  1, 0,  0],\n",
      "                      [0,  0, 1, dt],\n",
      "                      [0,  0, 0,  1]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 3**: Design the Motion Function\n",
      "We have no control inputs to our robot (yet!), so this step is trivial - set the motion input $\\small\\mathbf{u}$ to zero. This is done for us by the class when it is created so we can skip this step, but for completeness we will be explicit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tracker.u = 0."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "##### **Step 4**: Design the Measurement Function\n",
      "The measurement function defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. At first this is a bit counterintuitive, after all, we use the Kalman filter to go from measurements to state. But the update step needs to compute the residual between the current measurement and the measurement represented by the prediction step. Therefore $\\textbf{H}$ is multiplied by the state $\\textbf{x}$ to produce a measurement $\\textbf{z}$. \n",
      "\n",
      "In this case we have measurements for (x,y), so $\\textbf{z}$ must be of dimension $2\\times 1$. Our state variable is size $4\\times 1$. We can deduce the required size for $\\textbf{H}$ by recalling that multiplying a matrix of size $m\\times n$ by $n\\times p$ yields a matrix of size $m\\times p$. Thus,\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "(2\\times 1) &= (a\\times b)(4 \\times 1) \\\\\n",
      "&= (a\\times 4)(4\\times 1) \\\\\n",
      "&= (2\\times 4)(4\\times 1)\n",
      "\\end{aligned}$$\n",
      "\n",
      "So, $\\textbf{H}$ is of size $2\\times 4$.\n",
      "\n",
      "Filling in the values for $\\textbf{H}$ is easy in this case because the measurement is the position of the robot, which is the $x$ and $y$ variables of the state $\\textbf{x}$. Let's make this just slightly more interesting by deciding we want to change units. So we will assume that the measurements are returned in feet, and that we desire to work in meters. Converting from feet to meters is a simple as multiplying by 0.3048. However, we are converting from state (meters) to measurements (feet) so we need to divide by 0.3048. So\n",
      "\n",
      "$$\\mathbf{H} =\n",
      "\\begin{bmatrix} \n",
      "\\frac{1}{0.3048} & 0 & 0 & 0 \\\\\n",
      "0 & 0 & \\frac{1}{0.3048} & 0\n",
      "\\end{bmatrix}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which corresponds to these linear equations\n",
      "$$\n",
      "\\begin{aligned}\n",
      "z_x' &= (\\frac{x}{0.3048}) + (0* v_x) + (0*y) + (0 * v_y) \\\\\n",
      "z_y' &= (0*x) + (0* v_x) + (\\frac{y}{0.3048}) + (0 * v_y) \\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "To be clear about my intentions here, this is a pretty simple problem, and we could have easily found the equations directly without going through the dimensional analysis that I did above. In fact, an earlier draft did just that. But it is useful to remember that the equations of the Kalman filter imply a specific dimensionality for all of the matrices, and when I start to get lost as to how to design something it is often extremely useful to look at the matrix dimensions. Not sure how to design $\\textbf{H}$? \n",
      "Here is the Python that implements this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tracker.H = np.array([[1/0.3048, 0, 0, 0],\n",
      "                      [0, 0, 1/0.3048, 0]])\n",
      "print(tracker.H)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 3.2808399  0.         0.         0.       ]\n",
        " [ 0.         0.         3.2808399  0.       ]]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 5**: Design the Measurement Noise Matrix\n",
      "\n",
      "In this step we need to mathematically model the noise in our sensor. For now we will make the simple assumption that the $x$ and $y$ variables are independent Gaussian processes. That is, the noise in x is not in any way dependent on the noise in y, and the noise is normally distributed about the mean. For now let's set the variance for $x$ and $y$ to be 5 for each. They are independent, so there is no covariance, and our off diagonals will be 0. This gives us:\n",
      "\n",
      "$$\\mathbf{R} = \\begin{bmatrix}5&0\\\\0&5\\end{bmatrix}$$\n",
      "\n",
      "It is a $2{\\times}2$ matrix because we have 2 sensor inputs, and covariance matrices are always of size $n{\\times}n$ for $n$ variables. In Python we write:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tracker.R = np.array([[5, 0],\n",
      "                      [0, 5]])\n",
      "print(tracker.R)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[5 0]\n",
        " [0 5]]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Step 6: Design the Process Noise Matrix\n",
      "Finally, we design the process noise. We don't yet have a good way to model process noise, so for now we will assume there is a small amount of process noise, say 0.1 for each state variable. Later we will tackle this admittedly difficult topic in more detail. We have 4 state variables, so we need a $4{\\times}4$ covariance matrix:\n",
      "\n",
      "$$\\mathbf{Q} = \\begin{bmatrix}0.1&0&0&0\\\\0&0.1&0&0\\\\0&0&0.1&0\\\\0&0&0&0.1\\end{bmatrix}$$\n",
      "\n",
      "In Python I will use the numpy eye helper function to create an identity matrix for us, and multipy it by 0.1 to get the desired result."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tracker.Q = np.eye(4) * 0.1\n",
      "print(tracker.Q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.1  0.   0.   0. ]\n",
        " [ 0.   0.1  0.   0. ]\n",
        " [ 0.   0.   0.1  0. ]\n",
        " [ 0.   0.   0.   0.1]]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 7**: Design Initial Conditions\n",
      "\n",
      "For our simple problem we will set the initial position at (0,0) with a velocity of (0,0). Since that is a pure guess, we will set the covariance matrix $\\small\\mathbf{P}$ to a large value.\n",
      "$$ \\mathbf{x} = \\begin{bmatrix}0\\\\0\\\\0\\\\0\\end{bmatrix}\\\\\n",
      "\\mathbf{P} = \\begin{bmatrix}500&0&0&0\\\\0&500&0&0\\\\0&0&500&0\\\\0&0&0&500\\end{bmatrix}$$\n",
      "\n",
      "In Python we implement that with"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tracker.x = np.array([[0, 0, 0, 0]]).T\n",
      "tracker.P = np.eye(4) * 500.\n",
      "print(tracker.x)\n",
      "print()\n",
      "print (tracker.P)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.]\n",
        " [ 0.]\n",
        " [ 0.]\n",
        " [ 0.]]\n",
        "\n",
        "[[ 500.    0.    0.    0.]\n",
        " [   0.  500.    0.    0.]\n",
        " [   0.    0.  500.    0.]\n",
        " [   0.    0.    0.  500.]]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implement the Filter Code"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Design is complete, now we just have to write the Python code to run our filter, and output the data in the format of our choice. To keep the code clear, let's just print a plot of the track. We will run the code for 30 iterations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tracker = KalmanFilter(dim_x=4, dim_z=2)\n",
      "dt = 1.0   # time step\n",
      "\n",
      "tracker.F = np.array ([[1, dt, 0,  0],\n",
      "                       [0,  1, 0,  0],\n",
      "                       [0,  0, 1, dt],\n",
      "                       [0,  0, 0,  1]])\n",
      "tracker.u = 0.\n",
      "tracker.H = np.array ([[1/0.3048, 0, 0, 0],\n",
      "                       [0, 0, 1/0.3048, 0]])\n",
      "\n",
      "tracker.R = np.eye(2) * 5\n",
      "tracker.Q = np.eye(4) * .1\n",
      "\n",
      "tracker.x = np.array([[0,0,0,0]]).T\n",
      "tracker.P = np.eye(4) * 500.\n",
      "\n",
      "# initialize storage and other variables for the run\n",
      "count = 30\n",
      "xs, ys = [],[]\n",
      "pxs, pys = [],[]\n",
      "\n",
      "sensor = PosSensor1 ([0,0], (2,1), 1.)\n",
      "\n",
      "for i in range(count):\n",
      "    pos = sensor.read()\n",
      "    z = np.array([[pos[0]], [pos[1]]])\n",
      "\n",
      "    tracker.predict ()\n",
      "    tracker.update (z)\n",
      "\n",
      "    xs.append (tracker.x[0,0])\n",
      "    ys.append (tracker.x[2,0])\n",
      "    pxs.append (pos[0]*.3048)\n",
      "    pys.append(pos[1]*.3048)\n",
      "\n",
      "bp.plot_filter(xs, ys)\n",
      "bp.plot_measurements(pxs, pys)\n",
      "plt.legend(loc=2)\n",
      "plt.xlim((0,20))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xFRSuqRa6/biNWt5lebbvezSo2kYBQvI9zc4kIiIi+Z9hwLhx0L8/3HUXAOfO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\ngSe/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c53240>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I encourage you to play with this, setting $\\mathbf{Q}$ and $\\mathbf{R}$ to various values.  However, we did a fair amount of that sort of thing in the last chapters, and we have a lot of material to cover, so I will move on to more complicated cases where we will also have a chance to experience changing these values.\n",
      "\n",
      "Now I will run the same Kalman filter with the same settings, but also plot the covariance ellipse for $x$ and $y$. First, the code without explanation, so we can see the output. I print the last covariance to see what it looks like. But before you scroll down to look at the results, what do you think it will look like? You have enough information to figure this out but this is still new to you, so don't be discouraged if you get it wrong."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "\n",
      "tracker = KalmanFilter(dim_x=4, dim_z=2)\n",
      "dt = 1.0   # time step\n",
      "\n",
      "tracker.F = np.array([[1, dt, 0,  0],\n",
      "                      [0,  1, 0,  0],\n",
      "                      [0,  0, 1, dt],\n",
      "                      [0,  0, 0,  1]])\n",
      "tracker.u = 0.\n",
      "tracker.H = np.array([[1/0.3048, 0, 0, 0],\n",
      "                      [0, 0, 1/0.3048, 0]])\n",
      "\n",
      "tracker.R = np.eye(2) * 5\n",
      "tracker.Q = np.eye(4) * .1\n",
      "\n",
      "tracker.x = np.array([[0, 0, 0, 0]]).T\n",
      "tracker.P = np.eye(4) * 500.\n",
      "\n",
      "# initialize storage and other variables for the run\n",
      "count = 30\n",
      "xs, ys = [], []\n",
      "pxs, pys = [], []\n",
      "\n",
      "sensor = PosSensor1([0,0], (2,1), 1.)\n",
      "\n",
      "for i in range(count):\n",
      "    pos = sensor.read()\n",
      "    z = np.array([[pos[0]], [pos[1]]])\n",
      "\n",
      "    tracker.predict()\n",
      "    tracker.update(z)\n",
      "\n",
      "    xs.append(tracker.x[0,0])\n",
      "    ys.append(tracker.x[2,0])\n",
      "    pxs.append(pos[0]*.3048)\n",
      "    pys.append(pos[1]*.3048)\n",
      "\n",
      "    # plot covariance of x and y\n",
      "    cov = np.array([[tracker.P[0,0], tracker.P[2,0]], \n",
      "                    [tracker.P[0,2], tracker.P[2,2]]])\n",
      " \n",
      "    stats.plot_covariance_ellipse(\n",
      "        (tracker.x[0,0], tracker.x[2,0]), cov=cov,\n",
      "         facecolor='g', alpha=0.15)\n",
      "\n",
      "        \n",
      "bp.plot_filter(xs, ys)\n",
      "bp.plot_measurements(pxs, pys)\n",
      "plt.legend(loc=2)\n",
      "plt.show()\n",
      "print(\"final P is:\")\n",
      "print(tracker.P)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lekucma1pZjS10NnQzvT0dJqirTQYzaSiGbQwhkUjs9KzmN04gznN05jT1szs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b3TDm6gsdo3WR34LEcBhuJimCaqrZFmJd1hAlVFWVUkWTlO5pZ1HM2j6brUbJOmZ2GbYvVBEARB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\niIiILMv/Bw6MtRhLW8RcAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe17eacd6a0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "final P is:\n",
        "[[ 0.30660483  0.12566239  0.          0.        ]\n",
        " [ 0.12566239  0.24399092  0.          0.        ]\n",
        " [ 0.          0.          0.30660483  0.12566239]\n",
        " [ 0.          0.          0.12566239  0.24399092]]\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Did you correctly predict what the covariance matrix and plots would look like? Perhaps you were expecting a tilted ellipse, as in the last chapters. If so, recall that in those chapters we were not plotting $x$ against $y$, but $x$ against $\\dot{x}$. $x$ *is correlated* to $\\dot{x}$, but $x$ is not correlated or dependent on $y$. Therefore our ellipses are not tilted. Furthermore, the noise for both $x$ and $y$ are modeled to have the same value, 5, in $\\mathbf{R}$. If we were to set R to, for example,\n",
      "\n",
      "$$\\mathbf{R} = \\begin{bmatrix}10&0\\\\0&5\\end{bmatrix}$$\n",
      "\n",
      "we would be telling the Kalman filter that there is more noise in $x$ than $y$, and our ellipses would be longer than they are tall.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The final P tells us everything we need to know about the correlation between the state variables. If we look at the diagonal alone we see the variance for each variable. In other words $\\mathbf{P}_{0,0}$ is the variance for x, $\\mathbf{P}_{1,1}$ is the variance for $\\dot{x}$, $\\mathbf{P}_{2,2}$ is the variance for y, and $\\mathbf{P}_{3,3}$ is the variance for $\\dot{y}$. We can extract the diagonal of a matrix using *numpy.diag()*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(np.diag(tracker.P))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.30660483  0.24399092  0.30660483  0.24399092]\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The covariance matrix contains four $2{\\times}2$ matrices that you should be able to easily pick out. This is due to the correlation of $x$ to $\\dot{x}$, and of $y$ to $\\dot{y}$. The upper left hand side shows the covariance of $x$ to $\\dot{x}$. Let's extract and print, and plot it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c = tracker.P[0:2, 0:2]\n",
      "print(c)\n",
      "stats.plot_covariance_ellipse((0, 0), cov=c, facecolor='g', alpha=0.2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.30660483  0.12566239]\n",
        " [ 0.12566239  0.24399092]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C3q0AwvROYPQIIQC2hXZ3oBfzFa3WVzWbZjNCAMPV7dMPAowTIQTAxDNNSysb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\n/w+MDQmZaDglpwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15a230320>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The covariance contains the data for $x$ and $\\dot{x}$ in the upper left because of how it is organized. Recall that entries $\\mathbf{P}_{i,j}$ and $\\mathbf{P}_{j,i}$ contain $p\\sigma_1\\sigma_2$.\n",
      "\n",
      "Finally, let's look at the lower left side of $\\mathbf{P}$, which is all 0s. Why 0s? Consider $\\mathbf{P}_{3,0}$. That stores the term $p\\sigma_3\\sigma_0$, which is the covariance between $\\dot{y}$ and $x$. These are independent, so the term will be 0. The rest of the terms are for similarly independent variables."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Effect of Order"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far in this book we have only really considered tracking position and velocity. That has worked well, but only because I have been carefully selecting problems for which this was an appropriate choice. You know have enough experience with the Kalman filter to consider this in more general terms.\n",
      "\n",
      "What do I mean by \"order\"? In the context of these system models it is the number of derivatives required to accurately model a system. Consider a system that does not change, such as the height of a building. There is no change, so there is no need for a derivative, and the order of the system is zero. We could express this in an equation as\n",
      "\n",
      "$$x = 312.5$$\n",
      "\n",
      "A first order system has a first derivative. For example, change of position is velocity, and we can write this as\n",
      "\n",
      "$$ v = \\frac{dx}{dt}$$\n",
      "\n",
      "which we integrate into the Newton equation\n",
      "$$ x = vt + x_0.$$\n",
      "\n",
      "This is also called a *constant velocity* model, because of the assumption of a constant velocity.\n",
      "\n",
      "So a second order has a second derivative. The second derivative of position is acceleration, with the equation\n",
      "\n",
      "$$a = \\frac{d^2x}{dt^2}$$\n",
      "\n",
      "which we integrate into \n",
      "\n",
      "$$ x = \\frac{1}{2}at^2 +v_0t + x_0.$$\n",
      "\n",
      "This is also known as a *constant acceleration* model.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another, equivalent way of looking at this is to consider the order of the polynomial. The constant acceleration model has a second derivative, so it is second order. Likewise, the polynomial $x = \\frac{1}{2}at^2 +v_0t + x_0$ is second order.\n",
      "\n",
      "When we design the state variables and process model we must choose the order of the system we want to model. Let's say we are tracking something with a constant velocity. No real world process is perfect, and so there will be slight variations in the velocity over short time period. You might reason that the best approach is to use a second order filter, allowing the acceleration term to deal with the slight variations in velocity. \n",
      "\n",
      "That doesn't work as nicely as you might think. To thoroughly undestand this issue lets see the effects of using a  process model that does not match the order of the system being filtered. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First we need a system to filter. I'll write a class to simulate on object with a constant velocity. Essentially no physical system has a truly constant velocity, so on each update we alter the velocity by a small amount. I also write a sensor to simulate Gaussian noise in a sensor. The code is below, and a plot an example run to verify that it is working correctly. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from book_plots import plot_track\n",
      "\n",
      "np.random.seed(124)\n",
      "class ConstantVelocityObject(object):\n",
      "    def __init__(self, x0=0, vel=1., noise_scale=0.06):\n",
      "        self.x = x0\n",
      "        self.vel = vel\n",
      "        self.noise_scale = noise_scale\n",
      "\n",
      "\n",
      "    def update(self):\n",
      "        self.vel += randn()*self.noise_scale\n",
      "        self.x += self.vel\n",
      "        return (self.x, self.vel)\n",
      "\n",
      "\n",
      "def sense(x, noise_scale=1.):\n",
      "    return x[0] + randn()*noise_scale\n",
      "\n",
      "\n",
      "obj = ConstantVelocityObject()\n",
      "\n",
      "xs = []\n",
      "zs = []\n",
      "for i in range(50):\n",
      "    x = obj.update()\n",
      "    z = sense(x)\n",
      "    xs.append(x)\n",
      "    zs.append(z)\n",
      "\n",
      "\n",
      "xs = np.asarray(xs)\n",
      "bp.plot_track(xs[:,0])\n",
      "bp.plot_measurements(range(50), zs)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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54IMPEm18LOmHgoSIiIiIpI3GjeGVV2DgQGjdGrDcKGXgwIHs2LEDgKpVqzJr\n1ixq1aplvTolWRQkRERERCRtVK0KP/wAJhO3b98mICCA2bNnExcXR968eQkMDKRXr15ky5bN2pVK\nMihIiIiIiEiaMRsGi7/8klGjRvHHH39gY2ODt7c3EyZMIE+ePNYuT56BgoSIiIiIpIl9+/YxdOhQ\nDhw4AEDdunWZPXs2lStXtnJl8jx01yYRERERSVXnz5+nffv21K5dmwMHDlCoUCGWLFnCrl27FCIy\nMI1IiIiIiEiquPXnn+xp1YoB+/bxa0wMjo6ODB8+nPfffx8XFxdrlyf/koKEiIiIiKSo6Oho5s2b\nx14/P1aEh1MZGPvOO0ycMoWiRYtauzxJIQoSIiIiIpIiDMNg3bp1vP/++5wPC+PYX+2mYcP4MijI\nqrVJytMaCRERERH51w4dOsQrr7xC69atCQsL4/0CBagAGCVK4B4YaO3yJBUoSIiIiIjIc7t48SKd\nO3emevXq7Nq1i7x58zI3KIhJf+0FYQoMBAcHK1cpqUFBQkRERESe2d27dxk9ejRlypRh6dKl2Nvb\n4+Pjw7lz53jvhRcwXbtm2YCufXtrlyqpRGskRERERCTZYmNjWbBgAf7+/ly/fh2ADh06MGXKFEqU\nKGHp9MYb8PPPEBEBNvq7dWalICEiIiIiT2U2m1m1ahXjxo0jNDQUgDp16hAUFESNGjUSv+CFF9K4\nQklrChIiIiIi8liGYbBx40b8/Pw4dsxyHyZPT08++OADWrdujclksnKFYi0KEiIiIiKSpB07duDr\n68u+ffsAKFKkCP7+/nTv3h07OzsrVyfWpiAhIiIiIgmEhITg5+fHli1bAMiXLx9+fn689957ODo6\nJv2iyEh43HOSKSlIiIiIiAgAJ0+eZOzYsfznP/8BIGfOnIwcOZLBgwfj4uLy+BcaBrz2GhQoAB9/\nDIUKpVHFYk0KEiIiIiJZ3Pnz5wkICGDJkiUYhoGTkxODBg3Cx8eHPHnyPP0A69fDrl2QNy84O6d+\nwZIuKEiIiIiIZFGXL19m0qRJfP7558TGxmJnZ0ffvn3x9fWlUHJHFWJjYdQoy9djx4Kra+oVLOmK\ngoSIiIhIFnP79m0WL17M6tWriYyMxMbGhu7du+Pv7//3XhDJtWgR/PILeHhAv36pUq+kTwoSIiIi\nIlnEpUuX+Oijj9g+Zw6RUVFEAm3atGHChAm88Dz7Pty/D+PGWb4ODAR7+xStV9I3BQkRERGRTO7E\niRN8+OFWES9aAAAgAElEQVSHLFu2jGyxsYQBRYHwihXJ8dpr4O7+fAc2m6FrV9i3D9q2TcmSJQPQ\nnuUiIiIimZBhGOzatYvmzZvz4osv8tVXX2EYBl6dOnHa1xeAHCdOwLvvWu6y1KsXXLnybG/i4gJT\np8KOHWCjj5VZjX7jIiIiIplIXFwca9eupVatWjRo0ICNGzfi5OTEgAEDCAsLY+nSpeRu1YojP/4I\nixdDvXqWKUrLlj3/HZcUIrIkTW0SERERyQQiIyP5+uuvmT59OqGhoQDkzZuXAQMGMGDAAPLly5eg\nv9nR0TItqWtXOHMGfvoJcuVKfOC4ODCZFBYkEV0RIiIiIhnY7du3+eCDDyhZsiR9+vQhNDSUEiVK\nMGvWLC4ePEhAkSKJQkQiZctChw5JP/ftt1CqFEycCL/9lvInIBmWgoSIiIhIBnT58mVGjhxJsWLF\nGD16NFevXqVy5cosW7aMsLAwBrz6Ks6NGkGfPrBixfO/0TffwP/+Z7k7U/HilvUUs2al2HlIxqUg\nISIiIpKBnDp1ip49e1KyZEmmT5/OvXv3aNSoEd9//z0//fQTHTt2xHbfPqhTB379FWrUgFdfff43\nXLgQNm+Gdu0gWza4ehUGDbK0S5amNRIiIiIi6ZxhGOzZs4dp06axfv16AGxsbGjbti0+Pj5Uq1bt\n786rVkGXLhAVBS1awPLlz7+I2vJG0KSJ5XHjBnz9tWWKU/v2//KsJKNTkBARERFJp8xmM99++y3T\npk1j3759ADg6OtKjRw+GDRuGp6dnwhdERsL771tCRL9+lilI2bKlXEH58sHQoSl3PMnQFCRERERE\nrOHyZdizB6pXhxIlLHdG+ktkZCRLlixh+vTpnDlzBoA8efIwYMAAvL29cXNzS/qYjo6wYQN8953l\nA/8jxxRJaQoSIiIiItZw69bf04OKFIG6dXlQpQorLl/GLziYq1evAlC8eHGGDx9Oz549yZ49+9OP\n+8ILlodIKlOQEBEREUlpcXGWfRm2b4ejR2HJksSjAxUqwFtvwe7dltGJlStxXrmSqsBV4KWXXsLH\nx4e2bdtia6uPbJL+6KoUERERSSmffAJbtsCuXXD37t/t/v5QpkzCviYTJ6dMYfq0aRxeupRacXHU\nBcweHmyeN4/GjRtjejR8HDoEwcFQt67ljkz37lkWVo8cmSanJvJPChIiIiIiKWXJEggJsXzt4QEN\nG1oeBQrEdzEMg+3btxMUFMTGjRsByx2YKnToQIWRI6lSpUrSx964ET780PIAy3qIyEjInx+6d0/F\nkxJJmoKEiIiISEoZMQIiIizhoVixBE/FxMSwcuVKgoKCOHr0KABOTk706tWLYcOGUbJkyScf+403\nIDraMhXqwAFLiGjUCFq1Sq2zEXkiBQkRERGRZ/Hnn/Djj9CyZeLn2rVL1HT79m0WLFjAxx9/zOXL\nlwEoUKAAAwYM4L333iNfvnzJe9/q1S0PsASK0FDLouqUvL2ryDNQkBARERFJrtBQePNNOH/ecovV\nJk0e2/V///sfH3/8MZ9//jnh4eEAlC9fnmHDhvHOO+/g6Oj4/HXY20PFis//epEUoCAhIiIikhw7\ndkDr1pbbtr70EpQrl2S3gwcPEhQUxOrVqzGbzQC8+uqrDB8+nNdeew0bG5s0LFok9ShIiIiIiDzN\nwoXQty/Exlpu2bpsGeTIEf90XFwc69evJygoiN27dwNga2tLp06dGD58OC+99JK1KhdJNQoSIiIi\nIk/y55+WW6zGxsLw4TB1avy6hAcPHrB48WI++ugjwsLCAHB1daVv374MHDgQd3d3a1YukqoUJERE\nRESeJE8eWLvWsj7i3XcBuHbtGp9++ilz5szh5s2bgGUH6iFDhtCrVy9cXFysWbFImlCQEBEREXma\nBg2gQQNOnz7NjBkz+Oqrr4iKigKgevXqjBgxgtatW2sHaslSdLWLiIiIPIFhGPz4449Mnz6d9evX\nx7e3aNGCESNGULdu3YQ7UItkEQoSIiIiIg998w1cuABDhhAbG8vatWuZPn06IX/tVu3g4EC3bt0Y\nNmwYZcuWtXKxItalICEiIiJiGBAUBD4+GMDK335j9Jo1/O9//wMgb968eHt74+3tjZubm1VLFUkv\nFCREREQka4uOhv794YsvAJjo6Ih/UBAAnp6eDBs2jG7duuHs7GzNKkXSHQUJERERybru3eP+q6+S\nPSSEB0BXYE1kJHXq1GHEiBG89dZbZPvrVq8ikpC2VhQREZEs6eTJk7Tr3p27ISH8DrwC4OXF3r17\n2b17N2+//bZChMgTaERCREREMr+bN8HODnLmJDQ0lPHjx7N8+XIMw8BkZ4dnx44sGzsWT09Pa1cq\nkmEoSIiIiEjmFBEB69fDkiWwaRM3R49m5KVLfPXVV8TFxWFnZ0efPn3w9fWlcOHC1q5WJMNRkBAR\nEZHM5dQpmDbNshv1vXsAmE0mlkyaxCKzmWzZstG7d2/GjBlD8eLFrVysSMalICEiIiKZy507sHgx\nAL8WKMDHN26wNC6OGyYTXbp0Ydy4cZrCJJICtNhaREREMp7ISNixI8mnbpYuzYZXXqGSgwMlrl3j\no7g4XmnXjhMnTvDVV18pRIikEI1IiIiISMZw8SJs3AgbNsC2bZY1EOfOgYcHALdv32bGjBnMnDmT\ne39NaWrZsiXjx4+ncuXK1qxcJFNSkBAREZH0r00bWLMmYVuVKvDHH9zLn59PPvmE6dOnc/v2bQBe\nf/11JkyYQPXq1a1QrEjWoCAhIiIi6YdhgMmUuN3DA3LkgKZNoVkzeOMNIvPkYd68eQS2aMH169cB\naNiwIRMnTqROnTppXLhI1qM1EiIiImJdMTEwYwbUqAETJiTdx9fXshfEmjXEduvGF999R5kyZRg6\ndCjXr1+nVq1abNu2jR9++EEhQiSNaERCRERErCc0FDp3hpAQy/fZsoG/f+J+uXJhNptZtXIl48aN\nIzQ0FIBKlSoxefJkmjdvjimpkQwRSTUakRAREZG0Zxjw2Wfw8suWEFGsGKxaBVu2JNHVYOPGjVSt\nWpUOHToQGhqKp6cny5Yt46effuLNN99UiBCxAo1IiIiISNozmy17PTx4AO+8A7NnQ65cibr9+OOP\n+Pr6snv3bgCKFCmCv78/3bt3x87OLq2rFpFHPHVE4tNPP6Vy5cq4urri6upK7dq12bhxY4I+AQEB\nFClSBGdnZxo2bMipU6dSrWARERHJBLJlg6+/hmXLYMmSRCHip59+4o033qB+/frs3r2bvHnzEhQU\nRFhYGO+++65ChEg68NQgUbRoUaZNm8ZPP/3E4cOHadSoEW+//TbHjh0DYOrUqcyYMYPZs2cTEhKC\nm5sbTZo0ITw8PNWLFxERkQzMwwM6dkzQdObMGdq1a0eVKlXYtGkTLi4uBAQEcP78eYYNG4aTk5OV\nihWRf3pqkGjRogWvvfYaHh4eeHp6MmnSJFxcXDh48CCGYTBz5kxGjx5Nq1atqFChAosXL+bevXss\nW7YsLeoXERGR9O7wYfjjjyd2uXjxIr169aJ8+fKsWrUKBwcHhg8fzvnz5/H39ydnzpxpVKyIJNcz\nLbaOi4tjxYoVREZGUr9+fS5cuMC1a9do2rRpfB9HR0fq16/P3r17U7xYERERyUDi4iAwEGrWhN69\nLQus/+HixYv069cPT09PFi5ciMlkok+fPpw9e5bp06eTL18+KxQuIsmRrMXWP//8M7Vq1SIqKgon\nJyeCg4MpW7ZsfFgoUKBAgv5ubm5cuXLlscc7dOjQvyhZ5Ol0jUlq0zUmaSEjX2f2ly9T0t8fl7+m\nQl/LkYPfDhzAsLV89Lhy5Qpffvkl69evJzY2FpPJxGuvvUbfvn0pWrQoV69e5erVq9Y8hSwhI19j\nkvpKly79xOeTFSTKlSvH8ePHuXPnDqtWraJDhw5s3779ia/RbdhERESypjwbN1J82jSy3b9PdL58\n/C8ggLs1agDw22+/8eWXX/Lf//6XuLg4bGxseO211+jVqxclS5a0cuUi8iySFSTs7Ozw8PAA4OWX\nXyYkJIRPP/2UcePGAXDt2jXc3d3j+1+7do2CBQs+9njVqlX7NzWLPNbDv6zoGpPUomtM0kKGv85W\nr4b796F1a+w/+4wyefNy7tw5Jk+ezFdffRUfILp06YKfnx9ly5a1dsVZToa/xiRN3Llz54nPP9eG\ndHFxcZjNZkqWLEnBggXZvHlz/HORkZHs3r2b2rVrP8+hRUREJKObMMESJlavJuzPP+nevTtly5Zl\n0aJFAHTr1o3Tp0/z1VdfKUSIZGBPHZEYNWoUb775Ju7u7vF3Y9q5cyebNm0CYMiQIQQGBlKuXDlK\nly4df1enTp06pXrxIiIikg7Z23OmYkUmd+vG0qVLMZvNZMuWjR49euDr64unp6e1KxSRFPDUIHHt\n2jU6d+7M1atXcXV1pXLlymzatIkmTZoA4OPjQ0REBN7e3ty6dYuaNWuyefNmsmfPnurFi4iIiJXF\nxoLt3x8nTp8+zcSJE1mxYgVmsxlbW9v4APFwmrSIZA5PDRIPhyGfxN/fH39//xQpSERERDKI9evh\n/fdhyxZC798nICCAFStWYBgGdnZ29O7dm9GjR1OiRAlrVyoiqSBZi61FREREEggOhnfegdhY/tOq\nFW2PHCEuLg47Ozt69erFqFGjKF68uLWrFJFU9FyLrUVERCQL+/JLjI4dITaW6dmy0TokBIB3332X\ns2fPMnfuXIUIkSxAQUJERESSLXrmTOjRA5PZzFhgZFwcbdu25eTJk3z22WcUK1bM2iWKSBrR1CYR\nERF5qpiYGBYuXMj9sWMZBgwDjr/6KgenTKF69erWLk9ErEBBQkRERB7LbDazatUqxowZw9mzZwE4\nUbYsnWbPZkbjxlauTkSsSUFCREREEjEMgy1btjB69GiOHDkCQOnSpZk8eTJt2rTBZDJZuUIRsTYF\nCREREUng4MGDjBo1iu3btwNQuHBh/P396dGjB3Z2dlauTkTSCwUJERERASybyfn5+bF27VpsgE8c\nHLAfPJgu/v44OztbuzwRSWd01yYREZEs7rfffqN3795UqFCBtWvX4uLoyJEXXmBgVBR9N27E2cHB\n2iWKSDqkICEiIpJF3bx5k5EjR+Lp6ckXX3yByWSif8+e/FGvHpV/+QVcXGDuXMiWzdqlikg6pCAh\nIiKSxdy/f5/AwEA8PDyYPn06UVFRtGvXjtOHD/PppUs4btkCefLADz9A3brWLldE0ikFCRERkSwi\nJiaGuXPn4unpiZ+fH3fv3qVJkyYcOnSIlStX4pkrF2zZAm5usGMHVKtm7ZJFJB1TkBAREcnkzGYz\ny5cv54UXXmBa//68cfUqNatVY+vWrWzevJmqVataOhYvDq1awa5d8OKL1i1aRNI93bVJREQkkzIM\ng+0rVrBl9GhK/formwGPh8998gmmWrUSv2jt2rQsUUQyMI1IiIiIZEL79++nYcOGxHbqxJRff6U3\nlhBh5MoFb7+NSftBiMi/pBEJERGRTOSXX37B19eXdevWAVDTyYnSRYvi3rUrdq+/jumll3QXJhFJ\nEQoSIiIimcClXbsYu3AhX3/9NWazGScnJ4YOHcrIkSPJlSuXtcsTkUxIQUJERCQD+/3SJUKbN6fa\nzz9zDLCxtaVPnz6MGzeOQoUKWbs8EcnEFCREREQyoJs3b/LJhAnUnT2bJmYzUUDP+vVpvmgRHh4e\nT329iMi/pSAhIiKSgdy7d4+ZM2eyZto0loeH8wJwx96em198wcDOna1dnohkIQoSIiIiGUBERARz\n585lypQp3L1xgzCgGPDAwwPXbdtwLVHCyhWKSFajICEiIpKOxcTEsHDhQiZMmMCVK1cAqF27Nvca\nN4bDh3Fetgxy5rRylSKSFSlIiIiIpENxcXEsWbIEf39/zp8/D8BLL73E5MmTeeONNzCZTGAYYDJZ\nuVIRyaoUJERERNIRwzDYsWMHc+fOjQ8QZcuWZeLEiXh5eWFj88hesgoRImJFChIiIiLpgGEYbNmy\nhTFjxhASEgJAsWLFmDZoEG08PcnWsqWVKxQRSUhBQkRExMr27NmDn58fO3fuBCBPnjz07NmTya1a\nYd+mDdy8CTt3Qs2aVq5URORvChIiIiJWcuTIEcaMGcN3330HQO7cufHx8aFOnToU3rsX+8aNISIC\nXnkFSpe2brEiIv+gICEiIpLGTp06xbhx41izZg0AOXLkYOjQoQwbNoxcrq5c9vamyNy5ls69esGc\nOWBvb8WKRUQSU5AQERFJI+fPn2f8+PEsWbIEs9mMg4MDAwYM4P333yd//vyWTvfv47Z8OYbJhOnD\nD2HYMC2qFpF0SUFCREQklV25coVJkyaxYMECYmNjsbW1pU+fPowZM4YiRYok7Jw9O5f79SMmXz5K\nDxtmnYJFRJJBQUJERCSV3Lhxgw8++IBPP/2UyMhIbGxs6Nq1K/7+/niULAnXriX9utat07hSEZFn\nZ/P0LiIiIvIs7ty5g7+/PyVLliQoKIjIyEi8vLz4+eefWfzll3icPAnVqkHjxmA2W7tcEZHnoiAh\nIiKSQsLDwwkMDKRkyZJMmDCB8PBw3njjDQ4fPszqVasof+6cJUC0aAFHjlhu6/rXpnMiIhmNpjaJ\niIgkxTAs/03GQucHDx4wZ84cpk6dyo0bNwCoX78+kydPpm7dupZObdvC6tWWrwsWhFGjoE8fcHJK\njepFRFKdRiRERET+afVqcHcHR0coXvyxowZRx47x+aRJlPbwYOTIkdy4cYNatWqxdetWduzY8XeI\nAGjWzBIgZs60HG/wYIUIEcnQNCIhIiLy0M2b4O0NK1f+3XbxIuTKlaBbdHQ0CxcupLW3N73NZnoA\nf9rZYV+8ODnz5MH08suJRzK6dIEOHRQeRCTT0IiEiIjIQwEBlhCRPbtlE7j79+HcOcidG4DY2FgW\nLlxI2bJl6devH7+ZzfyZLRvZgPwxMbiePYtpwwZwdk58bFtbhQgRyVQ0IiEiIvLQhAlw/ToEBoKH\nh6XNw4O4uDiWL1/O+PHjOXv2LAAvvPAC58aP5yUvL4iNtdzK9fff4Y8/LFOiREQyOQUJERGRh3Ln\nhhUr4r81m82sXr0af39/Tp8+DYCnpycBAQF06NCBbNmyWTra20PRopaHiEgWoSAhIiJZz+3blvUQ\npUol+bTZbObbb7/F39+f48ePA1CiRAnGjRtHly5dsLXV/z5FRLRGQkREspbvv4cXX4Q2bSA6OsFT\nD0cgXn75ZVq1asXx48dxd3dn3rx5nDlzhh49eihEiIj8RUFCRESyhrt3Lfs2vP46/PabZTrSzZsA\nxMXFsXLlSipVqkTbtm05fvw4hQsX5pNPPiEsLIy+fftib29v5RMQEUlf9GcVERHJ/LZvh+7dLbdy\ntbe3LKoePpxYYOXSpUyaNCl+DYS7uzujR4+mZ8+eOGrRtIjIYylIiIhI5nfhgiVEVK0KixcTW7Ys\nS5cuZfLkyYSFhQFQvHhxfH196datGw4ODlYuWEQk/VOQEBGRzK9HD3B0JObtt/l6xQomt2jB+b92\nq/bw8MDPz48uXbpgZ2dn5UJFRDIOBQkREcn0oqKjWRweTmD58vz6668AlC5dmjFjxtCpUyctoBYR\neQ76l1NERDKPS5fgxAl44w0AIiMjWbhwIR988AGXLl0CoFy5cowdO5b27dv/vQ+EiIg8MwUJERHJ\nHP7zH+jVC6Kjid6/ny9+/JFJkyZx5coVACpWrMjYsWPx8vJSgBARSQEKEiIikrE9eADDh8O8eQBc\nfukl3n7zTQ79NYWpcuXKjBs3jrfffhsbG931XEQkpShIiIhIxnXyJLRrB6dOEWdry4f58zP66FHA\nMoVp0qRJtG7dGpPJZOVCRUQyHwUJERHJuMxmzGfPcsnJiZYRERz7/XeKFi3K+PHj6dKlixZRi4ik\nIv0LKyIiGdJPP/2Er68vUdHRHACc8+XjIz8/3nvvPW0kJyKSBhQkREQkQwkNDWXs2LEEBwcD4OLi\nwvsjRjB06FBcXFysXJ2ISNahICEiIulfTAw3Fy1iVEgIixYtIi4uDgcHBwYMGMCoUaPIly+ftSsU\nEclyFCRERCRd+/PwYe6+9RYlfv+d+wDZstG7d2/GjRtH0aJFrV2eiEiWpSAhIiLpz59/ErViBYdW\nrKDijz9SArgElGnYkFPz5lGmTBkrFygiIgoSIiKSdgwDbt6E8+fhwgUID7dsIveIuLg41s6bR1s/\nP+r81banQAFyLF9OQMOGaV+ziIgkSUFCRERS382b0KiRJUCEh//dnjMn9OwJJhOGYbBp0yZ8fHw4\nc+IEkUBUoULU8Pamjq8vaC8IEZF0RUFCRERSX65c8MsvEBNjCQ8eHlCypOURG8vRkycZOXIkW7du\nBaB48eLYTpnCO+3bazdqEZF0SkFCRERSX7ZscPgwFCkCuXPHjy5cunSJMb178/XXX2MYBrly5cLP\nz48BAwZoLwgRkXROQUJERNLGiy/Gf3nnzh0++OADZs6cSWRkJHZ2dgwYMIAxY8aQJ08eKxYpIiLJ\npSAhIiIpLyoKHBwSNcfExDB//nzGjx/PjRs3AGjfvj2BgYF4eHikdZUiIvIvaOKpiIikrOPHLWsg\nVq+ObzIMg7Vr11KhQgUGDhzIjRs3qFevHgcOHGDFihUKESIiGZCChIiIpJzoaOjaFa5cgR9+AGDf\nvn3Uq1cPLy8vwsLCKFu2LOvWrWPnzp383//9n5ULFhGR5/XUIDFlyhSqV6+Oq6srbm5utGjRgpMn\nTybqFxAQQJEiRXB2dqZhw4acOnUqVQoWEZF0bOJEOHYMPDw40qEDzZs3p3bt2uzZs4f8+fMzZ84c\nfv75Z1q2bIlJt3MVEcnQnhokdu7cyYABA9i3bx8//PADtra2NG7cmFu3bsX3mTp1KjNmzGD27NmE\nhITg5uZGkyZNCH/0XuEiIpK5HTwIU6ZgmEyMKlCAqg0asHHjRrJnz46fnx9nz56lX79+2NnZWbtS\nERFJAU9dbL1p06YE33/99de4urqyd+9emjdvjmEYzJw5k9GjR9OqVSsAFi9ejJubG8uWLaNPnz6p\nU7mIiKQfZjMRnTrhFBfHDGDqvn04OzszcOBARowYQb58+axdoYiIpLBnXiNx9+5dzGYzuXPnBuDC\nhQtcu3aNpk2bxvdxdHSkfv367N27N+UqFRGRdOn48eO0btOGRufO8S0w2dGRESNGcOHCBT744AOF\nCBGRTMpkGIbxLC9o164d586d49ChQ5hMJvbu3UvdunW5ePEi7u7u8f169uzJlStX4kc07ty5E/9c\nWFhYCpUvIiLWcvbsWRYsWMAPfy2qdnBwwMvLi65du5I3b14rVyciIv9W6dKl4792dXVN9Pwz7SMx\nbNgw9u7dy+7du5O1SE4L6UREMp/z58+zYMECtm3bhmEY2Nvb07p1a7p166bRBxGRLCTZQWLo0KEE\nBwezfft2SpQoEd9esGBBAK5du5ZgROLatWvxz/1TtWrVnrNckSc7dOgQoGtMUk9WvsZOnz7NhAkT\nWLFiRXyA6Nu3L6NGjaJw4cLWLi9TycrXmaQNXWOSHI/OKEpKstZIDB48mJUrV/LDDz9QpkyZBM+V\nLFmSggULsnnz5vi2yMhIdu/eTe3atZ+jZBERSU9Onz5N586dqVChAsuXL8fW1pb+/ftz/uhRPvnk\nE4UIEZEs6qkjEt7e3ixZsoR169bh6urK1atXAXBxcSF79uyYTCaGDBlCYGAg5cqVo3Tp0kyaNAkX\nFxc6deqU6icgIiKp4/jx40yePJlVq1ZhGAZ2dna8++67+Pr6UixnTqhUCVq0gOnTwdHR2uWKiEga\ne2qQmDt3LiaTiVdffTVBe0BAAOPGjQPAx8eHiIgIvL29uXXrFjVr1mTz5s1kz549daoWEZFUc+jQ\nISZNmsQ333wDgL29Pd27d8fX15fixYtbOnXvDpcuQUgI2D7TcjsREckknvqvv9lsTtaB/P398ff3\n/9cFiYiIdezZs4dJkybF323P0dGRPn36MHLkyARr4PjmG1i82DIKsXixgoSISBalf/1FRLIwwzDY\nvn07EydOZMeOHQBkz56d/v37M3z4cAoUKJDwBTduwMONRqdMgXLl0rZgERFJNxQkRESyIMMw2LRp\nE//f3n3HVVn3fxx/HaaogDkQB7lCzdQyR+6NgZZbwb3LHJmtO+807c6VdZf9VExT3ASaE1LDnChW\n5tbu29vSXLhzgSDjnN8fl6KYA4TDYbyfj8d5BNf4fj9Xj2923l7X9f1+8skn7Ny5EzDmCH/zzTcZ\nMWLEw9eBGDMGLlyAJk3gzTezsGIREcluFCRERPIQs9nMmjVrGD9+PLt37wagSJEijBw5kqFDh1Ko\nUKFHNzBhAiQkwIcfgl2aJv4TEZFcSkFCRCQPSE5OZtmyZUyYMIFDhw4BULx4cd59910GDx5MwYIF\n09ZQ4cIwd64VKxURkZxCQUJEJBdLSkoiJCSE8ePHc+TIEQBKlSrFP/7xDwYOHIiLi4uNKxQRkZxK\nQUJEJBdKSkpiyZIlTJgwgaNHjwJQtmxZRo0aRZ8+fXB2dn50A7GxsGMH/O9/MGxYFlQsIiI5jYKE\niEgukpiYyOLFi5kwYQJ//PEHABUqVODDDz+kZ8+eODo6PvhEsxm2boXNm43Pzz9DYiLY20Pv3uDm\nloVXISIiOYGChIhILpCQkMDChQuZOHEix48fB8Db25vRo0fTvXt3HB631oPJBN27w7lzxu92dlCr\nFjRrBrduWbl6ERHJiRQkRERysISEBObPn8/EiRM5ceIEAJUqVWL06NEEBATcDRBJSbB7t3G3oWtX\nKF8+dUMmEwwcCDExRnho3BgeN4OTiIjkaQoSIiJZISkpU1eAvnXrFkFBQUyaNIlTp04BULlyZcaM\nGYO/vz/29vbG4nHr18P338MPP8CVK8bJrq4wdOjfG/3kk0yrT0REcj8FCRERazpwACZOhKtXjS/1\n975xnyAAACAASURBVNuxA5YsAT8/aN4cChR4ZHPx8fHMnTuXyZMnc/r0aQCee+45xowZQ+fOnY0A\nccdnn8GUKXd/r1ABWrSA55/PjCsTEZE8TkFCRMQafvrJCBBhYcbvjo5w4gSUKZP6uOXLYeZM4+Pk\nBI0aGaGiY0coVy7lsBs3bhAUFMSUKVOIjo4GoFq1avzrvfdo++KL2D333N9raNsW9u6FNm2gdWvw\n9rbW1YqISB6kICEiktn8/WHpUuNnFxcYNAjefRe8vP5+bN++4O4O69bBL7/Axo3Gx9UVXnuN48eP\nM336dObMmcP169cBaFupEp/UrUu106cxDRgA1aoZ7z/cr0EDiIiw3nWKiEiepiAhIpLZqlY1gsGw\nYfDWW+Dh8fBjq1c3PmPHwuXLEBGBZd06fi5UiCkdO7J69WrMZjMAbV56iZATJyh45AjcXlwOOzsj\nrNy6BY9bG0JERCQTKUiIiGS2t94yQsRTT6XrtPgCBQi5dYupBw6wf9EiABwdHenZsycjRozgxRo1\njPccChcGX1/jkaWXX4YiRaxxFSIiIo+kICEikk6mpCSYPx/Cw2HZMmPq1Hu5uqarvbNnzzJz5ky+\n/vprLl68CICHhwdvvPEGgwcPxtPT8+7BmzYZj0jd+1K1iIiIDShIiIikg/vWrTz9+ed3F25bv954\nOfoJ7N69m6lTpxIaGkpiYiIAL7zwAm+99RYBAQE4P+hRpbJln7ByERGRzKUgISKSVpcuUX70aOzj\n4+HZZ2HUKPDxSVcTSUlJrFq1iqlTp7Jjxw4A7Ozs6NixIyNGjKBRo0aY7r/DISIikg0pSIiIpNXU\nqdjHx3Otbl3cd+wwXnROo8uXLzNnzhwCAwM5efIkAO7u7gwcOJBhw4ZRVncaREQkh1GQEBFJq3Pn\nsJhMRA8ahHsaQ8S+ffuYNm0awcHBxMfHA1CxYkXefPNN+vTpQ8GCBa1ZsYiIiNUoSIiIpNWcORx8\n9VUSSpV65GGJiYmsWrWKadOmERkZmbLd19eX4cOH4+vri1067maIiIhkRwoSIiLp8KgQcfHiRb75\n5hsCAwM5c+YMAK6urvTr14+hQ4dSsWLFrCpTRETE6hQkREQyaPfu3UybNo2QkBBu3boFQKVKlRg+\nfDi9e/fGNZ3TwYqIiOQEChIiIk8gMTGR5cuX83//93/s3LkTAJPJxCuvvMLw4cNp2bKlHl8SEZFc\nTUFCRORR4uMhX76UXy9dusTKlSsJCwvj7NmzgDH70oABAxgyZAgVKlSwVaUiIiJZSkFCRORhEhOh\nalUsdeuypUsXAhcvZuXKlSQnJwNQpUoVhg8fTs+ePTX7koiI5DkKEiIiD3F95kzc/viDP06epMWS\nJVgAe3t7mjZtypgxY2jWrJkWjxMRkTxLQUJE5B4Wi4XNmzcze+ZMPvnuO9yAjxMTKe3lxaBBg6hZ\nsyYeHh7UqlXL1qWKiIjYlIKEiAjGuw/z589n9uzZHD16lK6AN3Auf366ffst89u0wd7enl9//dXW\npYqIiGQLChIikmdZLBa2bdvGrFmzWL58OQkJCQB4lSrF/yUmwoULeH75Ja3btrVxpSIiItmP5iYU\nkTznr7/+4ssvv6RKlSo0bdqUb7/9lsTERNq0acOaNWs4dvgwxbt0gQoVoE8fW5crIiKSLemOhIjk\nCcnJyWzcuJGgoCBWrlyZcvehZMmSDBgwgIEDB/L000/fPWH6dGPWJkdHG1UsIiKSvSlIiEiu9scf\nfzB//nzmz5/P6dOnAWPhOF9fX15//XVeeeUVHBwe8kehQoSIiMhDKUiISK4TGxvL8uXLmTdvHlu2\nbEnZXr58efr370/v3r3x8vKyXYEiIiK5gIKEiOQKFouFn376iXnz5hESEsKNGzcAyJ8/P507d6Z/\n//40atQIOzu9GiYiIpIZFCREJEc7d+4cixYtIigoiP/+978p2+vVq0f//v3p2rUrbm5uaWvsyBGo\nVMlKlYqIiOQuChIikuMkJCSwdu1agoKCWLt2LcnJyQAUL16cPn360LdvX5599tn0NbprF9SpAx07\nwnffgVasFhEReSQFCRHJEe48urRo0SJCQ0P566+/AHBwcKB9+/b0798fX19fHJ/0BemJE41/Vqig\nECEiIpIGChIikn3dvMmpVav4z7x5mKOi2H/zJjNv76patSr9+vWjZ8+eeHh4ZKyfgwdh1SrIlw/e\nfjvDZYuIiOQFChIiku1c3rKF5F69KHz6NF7AnfmVyjs4cHnkSHr27En16tXvnrBrF1SuDK6uT9bh\npEnGPwcOBE/PjJQuIiKSZyhIiIhtxMfDgQPGewnAzZs3WbNmDYsWLWLv+vVEm80kAwfs7Lj8zDN4\ntG9P5T59mFKlSup2zp4FPz9wd4eFC6FBg/TVcfQohIYaa0a8917mXJuIiEgeoCAhIlkvPh7q18fy\n229sWrmSRaGhLF++nJiYGMB47+H9unV56bXX8OvSher58z+8rdhY8PKCffugcWP44AMYOxacnNJW\nS7FixvE3bsC9K1uLiIjIIylIiEiWslgsXBgyhOJ793LTZKJv69acvr2vbt269OzZk65du1KsWLG0\nNfjMM/DzzzBuHEyebLw0vW4dLFkCaZm5qVAh+OijJ70cERGRPEtBQkSyxIkTJwgODmb/nDksOXYM\nM9DSYsG5QgXG9uxJjx498Pb2frLGnZyMANG6NfTqBfv3w9WrmVq/iIiIpKYgISJWc+XKFZYtW8aS\nJUvYtm0bTsAewB7Y+MILfBEYSN26dTFl1nSrDRsaIWLTJqhXL3PaFBERkQdSkBCRTBUfH8/atWtZ\nvHgx33//PQkJCQC4uLgwuk4dqkRGYqlQgRZRUeDikvkFuLlB+/aZ366IiIikoiAhIhlmNpuJjIxk\n8eLFLFu2jGvXrgFgZ2eHj48PPXv2pEOHDri6uhpTtVos1gkRj7NoEbz6KiQlwU8/QZs2WnxORETk\nCSlIiMgTO3ToEIsXLyY4OJhTp06lbH/xxRfp0aMHAQEBlCxZMvVJtWtncZW3/fAD9O4NpUvDSy/B\n8uUwbBhMm2abekRERHI4BQkRSZejR48SGhpKSEgIhw8fTtlepkwZevToQY8ePahy/1oP2UH58kaA\n+PlnOH17nqhu3Wxbk4iISA6mICEij3XixAmWLl1KSEgIe/bsSdleuHBhOnfuTK9evahfvz52dnY2\nrPIxvL1h+3Zjdqd//ct4rKl+fVtXJSIikmMpSIjIA509e5Zly5YRGhpKVFRUynY3Nzfat29PQEAA\nLVu2xNHR8eGNJCQY7yI0bpwFFaeBg4OxZsTIkZAvn62rERERydEUJEQkxaVLl1ixYgUhISFs2bIF\ni8UCGDMutW3bloCAAHx9fcmX1i/hkyYZC8WNG2esHp1duLraugIREZEcT0FCJI+7du0aq1atIiQk\nhB9//JGkpCQAnJycaN26Nf7+/rzyyisULFgwfQ3v3w/jxxs/N2mSyVWLiIiIrSlIiORBN27cICws\njKVLl7Ju3bqUtR7s7e3x9fUlICCA9u3b4+7u/mQdJCZC377GNKtDh0LTpplWu4iIiGQPChIieURs\nbCzh4eEsXbqUtWvXEh8fD4DJZKJZs2YEBATQsWNHihYtmvHOJk+GffugbFnjZxEREcl1FCREcrGb\nN2+ydu1ali5dSnh4OHFxcYARHho1akTXrl3p1KkTJUqUyLxOb92CefOMn+fOhfQ+EiUiIiI5goKE\nSC4TFxfH+vXrCQ0NJSwsjJs3b6bsq1+/Pl27dqVz586UKlXKOgU4O8PevRAeDs2bW6cPERERsTkF\nCZFcID4+noiICEJDQ1mzZg0xMTEp+1566SW6du1Kly5d8PLyunOC8R7Do6ZuzQh3d+jRwzpti4iI\nSLagICGSQ928eZOIiAiWL1/OmjVruH79esq+WrVqpYSHsmXLpj4xMhIGDTJehv7gg9T7EhNh2DAY\nPBhq1LD6NYiIiEjOpSAhkoNcv36d77//nhUrVrB27dpUjy3VqFEDf39/unTpQvny5R90MvzjH/D1\n18bvS5fCe++Bvf3dYxYvhtmzjc+rr8KYMVC7tpWvSkRERHIiBQmRbO7y5cusWbOGFStWEBERkTJV\nK0Dt2rXp1KkTHTt2xNvb++GNhIXBG2/AmTPG6s6jRsGHH6YOEQB+fvDOOzBzpnFOWBj4+sKECfDi\niw9vPzISXnoJnJwyeLUiIiKSUyhIiGRD586dY+XKlaxYsYLNmzeTnJwM3J1tqVOnTnTo0IGnn376\n8Y1ZLDB1qhEi6tSBOXOgWrUHH+vpCZ9/bty5+OILmD4d1q83HoV6WJD47Tdo2RIqVYKdO6FAgSe8\nahEREclJFCREsokTJ06wYsUKli9fTlRUFBaLBQAHBwd8fHzo1KkT7du3p3jx4ulr2GQyHlUKDzfe\nf7j/LsSDFCsGkybBu+/CwoXQvv2Dj0tKgn79ICHBCCkKESIiInmGgoSIjVgsFvbu3UtYWBhhYWHs\n3r07ZZ+zszOtWrWiU6dOvPrqqxQuXDhjnVWoACNGpP+8IkVg5MgH77txwwgYv/wCpUvDv/+dsRpF\nREQkR7F73AHbtm2jbdu2lC5dGjs7OxYsWPC3Y8aNG0epUqXInz8/zZo147fffrNKsSI53c2bNwkL\nC+P111+ndOnS1KxZk3HjxrF7924KFCjA4DZtWB4UxMULF1izZg19+vRJe4hISoIvv4RTp6x7EXdM\nnw6bNhk/z55tTPkqIiIiecZjg0RsbCzVq1fnq6++wsXFBZPJlGr/p59+yhdffMH06dPZtWsXHh4e\n+Pj4pJrHXiQvO3PmDLNmzaKLry9tnnqKtW3bsnT2bKKjoylVqhSvv/46YWFhXLx4kZnnz9Oxf39c\nS5aEypWhRQvo0weOH390JwcOQL168PbbxkvVtx+LsqrChaF8eWPmJz8/6/cnIiIi2cpjH23y8/PD\n7/aXhL59+6baZ7FYmDp1KqNGjaJDhw4ALFiwAA8PD4KDg3nttdcyv2KRbM5sNrN7927Cw8NxDgri\n2dOn8QFev+eY+r17U/Wtt3jhhRdSh3MXF8ifH2Jj4cgR4wPGNKwP0qoVXLsGe/YYdyS8vIwgcV/g\nt4rXXzc+IiIikidl6B2J48ePc/78eVq1apWyLV++fDRu3JioqCgFCclat27x1MaNxFapkuVdx8bG\n8uOPPxIeHk54eDjnzp0DIBjocPuYZAcHzJUr41izJr2GD3/wgm/bthl3E65dM2ZZOn3a+Gfp0g/u\n+JdfjGNNJhg61HhB2tXVKtcoIiIicq8MBYk7X5bun0XGw8OD6Ojoh57366+/ZqRbkdQsFgqvW0ep\nWbOoEB1NkpsbR6ZM4UbNmlbt9vLly0RGRhKzZg17/vtfIhMTU/YVL16chg0b4uTpyZEiRUisUoVb\nZcpgcXBIqZm0/HdQpIjxOXTogbud5s/H6eJFEgsX5laZMnfvYIjV6c8xyQoaZ2JtGmPyKI9cowor\nztp0/7sUIlZjMlE4IgLn6GiSXF1xuH4d72HDOPHPf3L51VczrRuLxcKff/7Jtm3b2Lp1K4cOHaKv\nxcIs4ArgX7Eiz7ZoQcOGDfH29k75b+BGplXwdwmlS5PwsLsVIiIiIlaUoSDh6ekJwPnz5yl9z5eZ\n8+fPp+x7kFq1amWkW5G/mzkTdu9mf6VKlJo+Hc/gYMpdvEi5DI615ORkdu7cyerVq1m9ejVHjx4F\nwARMsrfnH7cXiss/eDCbZ8wAu8fOXyA53J2/vdOfY2JNGmdibRpjkhbXrl175P4MBYly5crh6elJ\nREQENW8/RhIfH8/27dv5/PPPM9K0yINdvmw86nO/atWgWjUsv/7K6ZEj8fT3h9atn6iL2NhYNmzY\nwOrVqwkPD+fSpUsp+woXLkwHPz/G/vknXjt2GIu7TZ9OwcGDn/SKRERERHKkxwaJ2NjYlL+FNZvN\nnDhxgn379lGkSBG8vLx46623mDhxIpUrV8bb25vx48fj6upK9+7drV685CFnzsC4cRAcDL/9BmXK\nPPr4tm3T1fzp06dZt24dYWFhbNiwgfj4+JR95cuXp127drRr144GDRrgEBlpTMvq6gpLl4Kv7xNc\nkIiIiEjO9tggsWvXLpo3bw4Y7z2MHTuWsWPH0rdvX4KCgnj//feJi4tj6NChXLlyhbp16xIREUGB\nAgWsXrzkAVeuwKefwldfQXy8cQdgyxZjbYUnYTaDnR2JiYlERUWxdu1a1q1bx8GDB1MdVqdOnZTw\nUKVKldTv/DRrBt98A7VrQ/XqT35tIiIiIjnYY4NE06ZNMZvNjzzmTrgQyVTffw+9ehlhAqBLFxg/\nHipWfKLmzh48iOMrrzDTy4vPDx7k+vXrKfsKFChAixYtaN26Na+++iolS5Z8dGMDBjxRDSIiIiK5\nhdVmbRLJsGefhZgY4w7Ap58adwDSITExkZ07d7Ju3TrWrVvHK/v3Mx4YdfIk0cDWZ5/Fz8+P1q1b\n07BhQ5ydna1yGSIiIiK5kYKEZF/ly8PBg8YdiDROJ3zp0iWioqL49NNP2bBhQ6rZBn53caFa6dL4\nHz3KTICXX4YpU4zHpR7EYjHugDRoALcf7xMRERERg4KE2N7x40ZQKFv27/sqVXrkqQkJCezYsYMf\nfviB9evXs3///vtOr0Tr1q3x8/OjUaNG5MuXDxYsgEGDYOpU+OMPWLECHBzub9g4ZuFCY5aoY8fA\nzS2DFyoiIiKSeyhIiO3ExMDkyfD55+DjA2FhaTrt2LFjrF+/nvXr17N582ZiYmJS9jk7O1O7dm0C\nAgLw8/OjfPnyf2+gTx8jtHToYDw+dX+I+Osv6NTJeKk7f36YN08hQkREROQ+ChKS9cxmYxrXf/wD\noqONbYUKwa1b8ID3FGJjY9myZUtKePj9999T7a9atSovv/wyvr6+uLi44Ozs/PgFdpo0gf37oVSp\n1Nv/+APatIEjR6BECQgPhxdfzMjVioiIiORKChKStSwW4+7Dpk3G77VrG1O71qt3zyEWDh06lPK4\nUmRkJAkJCSn7CxUqhI+PD76+vrRq1SrVqup3VupMEy+vv2/7808jTFSrZswa9aBjRERERERBQrKY\nyQSNGxuLyk2ebEzvameH2WwmKiqKkJAQVq1axZkzZ+45xUSdOnXw9fXF19eX2rVr43D/40iZpUUL\n4xGr+vX1OJOIiIjIIyhISNZ7/314+20sBQuya9cuQkNDWbp0KadPn045xNPTE19fX15++WV8fHwo\nUqRI1tWnlapFREREHktBQqzDYoHISGjUKNXUrRaLhQP/+x8hISGEhoZy/PjxlH1lypTB39+frl27\n8uKLL6ZeTVpEREREshUFCcl8Bw/CyJGwcSOsWgXt2vGf//yH0NBQQkJCOHLkSMqhJUqUoGvXrgQE\nBPDSSy8pPIiIiIjkEAoSknnOnIGPPoL588FsJtndnfDgYD766CMOHDiQcljRokXp0qUL/v7+NGzY\nEPuHLQgnIiIiItmWgoRkjqgoaNkS4uJItrNjuYcHb1y4wF9LlwLGTEsdO3bE39+f5s2bW+9laRER\nERHJEvo2JxmWlJTEjxcvUsNkYofJxAdmM0cvXKBgwYL0aNeOgIAAWrVqhZOTk61LFREREZFMoiAh\nT+zo0aPMmzePBQsWEB0djRsQY2eHX+vWTOzblzZt2uDi4mLrMkVERETEChQkJF1url/Pjg0b+GTX\nLiIjI1O2e3t7079/f3r37k3JkiVtWKGIiIiIZAUFCXksi8XCvm+/hVGjqHHyJBWBX4ACBQrQtWtX\n+vfvT4MGDTTjkoiIiEgeoiAhD3Xu3DlWTJ9O0enT6XTtGvZADLDBy4tZ//wnHXv0wNXV1dZlioiI\niIgNKEhIKnFxcYSHh7No0SLWrl3L9uRk6gJJwM4aNSg2bRoDGzSwdZkiIiIiYmMKEoLZbGbr1q0s\nXryY7777juvXrwPg4ODAhrp1KQMUmzOHes89Z9tCRURERCTbUJDIww4dOsTiRYs4MH8+hS9cYMnt\n7bVq1aJHjx5069aN4sWL27RGEREREcmeFCTymDNnzvDtt9+yc84cXjhyhAGANxBnMlHpvffo0q8f\nlStXtnWZIiIiIpLNKUjkAdevX2fFihUsXryYTRs3EgW8e8/+hMKFyde9O2PeeQc8PGxVpoiIiIjk\nIAoSuVRiYiI//PADixcvZvXq1cTHxwPg7OxMcrFiJFy9in2XLtj36IFTkybgoKEgIiIiImmnb4+5\nzB+HDvHjpElcXrOGjTExbLq9vUmTJvTq1YtOnTpRKCEBChUCJyeb1ioiIiIiOZeCRC5wa98+/hg9\nGktkJN7Xr/P67e0vFSyIz4cf0r17d55++mmb1igiIiIiuYuCRA528OBB5syZw8mgIFbGxABgBk4+\n9RSOzZrRvHt3WnTqZNsiRURERCRXUpDIzpKSYP9+2L7d+MTEELNsGSEhIcyZM4eff/4ZgILAXE9P\nPDt3puF77+nug4iIiIhYnYJEdvW//0HbtnDkSMoms8lERU9PzsbGAuDm5kbPnj0ZOHAgNWrUsFWl\nIiIiIpIHKUhkR4mJ4OsLx49zo1AhfjSZCL9yhe0WC2djY2nYsCGDBg2ic+fO5M+f39bVioiIiEge\npCCRVrduQXIyWPmLu9lsZtPWrewqU4ZnT5yg59WrxAJFixalT58+DBw4UAvGiYiIiIjNKUik1Qcf\nwIYNsHQpVKmS6c3/+eefzJ8/n3nz5nHy5EkATCYTLX18GDRoEO3atcNJ07WKiIiISDahIJEWsbGw\nfj38979QqxZMmwb9+4PJlKFm4+LiWLVqFXPnzmXjxo0p28uWLUu/fv3o06cPZcqUyWj1IiIiIiKZ\nTkEiLQoUgF27YNgwWLAABg6EjRvh66/BzS1dTVksFvbs2UNQUBDBwcGYrl6lMcaK0506dWLAgAE0\nbdoUOzs761yLiIiIiEgmUJB4kK1b4eef4e23weH2v6KCBWH+fGjRAt54A779FgoXhunT09Tk5cuX\nWbJkCXPnzuXAgQMAlAc2OTvjlZBA7OLFuHbubJ3rERERERHJZAoS94uLM+44/P67ER6GDEm9v1cv\nqFMH3nsP/vWvRzZlNpuJiIggKCiI1atXk5CQAECRIkUY07w5Q3/8EYcrV+D553GtW9daVyQiIiIi\nkukUJO738cdGiHjuOSNQPEilSrBmzUObuHTpEkFBQXz99dccP34cADs7O/z8/Ojfvz/t4uJwHDTI\nmAmqdWsICQFXV2tcjYiIiIiIVShI3GvPHvj8c+Ml6jlzIB2zJFksFnbu3MmsGTMI+e67lLsPZcuW\nZcCAAfTt25fSpUvDtWvwzDNGiBgyBL766u7jUyIiIiIiOYS+wd6RmAgDBhhrRYwYAWl81CgmJoYl\nS5YQGBjIfw4cYAvgBRxo3ZrBQ4fy8ssvY29vf/cEd3dYuRJ+/dXoJ4MzP4mIiIiI2EL2DxLLlsGq\nVTBhApQta71+rl6FQoWMPsaPf+zhhw8fZubMmSxcuJAbN24A0M3NjfrXr1MfjDsOL74I94aIOxo2\nND4iIiIiIjlU9p5j9NYtYyG44GCIiLi7/exZWL48c/sqVgw2bYLISOMl6wdISEggJCSEJk2aULVq\nVWbMmMGNGzdo0KABS5YsYd6FC8Z6E8WKGdPDPv986rpFRERERHKJ7H1HYuZMOHYMnn3WWAAO4MYN\naNQIjh837lZ07Jh5/ZlMULr03zafPHmSWbNmMWfOHC5cuABAwYIF6dWrF4MHD6Z69ep3D375Zdi/\nH3r2NILJhAnQuDHky5d5dYqIiIiI2Fj2vSNx9Sp88onx85Qpd19IdnWF3r3BbIZu3Yy/+beChIQE\nVqxYQZs2bShXrhwTJ07kwoULVK1alcDAQKKjowkMDEwdIu4oUcK4E/HJJ7Bzp7EmhYiIiIhILpJ9\n70hMnAh//QVNm0KbNqn3jRkDly7BtGnQvr3xN/+1a2dKt4cPHyYoKIhFixZx8eJFABwdHfH392fI\nkCE0aNAAU1pekLa3h9GjjUXtXFwypTYRERERkewi+wYJe3twdr47Heu9TCaYOtUIGkuWgJ8fHDgA\nJUumvX2LBSZPhl69uO7mRkhICEFBQfx8z92DqlWrMmDAAHr06EGxYsWe7Dry53+y80REREREsrHs\nGyQmTTL+Nv9hX+Dt7GDePOMRqOefNx4nSgdLaCimf/6Ty+PHU85s5kZ8PABubm5069aNAQMGUKtW\nrbTdfRARERERyWOyb5CAh4eIOxwdjalh07GgW3R0NEtnzqTXpEkUAUbdvMkNoGnTpvTv359OnTqR\nX3cRREREREQeKXsHibRIQ4hISEjg+++/Z+7cuaxbt455ZjNFgCgnJzzeeYej/fvzzDPPWL9WERER\nEZFcIucHiUc4deoUs2fP5ptvvuH8+fMAtLG3pzeQ7OTESwcOUL9SJdsWKSIiIiKSA2WfIJGUBL/8\nAvXrZ6gZs9nMjuBgrowbR+djx0i0WAB47rnnGDBgAIPi4mDsWOw/+QQUIkREREREnkj2CRLz5sFr\nr8HQoTB9erpPv3LlCvPnz+frwECW/f47jYDZJhM/+PszZOhQGjZsePfF6fbtoWLFzK1fRERERCQP\nyR5BIiYGPvrI+LlRo3SdumfPHmbMmMG3335LXFwcAB8VK8ayq1fpm5hIXy8vaNgw9RSyVapkVuUi\nIiIiInlS9ljZ+t//hnPnoE4d6Nr1sYfHx8ezcOFC6tatS82aNQkKCiIuLg4fHx9WrlzJd9HROK5Z\nY7yI/fnn8OmnWXARIiIiIiJ5h+3vSJw7B599Zvz8oMXn7nHs2DG+/vprgoKCuHz5MgCFChWiX79+\nDB48mIr3Pq7k6wuLFkH37jBqlLFCdt26VrwQEREREZG8w/ZB4rPPIDYW2rV74GNNFouFTZs28cUX\nX7Bu3Tost1+erlGjBkOHDqVbt24PX/chIMBY/frGDYUIEREREZFMZPsg8fHH4OpqfOm/R1JSmAtf\nzgAABvdJREFUEsuWLeOzzz5j7969ADg7O+Pv78+QIUOoU6dO2ladHjLEGlWLiIiIiORptg8SBQvC\nuHEpv8bExDB37ly+/PJLTpw4AYCHhwfDhw9n8ODBFC1a1EaFioiIiIjIHbYPEredP3+eadOmERgY\nyJUrVwCoWLEi77zzDr169cLFxcXGFYqIiIiIyB02DxJHjhzh3//+NwsXLuTWrVsA1KtXj/fff5+2\nbdtiZ5c9JpYSEREREZG7bBYkoqKi+Oyzz1i9ejUWiwWTyUS7du147733aNCgga3KEhERERGRNLBJ\nkNj51FNMvnqVMIwXqHv37s0777xDpUqVbFGOiIiIiIikk02CRL2rV5lsZ0f1999n2IgReHp62qIM\nERERERF5QjZ7tKncd98xvkMHW3UvIiIiIiIZYJs3mVu2xKV9e5t0LSIiIiIiGWebIPHZZ5CWxeRE\nRERERCRbMlksFktWdHTt2rWs6EZERERERDKZu7v737ZpkQYREREREUk3BQkREREREUm3LHu0SURE\nREREcg/dkRARERERkXRTkBARERERkXRTkBARERERkXTLsiARGBhIuXLlcHFxoVatWmzfvj2rupZc\nZtu2bbRt25bSpUtjZ2fHggUL/nbMuHHjKFWqFPnz56dZs2b89ttvNqhUcqpJkyZRu3Zt3N3d8fDw\noG3bthw+fPhvx2mcSUbMmDGD559/Hnd3d9zd3alfvz5r165NdYzGmGSmSZMmYWdnx/Dhw1Nt1ziT\nJ5UlQSI0NJS33nqL0aNHs2/fPurXr4+fnx+nTp3Kiu4ll4mNjaV69ep89dVXuLi4YLpvccNPP/2U\nL774gunTp7Nr1y48PDzw8fEhJibGRhVLTrN161aGDRvGzp072bRpEw4ODrRs2ZIrV66kHKNxJhnl\n5eXFlClT2Lt3L7t376Z58+a0b9+e/fv3Axpjkrl++uknvvnmG6pXr57q/5saZ5IhlixQp04dy2uv\nvZZqm7e3t2XUqFFZ0b3kYgULFrQsWLAg5Xez2Wzx9PS0TJw4MWVbXFycxdXV1TJr1ixblCi5QExM\njMXe3t4SHh5usVg0zsR6ChcubJk9e7bGmGSqq1evWipUqGDZsmWLpWnTppbhw4dbLBb9WSYZZ/U7\nEgkJCezZs4dWrVql2t6qVSuioqKs3b3kMcePH+f8+fOpxlu+fPlo3Lixxps8sevXr2M2m3nqqacA\njTPJfMnJyYSEhBAfH0/jxo01xiRTvfbaa3Tp0oUmTZpguWfWf40zySgHa3dw6dIlkpOTKV68eKrt\nHh4enDt3ztrdSx5zZ0w9aLxFR0fboiTJBUaMGEGNGjWoV68eoHEmmefgwYPUq1ePW7du4eLiwtKl\nS6lUqVLKlziNMcmob775hmPHjhEcHAyQ6rEm/VkmGWX1ICGSXdz/LoVIWrz99ttERUWxffv2NI0h\njTNJj8qVK3PgwAGuXbvGsmXLCAgIYPPmzY88R2NM0urIkSN8+OGHbN++HXt7ewAsFkuquxIPo3Em\naWH1R5uKFi2Kvb0958+fT7X9/PnzlChRwtrdSx7j6ekJ8MDxdmefSFqNHDmS0NBQNm3aRNmyZVO2\na5xJZnF0dKR8+fLUqFGDiRMnUrduXWbMmJHy/0eNMcmInTt3cunSJZ577jkcHR1xdHRk27ZtBAYG\n4uTkRNGiRQGNM3lyVg8STk5O1KxZk4iIiFTbN2zYQP369a3dveQx5cqVw9PTM9V4i4+PZ/v27Rpv\nki4jRoxICREVK1ZMtU/jTKwlOTkZs9msMSaZokOHDhw6dIj9+/ezf/9+9u3bR61atejWrRv79u3D\n29tb40wyxH7cuHHjrN2Jm5sbY8eOpWTJkri4uDB+/Hi2b9/OvHnzcHd3t3b3ksvExsby22+/ce7c\nOebOnUu1atVwd3cnMTERd3d3kpOTmTx5MpUqVSI5OZm3336b8+fPM3v2bJycnGxdvuQAQ4cOZeHC\nhSxbtozSpUsTExNDTEwMJpMJJycnTCaTxplk2AcffEC+fPkwm82cOnWKqVOnEhwczJQpU6hQoYLG\nmGRYvnz5KFasWMrHw8ODJUuWUKZMGfr06aM/yyTjsmp6qMDAQEvZsmUtzs7Ollq1alkiIyOzqmvJ\nZTZv3mwxmUwWk8lksbOzS/m5X79+KceMGzfOUqJECUu+fPksTZs2tRw+fNiGFUtOc//YuvP5+OOP\nUx2ncSYZ0bdvX0uZMmUszs7OFg8PD4uPj48lIiIi1TEaY5LZ7p3+9Q6NM3lSJoslDW/ciIiIiIiI\n3CNLVrYWEREREZHcRUFCRERERETSTUFCRERERETSTUFCRERERETSTUFCRERERETSTUFCRERERETS\nTUFCRERERETSTUFCRERERETS7f8Bi6FDx9/nUDgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1659569e8>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I am satified with this plot. The track is not perfectly straight due to the noise that we added to the system - this could be the track of a person walking down the street, or perhaps of an aircraft being buffeted by variable winds. There is no *intentional* acceleration here, so we call it a constant velocity system. Again, you may be asking yourself that since there is in fact a tiny bit of acceleration going on why would we not use a second order Kalman filter to account for those changes? Let's find out.\n",
      "\n",
      "How does one design a zero order, first order, or second order Kalman filter. We have been doing it all along, but just not using those terms. It might be slightly tedious, but I will elaborate fully on each - if the concept is clear to you feel free to skim a bit. However, I think that reading carefully will really cement the idea of filter order in your mind."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Zero Order Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A zero order Kalman filter is just a filter that tracks with no derivatives. We are tracking position, so that means we only have a state variable for position (no velocity or acceleration), and the state transition function also only accounts for position. Using the matrix formulation we would say that the state variable is\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x\\end{bmatrix}$$\n",
      "\n",
      "The state transition function is very simple. There is no change in position, so we need to model $x=x$; in other words, *x* at time t+1 is the same as it was at time t. In matrix form, our state transition function is\n",
      "\n",
      "$$\\mathbf{F} = \\begin{bmatrix}1\\end{bmatrix}$$\n",
      "\n",
      "The measurement function is very easy. Recall that we need to define how to convert the state variable $\\mathbf{x}$ *into* a measurement. We will assume that our measurements are positions. The state variable only contains a position, so we get\n",
      "\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1\\end{bmatrix}$$\n",
      "\n",
      "\n",
      "That is pretty much it. Let's write a function that constructs and returns a zero order Kalman filter to us."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ZeroOrderKF(R, Q):\n",
      "    \"\"\" Create zero order Kalman filter. Specify R and Q as floats.\"\"\"\n",
      "    kf = KalmanFilter(dim_x=1, dim_z=1)\n",
      "    kf.x = np.array([0.])\n",
      "    kf.R *= R\n",
      "    kf.Q *= Q\n",
      "    kf.P *= 20\n",
      "    kf.F = np.array([[1.]])\n",
      "    kf.H = np.array([[1.]])\n",
      "    return kf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "First Order Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A first order Kalman filter tracks a first order system, such as position and velocity. We already did this for the dog tracking problem above, so this should be very clear. But let's do it again.\n",
      "\n",
      "A first order system has position and velocity, so the state variable needs both of these. The matrix formulation could be\n",
      "\n",
      "$$ \\mathbf{x} = \\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "As an aside, there is nothing stopping us from choosing \n",
      "\n",
      "$$ \\mathbf{x} = \\begin{bmatrix}\\dot{x}\\\\x\\end{bmatrix}$$\n",
      "\n",
      "but all texts and software that I know of choose the first form as more natural. You would just have to design the rest of the matrices to take this ordering into account. \n",
      "\n",
      "So now we have to design our state transition. The Newtonian equations for a time step are:\n",
      "\n",
      "$$\\begin{aligned} x_t &= x_{t-1} + v\\Delta t \\\\\n",
      " v_t &= v_{t-1}\\end{aligned}$$\n",
      " \n",
      "Recall that we need to convert this into the linear equation\n",
      "\n",
      "$$\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix} = \\mathbf{F}\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "Setting\n",
      "\n",
      "$$\\mathbf{F} = \\begin{bmatrix}1 &\\Delta t\\\\ 0 & 1\\end{bmatrix}$$\n",
      "\n",
      "gives us the equations above. If this is not clear, work out the matrix multiplication:\n",
      "\n",
      "$$ x = 1x + dt \\dot{x} \\\\\n",
      "\\dot{x} = 0x + 1\\dot{x}$$\n",
      "\n",
      "Finally, we design the measurement function. The measurement function needs to implement\n",
      "\n",
      "$$z = \\mathbf{Hx}$$\n",
      "\n",
      "Our sensor still only reads position, so it should take the position from the state, and 0 out the velocity, like so:\n",
      "\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1 & 0 \\end{bmatrix}$$\n",
      "\n",
      "As in the previous section we will define a function that constructs and returns a Kalman filter that implements these equations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.common import Q_discrete_white_noise\n",
      "\n",
      "def FirstOrderKF(R, Q, dt):\n",
      "    \"\"\" Create zero order Kalman filter. Specify R and Q as floats.\"\"\"\n",
      "    kf = KalmanFilter(dim_x=2, dim_z=1)\n",
      "    kf.x = np.zeros(2)\n",
      "    kf.P *= np.array([[100,0], [0,1]])\n",
      "    kf.R *= R\n",
      "    kf.Q = Q_discrete_white_noise(2, dt, Q)\n",
      "    kf.F = np.array([[1., dt],\n",
      "                     [0. , 1]])\n",
      "    kf.H = np.array([[1., 0]])\n",
      "    return kf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Second Order Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A second order Kalman filter tracks a second order system, such as position, velocity and acceleration. The state variables will need to contain all three. The matrix formulation could be\n",
      "\n",
      "$$ \\mathbf{x} = \\begin{bmatrix}x\\\\\\dot{x}\\\\\\ddot{x}\\end{bmatrix}$$\n",
      " \n",
      "\n",
      "So now we have to design our state transition. The Newtonian equations for a time step are:\n",
      "\n",
      "$$\\begin{aligned} x_t &= x_{t-1} + v\\Delta t + 0.5a_{t-1} \\Delta t^2 \\\\\n",
      " v_t &= v_{t-1} \\Delta t + a_{t-1} \\\\\n",
      " a_t &= a_{t-1}\\end{aligned}$$\n",
      " \n",
      "Recall that we need to convert this into the linear equation\n",
      "\n",
      "$$\\begin{bmatrix}x\\\\\\dot{x}\\\\\\ddot{x}\\end{bmatrix} = \\mathbf{F}\\begin{bmatrix}x\\\\\\dot{x}\\\\\\ddot{x}\\end{bmatrix}$$\n",
      "\n",
      "Setting\n",
      "\n",
      "$$\\mathbf{F} = \\begin{bmatrix}1 & \\Delta t &.5\\Delta t^2\\\\ \n",
      "0 & 1 & \\Delta t \\\\\n",
      "0 & 0 & 1\\end{bmatrix}$$\n",
      "\n",
      "gives us the equations above. \n",
      "\n",
      "Finally, we design the measurement function. The measurement function needs to implement\n",
      "\n",
      "$$z = \\mathbf{Hx}$$\n",
      "\n",
      "Our sensor still only reads position, so it should take the position from the state, and 0 out the velocity, like so:\n",
      "\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1 & 0 & 0\\end{bmatrix}$$\n",
      "\n",
      "As in the previous section we will define a function that constructs and returns a Kalman filter that implements these equations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def SecondOrderKF(R_std, Q, dt):\n",
      "    \"\"\" Create zero order Kalman filter. Specify R and Q as floats.\"\"\"\n",
      "    kf = KalmanFilter(dim_x=3, dim_z=1)\n",
      "    kf.x = np.zeros(3)\n",
      "    kf.P[0,0] = 100\n",
      "    kf.P[1,1] = 1\n",
      "    kf.P[2,2] = 1\n",
      "    kf.R *= R_std**2\n",
      "    kf.Q = Q_discrete_white_noise(3, dt, Q)\n",
      "    kf.F = np.array([[1., dt, .5*dt*dt],\n",
      "                     [0., 1.,       dt],\n",
      "                     [0., 0.,       1.]])\n",
      "    kf.H = np.array([[1., 0., 0.]])\n",
      "    return kf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Evaluating the Performance"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have implemented the Kalman filters and the simulated first order system, so now we can run each Kalman filter against the simulation and evaluate the results. \n",
      "\n",
      "How do we evaluate the results? We can do this qualitatively by plotting the track and the Kalman filter output and eyeballing the results. However, we can do this far more rigorously with mathematics. Recall that system covariance matrix $\\mathbf{P}$ contains the computed variance and covariances for each of the state variables. The diagonal contains the variance. If you think back to the Gaussian chapter you'll remember that roughly 99% of all measurements fall within three standard deviations if the noise is Gaussian, and, of course, the standard deviation can be computed as the square root of the variance. If this is not clear please review the Gaussian chapter before continuing, as this is an important point. \n",
      "\n",
      "So we can evaluate the filter by looking at the residuals between the estimated state and actual state and comparing them to the standard deviations which we derive from $\\mathbf{P}$. If the filter is performing correctly 99% of the residuals will fall within the third standard deviation. This is true for all the state variables, not just for the position. \n",
      "\n",
      "So let's run the first order Kalman filter against our first order system and access it's performance. You can probably guess that it will do well, but let's look at it using the stardard deviations.\n",
      "\n",
      "First, let's write a routine to generate the noisy measurements for us."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def simulate_system(Q, count):\n",
      "    obj = ConstantVelocityObject(x0=0, vel=1, noise_scale=Q)\n",
      "    zs = []\n",
      "    xs = []\n",
      "    for i in range(count):\n",
      "        x = obj.update()\n",
      "        z = sense(x)\n",
      "        xs.append(x)\n",
      "        zs.append(z)\n",
      "    return np.asarray(xs), zs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And now a routine to perform the filtering."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def filter_data(kf, zs):\n",
      "    # save output for plotting\n",
      "    fxs = []\n",
      "    ps = []\n",
      "\n",
      "    for z in zs:\n",
      "        kf.predict()\n",
      "        kf.update(z)\n",
      "\n",
      "        fxs.append(kf.x)\n",
      "        ps.append(kf.P.diagonal())\n",
      "\n",
      "    fxs = np.asarray(fxs)\n",
      "    ps = np.asarray(ps)\n",
      "    \n",
      "    return fxs, ps"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And to plot the track results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_kf_output(xs, filter_xs, zs, title=None):\n",
      "    bp.plot_filter(filter_xs[:,0])\n",
      "    bp.plot_track(xs[:,0])\n",
      "    \n",
      "    if zs is not None:\n",
      "        bp.plot_measurements(zs)\n",
      "    plt.legend(loc='best')\n",
      "    plt.ylabel('meters')\n",
      "    plt.xlabel('time (sec)')\n",
      "    if title is not None:\n",
      "        plt.title(title)\n",
      "    plt.xlim((-1, len(xs)))\n",
      "    plt.ylim((-1, len(xs)))\n",
      "    #plt.axis('equal')\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we are prepared to run the filter and look at the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "R = 1\n",
      "Q = 0.03\n",
      "\n",
      "xs, zs = simulate_system(Q=Q, count=50)\n",
      "\n",
      "kf = FirstOrderKF(R, Q, dt=1)\n",
      "fxs1, ps1 = filter_data(kf, zs)\n",
      "\n",
      "plt.figure()\n",
      "plot_kf_output(xs, fxs1, zs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TNvr160eNGjWYNGkSq1ev5v3338fNzY3PP/+c9u3b88EHH7Bw4ULGjBlDw4YN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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15a24e8d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It looks like the filter is performing well, but it is hard to tell exactly how well. Let's look at the residuals and see if they help. You may have noticed that in the code above I saved the covariance at each step. I did that to use in the following plot. The ConstantVelocityObject class returns a tuple of (position, velocity) for the real object, and this is stored in the array `xs`, and the filter's estimates are in `fxs`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_residuals(xs, filter_xs, Ps, title, y_label):\n",
      "    res = xs - filter_xs\n",
      "    plt.plot(res)\n",
      "    bp.plot_residual_limits(Ps)\n",
      "    plt.title(title)\n",
      "    plt.ylabel(y_label)\n",
      "    plt.xlabel('time (sec)')\n",
      "    \n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_residuals(xs[:,0], fxs1[:,0], ps1[:,0], \n",
      "               'First Order Position Residuals',\n",
      "               'meters')   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cU1NLAwrKsiX9lvoIIaSnUQDUR40alYDw8EBwHAPHVWH06DDMnasEY0dhMOTi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\nkylTpri+HzBggDIyMtStWzetX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       "text": [
        "<matplotlib.figure.Figure at 0x7fe15a230a58>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How do we interpret this plot? The residual is drawn as the jagged line - the difference between the measurement and the actual position. If there was no measurement noise and the Kalman filter prediction was always perfect the residual would always be zero. So the ideal output would be a horizontal line at 0. We can see that the residual is centered around 0, so this gives us confidence that the noise is Gaussian (because the errors fall equally above and below 0). The yellow area between dotted lines show the theoretical performance of the filter for 1 standard deviations. In other words, approximately 68% of the errors should fall within the dotted lines. The residual falls within this range, so we see that the filter is performing well, and that it is not diverging.\n",
      "\n",
      "But that is just for position. Let's look at the residuals for velocity. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_residuals(xs[:,1], fxs1[:,1], ps1[:,1], \n",
      "               'First Order Velocity Residuals',\n",
      "               'meters/sec')   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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w4AHi4uKMOkefzkOrbGkqpZAUXBCViIiIiKieazAtQKZKTExEmzZtZHWenp66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\nxasAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165928198>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, as expected, the residual falls within the theoretical performance of the filter, so we feel confident that the filter is well designed for this system.\n",
      "\n",
      "\n",
      "Now let's do the same thing using the zero order Kalman filter. All of the code and math is largely the same, so let's just look at the results without discussing the implementation much."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf0 = ZeroOrderKF(R, Q)\n",
      "fxs0, ps0 = filter_data(kf0, zs)\n",
      "\n",
      "plot_kf_output(xs, fxs0, zs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qxIYNG2jUqFHC9hMnThAUFJTws65Xrx4VKlRgwYIF9OnTh3LlylGpUiUWLFhA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\nDA0MtZBUCCGEeDppYoQQVdaDBw/YsGEDX331FbGxsQCYm5szduxY3n7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PZi5+tGvWk6bO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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe166a61a58>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we would expect, the filter has problems. Think back to the g-h filter, where we incorporated acceleration into the system. The g-h filter always lagged the input because there were not enough terms to allow the filter to adjust quickly enough to the changes in velocity. The same thing is happening here, just one order lower. On every `predict()` step the Kalman filter assumes that there is no change in position - if the current position is 4.3 it will predict that the position at the next time period is 4.3. Of course, the actual position is closer to 5.3. The measurment, with noise, might be 5.4, so the filter chooses an estimate part way between 4.3 and 5.4, causing it to lag the actual value of 5.3 by a significant amount. This same thing happens in the next step, the next one, and so on. The filter never catches up.\n",
      "\n",
      "Now let's look at the residuals. We are not tracking velocity, so we can only look at the residual for position."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_residuals(xs[:,0], fxs0[:,0], ps0[:,0], \n",
      "               'Zero Order Position Residuals',\n",
      "               'meters')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zcw/G3LGvwMLEut2fVyLRQU/XPujp2qdV+1dWV+D3Y2sQdeuEUvnF2yeRkhmH\n+ZPf6vAb5Yy8FGw+/B2SMm+rbNPV0cPEwXMwJji8S01Q0Jj6mcsgAIDqDb+B1BCvzFiO9fu/wI2k\nKEV5SUURVm//AC9MXdrqz7+91MpqcC3xAs5dP4jbKVcgou57/uuJkcguSMOcsJc7RQtfe4uOO4Nf\nDn6tduzagwQIcLB2hZu9D9zsveFu7wMnG/dWdW1sL93jCiIiIqJWEUURBy9sxR/nflXZpq9ngBkj\nFiA0YFynvYkzkBri6fFvoJdrH2w99iOqa6sU23KKMvDl7+8gfNh8jAiaovHXUFNbg0NR23Downa1\n3XK8nAMwd8zLsLN01mgcnZFUTx/PT30Xm498h8iYY4ryquoKfL/7H5g3YQn6+gzp8LiyC9Jw7sYh\nnL95DKUV6hdmPHv9EKxM7TB+0KwOjk5z5KIcByK24EDklgbrWJnaws3BB+72PnCz94GrnZfWWjgb\nwkSGiIjoIVVdU4X/HVqN6LgzKtu8nQPw5LjXYG1ur4XIWkYQBAz2HwN3h57YsH8V0vOSFdtkslps\nP7EWcanXMHfsqzA2MNVIDHcybmHz4e+QmX9XZZuB1AjTh81DaOC4Vo0h6C50dHTx5LjXYGJojqOX\ndinKZbJarN//BWaHvYihvSdoPI6a2mpcjj+Hc9cPNrje0YP2nfsfLM1sMdB3lGaD6wBVNZX45eDX\nuBJ/TmVbiP8YBHmHws3eu83j4DoCExkiIqKHUEFJDn7atxKp2YlK5RKJDh4Z+gxG9ZvW5W66Haxc\nseTxz7Hz5HqcuXZAadvVhPO4m52IeRPfhKeTb7s9Z1V1Bfae/QWnruxXdEe6X6DnIMwevUgj3fK6\nIkEQED58PkyNzLH79EZFuQgRW45+j+LyQkwcNFsjrWfpuck4d+MQLsQcR3lVaaN13ey8kVOUodTV\n8tdD38Lc2Err3eDaIr84Gz/t/RRpuUlK5ToSXcwOexGhAWO1E1grMZEhIiJ6yCSm38K6P/6JkvJC\npXIjA1MsmPw39HTtraXI2k6qq485YS+ip2tvbD78HSqryxXbCkpysHrbe5gS+iTGDJjR5kTtZtIl\nbDn6vdoFP00NzfHY6IXo6z2k03bL06Yx/WfAxNAMmw9/B/l9M5/9GbEZpeVFmDnq+XZJpKtqKnEp\n9jTOXT+kdszS/QylRhjgOwpDAsfB2bYH4lKv4z+7lkEmq+smKJPXYt2+f+L1WStbvfijNiWmx2Dt\nvn+qdKGZ799wAAAgAElEQVQzMTTHc1PegZezv5Yiaz0mMkRERA+RiBtHsOXY94qbs3qO1m54Ydp7\nsDF30FJk7aufz1C42nlhw/5VSMmOV5TLRTn2nt2EuNRreGr8GzAzbrz7jCiKKKssQX5xdt1PSQ4K\nSnKQmXcXt+9eUbvPYL8whI94VmPd2LqLwf5jYGRgig37VyktuHrq6n6UVRbjyXGvQ0+3ZQPJ5aIc\nmXkpSEi7iYT0m7iRdBFV1RWN7uPp6IfQwHHo5zNUaUFVH5dAPDXuNWw88KWirKK6HD/s/hhL5nwO\nc5Ousw7OuRuH8fvRNSpjt5xtPPDCtPdgZWanpcjahtMvEzWBU+SSpjws51ZxWSFuJEUhMT0Gujp6\n8HPvC1+3fp16BfaurKHzSiaXYffpjTgevUdln0DPQXhmwuJON5C3PdTKarD3zCYcU/O6zYws8fSE\nN+Bg5Yq84mwUlGQjvzgH+SU595KWbBQU5yhNINAYazN7PD7mZfRyC2rvl6F1mvx9lZB2Ez/u/URl\nxrxerkF4buq7jZ6XMrkMqdmJSEi/gfi0m0hMu9lktzEAMDYwxUC/0QgNGNfkAqqHonZg75mflcqc\nbTzw+qyVnf6aaey67+MVgqfHv96qKZPbE9eRuYeJDGnCw3KzSR2vu55boigiM/8uriVG4nriBSRn\nxqqMHdDTlcLPvR96ew5GYI8BMDY001K03Y+686q8shQb/lyFWymXVeqPHzgLk0PndrnxMC11PfEC\nfjm0GuWVJe1+bEGQYFTfqZgc+gT09Qza/fidgaZ/X6XnJuH7Xf9QWRzVzc4bi6Z/CFOjuvu6mtpq\nJGfFISHtBuLTbuBOxm216/Q0pKdLb4QGjkcfr5Bmt/aIooitx37A6QfGXfm698Oiae932mm0y6tK\nseHPf6ldF2rCoNmYFPJ4p7jumcjcw0SGNKG73myS9mnj3CqrLMGFmOMQRRH2Vs6wt3KBpaltm/+Y\nyWS1SEiPwfXESFy7E4m8oqxm7ysRJPByDkAfr8Ho7Tmoy3Zx6CwePK+yCtLw055PkF2YrlRPT1eK\nJ8e9huCewzo8Rm0pKMnFzwe+REL6zXY7ppONB+aOeQXuDj7tdszOqCN+X+UVZ+E/O5cj54Fz1c7C\nCX19hiAh7SaSsmJVukU2xczIEoP9wxASMBa2Fo6tik0ml2HtvpW4cSdKqTzEfwzmjn21042Dyi5I\nw497P0V2QZpSeWe87pnI3MNEhjSBiQxpSkefW4Wlefj37+8i/4GByXq6UthZOsPe0gX2Vi6wt3SG\ng5ULbC2coKcrbfB45VWliEmKxvXESNxMvqR2IcXWcLHzRB/PwejjFQJHa7dOd4PQEURRhFyUt2o1\n8fvPq5tJF7Hxz3+h4r4B7wBgYWKN56cuhZu9d7vE25XI5DIcOP8bDkZuUzvLmDpSPQNYmdrCyswO\nVqa2sLz3r52lE1xsPR+Kc7Sjfl+VlBdize6PcTc7odXHMJQawdPZH15O/vByDoCbvXerrqUHVdVU\nYvW291VimxwyFxMHz2nz8dtLTHI0Nvy5SuV3cme97pnI3MNEhjSBiQxpSkeeW+VVpfh663vIyEtp\n9j4CBFiZ28HB0rWu9cbSBTYWjkjPTcK1xEjEp92AXC5r1rFc7DwR6DEQ5VWluJZwHgWluc3az8bc\nAX286pIaD4eekLTDzUhndyn2NLYe+wHllaWwMrerSzAtnRVJpp2lC0wMzRq8eY6KioIoiijRScPu\n0z9DvG9GKADwcOyF56e8CzNjy454OZ3W7ZQr+O3of5BXlAVDfWNFklL3rx2szGxhaWoLazM7GBmY\nPhTJSmM68vdVZXUF1u37Z4OTKTzI1MgCXvcSF2/nADhau2nsd0VxWQG+/P0d5BdnK5U/Oe41DPYP\n08hzNpcoijhxeR92nlqvet079MLzUzvndc9E5h4mMqQJTGRIUzrq3KqprcZ/di1HQjMXfmsPOjq6\n6OXSB4GegxDQYwAsTW0U20RRxN3sBFxLPI+rCeebnVyZG1th2tCnMdB3VLe9qTxxeR+2n1jbZD0j\nA9O65OZeglPfomZtbo+oqAs4F/8HEnOuqew32C8Ms8NeavFMUN2VKIqoldU02vJIdTr6b2FNbQ1+\nOfhvtYu1WpnZKVpbvJ39YWvh1KG/E7LyU/HV7+8qTSogkejgpekfaWWih5raaly/E4XzNw7jZvIl\nle2D/EZjTthLnfY8ZyJzDxMZ0gQmMqQpHXFuyeUyrP9zlcoKzq52XtDV0UNWfmqzZvhpDmNDMwR6\nDECg50D4uvVt9kw42QXpuJYYiWsJ53En41aT3X383IMxJ+wlWJnZtkfYnYIoitgf8Sv+itzapuPo\n6OhCTyJFZY1yVzJBkCB82HyM6jet2yaBpFna+Fsol8tw/PI+xCRfgrWZPbycA+Dl5N8prv2EtBv4\nbucy1MpqFGX6UkO88dhKONt6aPz55XIZ4tNuIOrWCVyOP6e0XlI9AQIeGTYPYcHTO/V1z0TmHiYy\npAlMZEhTNH1uiaKIbcd/wqmr+5XKezj64pVHl0Oqqw9RFFFaUYSsgjRk5afW/RSkISv/rspYGnXs\nLV0Q6DkQvT0HtUvXr+KyQly/E4mrCedx++6VBgf16usZ4JGhz2Bon4mdYtadtpDLZdh67Eecuf6X\nRo5vKDXC/Mlvw8+9n0aOTw8H/i1UdSn2NDb8uUqpzNzEGktmf6bUCt1eRFFEem4SLtw6gYuxp1BU\nmtdgXQOpEeZNXIKAHp3/82rL/XvnnC+OiIja7NCFbSpJjL2VCxY+8j6kunVruAiCAFMjC5gaWcDb\nOUCpblVNJbIL0pFdkIrM/FRkFaQitygTxvqm8PMIRmCPgbCzdGrXmM2MLTAkcDyGBI5HZXUFbiZd\nxLWEui5o9y+YV1VTia3Hf8SluDOYO+aVdo+jo9TU1mDTX1/hcvxZpXKprj7mT3oLlqY2/5dkFqQh\nqyAV2QVpqKmtbuCIyuwsnbFw2nuws3TWRPhED7XgnsNQUJKL3ac3KMqKSvPww54VeP2xT2Gob9Qu\nz5NfnIOLt08i6vaJZnXFdbH1xNMTFje5Pk53wBYZoibwWyjSFE2eW+duHMbmw98qldV9U/hPWJpq\nv1tGS2UXpGHz4e/UTpurpyPF5NC5GNXvkXaZmaijVFZXYO2+lYi9e1Wp3MjAFC9O/xAeDj3V7icX\n5SgoyUFW/r3E5t6/WQVpKCkvVNTz9+iPZyYuhpG+iUZfBz0c+LdQvYZavnu5BuHF6R+2eo2Z8spS\nRMedQdTtk80a32hqaI7gXsMxoNdIuNl7d+quZA9i17J7mMiQJvCXN2mKps6t64kXsHbfSsjvm7XG\nUN8Yb8xaCUdrt3Z9ro4kF+U4c+0v7Dm9EVVqFsBzs/PG3LGvdkj/9LYqKS/CD7s/Rkp2vFK5hYk1\nXgpf1upvUssrS3Hi3BFIBAnGj5zapW5mqHPj38KGyeUyrP3jM1xPjFQq93Tyg425g0p9Afeuy3vX\np+Iqvfe4pLwQt1IuN7lejlTPAH28BmOg7yj0dO3Tpb7IuR+7lhEREQDgTsZtrP/zC6UkRldHDwun\nvdelkxigbuHM4X0mIcBjALYc/R4xD8zOk5Idjy9+exPjBzyGcQMf67Qzc+UX5+A/u5apLFRnZ+mM\nl8OXtWkgs5GBCWxN67qRMYkh6hgSiQ7mT3wT32z/AMlZcYryxPQYJKbHtO9zCRL4uvfDQN+RCPQc\nBH09g3Y9flfDRIaIqJvIyk/FD3tWKI2fEAQJ5k18E14PjH/pyqzMbPHi9A9x4dZx7DixTmnWNblc\nhgORW3Al4Rzmjn21we5Z6lTVVCI9NxlpOXeQlnMHqbl3kJGXAn09A/T2HISQgLFwt/dpU4KQkXcX\n/9m1TGWQrpudNxZN/xCmRuxNQNQVSfX0sfCR9/Hl7+8gryir3Y/v4dALA3xHoJ/PUJgaWbT78bsq\nJjJERN1AUWk+vt+1HOWVJUrls0YtRJB3iJai0hxBEDDIbzR83fph2/EfVQbLZ+Sl4Kvf38WovlMx\nJfRJSPX0lbYXlxUg9V7CkpZ7B6k5d5BTkK526ufqmkqcvX4QZ68fhKO1Gwb7j8FA35Etvpm4k3Eb\nP+z+WGW6656uffD81KUwaOZ01UTUOZkaWeCl6R9h9bYPUFxe0Obj2Vo4YYDvSAzoNQK2Fo7tEGH3\nw0SGiKiLK68qxfe7lqtMlzxh0GwM6zNRS1F1DDNjCyyY8jdciT+H34/9oDTYXRTlOBa9B9cSIxEW\nHI784myk5tYlL/fXa4mMvBTsOrUee878jMAeAxHiPwZ+HsFN9k2/mXQJ//3jM1TXVimV9/Uegqcn\nLO603eCIqGXsLJ2x9KmvEZt6DdU19dd73Rck949KV3xpcl9h/f8EQYCzjQdc7bzYRbQJTGSIiLqw\nmtpqrN27Eul5yUrloQHjMDlkrpai6nhB3qHwdgnErpPrcT7mqNK23KJM/H5sTbs+n1wuw9WECFxN\niICZkSUG+Y3G4IAxsFczzfHF2yex6eDXkMtlSuVDe0/ErFEvtHntHSLqXIwNzdDPZ6i2w3goMJEh\nIuqi5HIZNv31b8Q/MDVnYI+BmB324kP3TZ6xgSmeHP8agnsNx29H/oOCZizoeT8BAmwtHOFs2wPO\ntj3gYtsDjtZuSM25g4gbh3HjTpTSJAr1issLcPjiDhy+uAOejn4YHDAG/XyGwkBqiJNX/sD242tV\nuqxNHDQHk0Ief+g+IyKi9sREhoioCxJFETtOrlMZG+Lh2AvzJ73VZafhbA9+7v2w9KnV2Htmk8ra\nDvX0dKRwsnFXSlqcrN2hr2aciqWpLXp7DkJxWQEu3DqBiBuHkVWQqva4iRkxSMyIwfYTa9HDsRdu\np1xRqTNz5PMY2Xdq214kERExkSEiaq2yimIkZcZCECRwtvGAmbFlh33DfihqO05eUb5Jt7dywaJp\n76sMbH8YGUgNMWv0QgT3HIajl3ahVlYLJxt3uNxLXGwtnFqc7JkZW2JM/3CEBU9HUmYszt88jIux\np1FVXaFSt7qmUiWJkUh08PT419G/14g2vTYiIqrDRIaIqIVyCjNwPHovIm4eVprq2NjAFE42HnCy\ncYeTjQecbTzgYOXapsRCFEWUVhQjtygDOYUZyC3MRGbBXVyOU26JMTe2wkvT/w5jQ7NWP1d35OXs\nDy9n/3Y9piAI6OHYCz0ce2HGiOdwJf4cIm4cVunidz+prj4WTHkH/h7B7RoLEdHDjIkMEVEz3cm4\njaOXduFqfITaaXrLKksQl3oNcanXFGWCIIGthWNdNyYbD0WiY2Vqp6gjiiJKygvrEpWiDOQUZt6X\nuGSgorq80bgMpUZ4KfyjNi2kSK2jr2eAQX6jMchvNHIKM3D+5hGcv3kURWX5ijpG+iZYNP0D9HD0\n1WKkRETdDxMZIqJGyOUyXL9zAUcv7kZiRstXaBZFObIL0pBdkKbUiqIvNYSZvjVq5TX4LXIVqmsq\nWxWfro4enp/2HpxsPFq1P7UfWwtHTB3yFCaHzMWtlMu4mhABABjT/1GuAUFEpAFMZIiI1KiurULk\nzWM4Fr0HOYXpDdYzN7aChakNMnKTVdYIaUxVdQVyqtUPGG8uPV0p5k1cAh+XwDYdh9qXRKIDf4/+\n8Pfor+1QiIi6NSYyRET3KSkvwqmr+3Hq6p8oqyhusJ6TjQfCgqcjuOcw6OroQS7KkVeUhfTcJKTl\nJiE9NxnpuUnILcpsc0xSXX3YWDjC1tyh7l8LR9iYO8LFrgeM9E3afHwiIqKuiIkMEWldZv5dRNw4\njNScOzDUN4afezD8PYJhYWLdYTFkF6Th2KU9iIw5hhpZdYP1fN36Iiw4HL3cgpRmKJPcGwtja+GI\nIO9QRXlVdQXS81KQfl9yk56bpDLuRV9qCFtzR9hYONz711FxPDOjjpsNjYiIqKtgIkNEWlFdU4Xo\nuDM4d/2QytiTK/HnANS1etR10QlGD4de0NFpv19ZMrkMWfl3kZKVgGuJ53E98YLaAfwAoCPRRf9e\nwzG633Q423q06Hn0pYaKGa7qiaKIgpJcnI48Bl2JHoaHjIaJoTmTFSIiohZgIkNEHepudiLOXT+I\nqNsnUdnEbFz1rReHo7bDUGqEXm594e/RH34e/WBubNXs55TLZcguTEdKVjzuZicgJSseqTmJSlMn\nq2MoNcLQ3hMxou+Udm0dEgQBVma2cLLwBACYGlm027GJiIgeFkxkiLqh6toq5BVlwcbcEXq6etoO\nBxVV5bh4+yTO3jiI1OzE1h2juhyX488qVrJ3sfWEv0cw/D36w92hp2JxQ7koR25hBlKy4pGSnYC7\n95KWqhbMCmZpaotR/aYhNGAcDNSs9E5ERETax0SGqJuoqa3BrZRoRMeewbXE86iqqYSxoRkmDpqN\nIYETOjyhEUURSZm3cfb6IUTHnm5yRi8v5wAM8h2ForJ83Ey6hOTM2Aa7egFAak4iUnMScfDCNhjq\nG6OnS2+UV5XhbnZCky09DXG180JYcDj6+gxp8arvRERE1LGYyBB1YTK5DLF3ryI69jSuJESgoqpM\naXtZRTG2n1iLY9F7MCX0SfTvNRwSQaLRmMoqihF56zgibhxGRl5Ko3VNDM0x2H80QgPGwc7SWVE+\ncfAclFYU41ZyNG4mX0JMcnSjM4hVVJXhyr01O1rC1NAcbvY+cLX3Qi/XIHg6+XGcChERURfRJROZ\nlStX4v3338crr7yCb775RtvhEHUouVyGhPQYXIo9jSvx51BaUdTkPvnF2dj011c4enEnpg19Bn7u\n/dr1hl0uyhGbchURN4/gSsI5yGS1DdYVIMDXvR9CA8Yi0HMgdHXUtxSZGJphgO9IDPAdCblchrvZ\nCbiZdAk3ky4iJSu+0dYadYwNTOFq7w03O2+42XvB1c4bFibWTFyIiIi6qC6XyEREROCnn35Cnz59\neANCD436blqXYk8jOu4MissKWnWctNwkrNn9D/i49MYjQ5+Gu0PPNsWVX5yNiJtHcP7mURSU5DRa\n18LEGiH+YxESMAZWZnYteh6JRAfuDj3h7tATk0IeR0l5EW6lRONmUl1rTXlliVJ9Q31juNl530tc\nvOBm7w1LU1v+ziAiIupGulQiU1RUhKeeegrr16/HsmXLtB0OkUaJoojUnERcij2F6NgzyG8iUQAA\nY0Mz9PMegn49h8HO0gkHI7fhzPW/IJfLlOrFpV7Dv7b8DX29h2DqkCeVunU1paa2GlcTziPixmHE\n3r3aaMuIRJAg0HMgQgPGwc+9HyTtNO7E1MgcA31HYaDvKMjlMiTfG9BvbGAKVzsv2Jg7MGkhIiLq\n5rpUIrNw4ULMmjULI0eOhCi2rFsJUVdSVlmCjX/+C7dSLjdZ11DfGEFeIejXcxh6uvZRGqQ+a/RC\njOo3DX+c+xWXYk+p7Hs5/iyuJkQgNGAcJobMaXRK49ScRETcOIyoWydRXlXaaEw25g4IDRiHwf5h\nMDO2bPI1tIVEoqOyTgsRERF1f4LYRTKCn376CT/++CMiIiKgo6OD0aNHo3fv3li9erWiTlHR/40V\niIuL00aYRG0mF+U4cmMzMoruNFhHVyKFq3VP9LAJgKOFZ7Nm2MorzcCl5GPIKFQ//bGORBf+ToMR\n4BwKqa4BAKCqtgJ3cm4gPusy8ssyGz2+jkQX7tZ+8LbvC3szN7aIEBERUZN8fHwU/zc3N2/Rvl2i\nReb27dt4//33cfr0aejo1N2wiaLIVhnqli7eOaw2idGR6MLF0gceNv5wtvRucJB8Q6xNHDEu4Amk\nFyYiOukY8soylLbL5LW4lnoGtzMvwd9pEArLc5GSdwtyUdbAEeuP6wQf+yB42AQoEiAiIiIiTesS\nLTIbNmzAggULFEkMAMhkMgiCAB0dHZSVlUFPT0+pRaalGR1RQ6KiogAAAwYM0Phznb95BP87pDwT\nn7ONB8b0n4FAz0HttjijXJTjctxZ/HH2f8gpymh6hwcYG5hioO8ohASMgZONR7vE9DDqyHOLHh48\nr0gTeF6RprTl/r1LtMjMmDEDgwYNUjwWRRHPPvssevbsiffeew96etpfuZyorZIyY/Hb0e+VyixM\nrPFS+DKYGVu063NJBAmCew5DkFcIzt44hAPnt6CkvLDRfeqnTQ4JGIvAHgM7fIFNIiIiovt1iUTG\n3NxcJUMzMjKCpaUl/P39tRQVUfspKs3H2n0rldZf0dOR4vmpS9s9ibmfjo4uhveZhEG+o3D88l4c\nvrgTVdUVSnWszewREjAGg/xGw9LUVmOxEBEREbVEl0hk1BEEgYOJqVuoqa3G2n0rVdaGeWLcq3Cz\n9+6QGPSlhpgwaDaGBE7AkYs7EXv3Khyt3TDYfwy8XQIgESQdEgcRERFRc3XZRObYsWPaDoGozURR\nxJaj3yM5S3mWvbH9H0X/XiM6PB5TI3OED5/f4c9LRERE1FL8mpVIi45H70VkjHJS7u8ejKlDntRS\nRERERERdAxMZIi2JSY7GrtMblMrsLJ3xzKQlkDRjXRgiIiKihxkTGSItyCnMwIY/V0EU5YoyA6kR\nXpj2Hoz0TbQYGREREVHXwESGqINVVJXjx72foKKqTFEmQMC8iUtgb+msxciIiIiIug4mMkRNqKmt\nQk5Jmsq0xK0hF+XY9NdXyMpPVSqfNvRpBPTgImNEREREzdVlZy0j6giZ+Xex4+K3qKqtwJGYzejr\nHYrB/mHwcm7dlMT7z23G9TsXlMr69xqBMf1ntFfIRERERA8FJjJEDZCLcvx6uC6JAYDqmkpExhxD\nZMwxWJnZYZDfaAz2C4O1uX2zjncp9jQOXtiqVOZi54m5Y1/hmkhERERELcREhqgB528eRVLGbbXb\n8ouzceD8Fhw4vwXeLoEY7BeGvj5DoK9noLZ+ak4ifj30jVKZqZEFXpi6FFJd/XaPnYiIiKi7YyJD\npEZZZQn2nPm5WXXjU68jPvU6th3/EX19htZ1PXPyV7SylJQX4ae9K1FdW6XYR0eii+emvANLU1uN\nxE9ERETU3TGRIVJj35lfUFZRrHisI9HFk+P+H24kXcTV+AjUyKpV9qmqqcT5m0dw/uYRWJvbY7Bf\nGPr3GoFfD3+LgpIcpbqzRi+Cp5Ofxl8HERERUXfFRIboAcmZcTh7/aBSWW+XoRjgOxIDfEeivKoU\n0bFncD6m4a5neUVZ2B+xGfsjNqtsGxE0GUMCx2kkdiIiIqKHBRMZovvI5TL8fmwNRIiKMlMDKwQ4\nhyoeG+mbYGjvCRjaewKy8lNxPuYYLsQcQ1FZfpPH93HpjRnDF2gkdiIiIqKHCRMZovucuX4Qd7MT\nlMoGe06AjkT9pWJv5YJHhj6NqaFP4FbKFUTGHMXVhPOoldWo1LUys8Ozk9+Gjg4vOyIiIqK24h0V\n0T0l5YXYd/YXpbK+3kPgZOnV5L4SiQ78PYLh7xGM8spSXIo9jfM3jyA5Kw4AYGpojhemvgcTQzON\nxE5ERET0sGEiQ3TPntM/o6KqTPFYqmeAGSMWIOF2UouOY2RggmF9JmJYn4nIKkhDbmEGPBx6wphJ\nDBEREVG7YSJDBCAxPQbnY44qlU0aPAeWpjYAklp9XHtLZ9hbOrctOCIiIiJSIdF2AETaJpPL8Pux\nH5TKHKxcMarvNC1FRERERERNYSJDD72TV/5Aem6SUtms0Qs5KJ+IiIioE2MiQw+1otJ8lbVeBvQa\nCR+X3lqKiIiIiIiag4kMPdR2nVqPquoKxWMDqRHCh8/XXkBERERE1CxMZOihFXv3Gi7GnlIqmxL6\nBMyMLbUUERERERE1FxMZeijVymqw9bjyAH9n2x4Y1meSliIiIiIiopZgIkMPpePRe5GVn6pUNnv0\nIuhIdLQUERERERG1BBMZeugUlOTgwPktSmUh/mPQw9FXSxERERERUUsxkaGHzo6T/0V1bZXisZG+\nCaYNfUaLERERERFRSzGRoYdKTHI0rsSfUyqbNvRpmBqZaykiIiIiImoNJjL00Kiprca2Yz8qlbnZ\n+yA0YKyWIiIiIiKi1mIiQw+NIxd3IqcoQ/FYgIDZoxdBwgH+RERERF0OExl6KOQVZeHQhe1KZUN7\nT4CbvbeWIiIiIiKitmAiQw+FbSd+Qo2sWvHYxNAcU4c8pcWIiIiIiKgtdLUdAJEmiaKIw1E7cONO\nlFL59GHPwMjAREtREREREVFbMZGhbqtWVoMtR9fg/M0jSuWejn4Y6DdaS1ERERERUXtgIkPdUllF\nMdb98Rni024olevq6GHW6EWQCOxVSURERNSVMZGhbierIA0/7l6hNEMZABhKjbBgyjtwtvXQTmBE\nRERE1G6YyFC3Env3Ktb98RkqqsqUym3MHbDokQ9gb+WipciIiIiIqD0xkaFu4+z1g/j92A+Qy2VK\n5V7OAXh+yjswNjTTUmRERERE1N6YyFCXJ5fLsPv0RhyL3qOybbBfGOaMeQm6OnpaiIyIiIiINIWJ\nDHVpVdUV2HjgS1y/c0Fl27Shz2Bs/xkQBEELkRERERGRJjGRoS6roCQHP+75BGm5SUrlerpSPDNh\nMYK8Q7UTGBERERFpHBMZ6pKSM2Px096VKC4vUCo3N7bCC9Peg5u9t5YiIyIiIqKOwESGupzouDP4\n5a+vUSOrVip3sfXEwkfeh4WJtZYiIyIiIqKO0iVWBfzuu+8QFBQEc3NzmJubY8iQIdi/f7+2w6IO\nJooi/orcivX7v1BJYvp4Dcbrsz5lEkNERET0kOgSLTKurq74/PPP4ePjA7lcjg0bNiA8PBwXLlxA\nUFCQtsOjDiCT1eLXw9/iwq3jKtvG9J+BaUOfhkToEnk5EREREbWDLpHIPPLII0qPV6xYge+//x6R\nkZFMZB4SO0/9VyWJkUh0MCfsJYQGjNVOUERERESkNV0ikbmfTCbD1q1bUVlZiREjRmg7HOoA0XFn\ncfKKcldCIwNTPDflb/Bx6a2lqIiIiIhImwRRFEVtB9Ec165dQ2hoKKqqqmBoaIjNmzdjypQpSnWK\nirMoTkEAACAASURBVIoU/4+Li+voEEkDSiryse/KOtTIqhRlxvrmGBfwJMwMrbQYGRERERG1lY+P\nj+L/5ubmLdq3ywwq8PX1xdWrVxEZGYlXX30Vjz/+OKKiorQdFmmQTF6LE7d3KCUxEkGCkb1mMokh\nIiIiesh1mRaZB40bNw4uLi5Yv369ouz+FpmWZnTU+Ww99iNOXVXuUjZz5PMY2Xdqh8ZRnzAPGDCg\nQ5+Xuj+eW6QJPK9IE3hekaa05f69y7TIPEgmk0Eul2s7DNKQ6LgzKklMkFcIRgRNaWAPIiIiInqY\ndInB/u+++y6mTp0KFxcXlJSU4Ndff8WJEydw4MABbYdGGpBTmIFfD3+rVGZtZo+5416FIAhaioqI\niIiIOpMukchkZWXhqaeeQmZmJszNzREUFIQDBw5g3Lhx2g6N2llNbTXW7/8CVdUVijIdiS6enfw2\njPRNtBgZEREREXUmXSKRuX8cDHVvu05tQGpOolJZ+PD5cLP31lJERERERNQZddkxMtT9cFwMERER\nETUXExnqFDguhoiIiIhagokMaZ3acTE6HBdDRERERA1jIkNap25czIzhz3JcDBERERE1iIkMaZXa\ncTHeoRjeZ7KWIiIiIiKiroCJDGmN2nEx5vZ4YizHxRARERFR45jIkFY0OC5m0tsw1DfWYmRERERE\n1BUwkSGt2HlqPcfFEBEREVGrMZGhDncp9jROX/1TqYzjYoiIiIioJZjIUIfKKczA5iPfKZVxXAwR\nERERtRQTGeowHBdDRERERO2FiQx1GK4XQ0RERETthYkMdYjLcWdV1ovp6z2E42KIiIiIqFWYyJDG\n5RVlYbOa9WLmjn2F42KIiIiIqFWYyJBG1cpqsP7PVaioLleU6Ug4LoaIiIiI2oaJDGnU3jObkJIV\np1Q2fdg8joshIiIiojZhIkMacy0xEsei9yiVBXoOwsi+U7UUERERERF1F0xkSCMKSnLwv0PfKJVZ\nmtriyXH/j+NiiIiIiKjNmMhQu5PJZdj455coryxRlEkECeZPehPGBqZajIyIiIiIugsmMtTu/ozY\njMSMGKWyqUOeQg9HXy1FRERERETdDRMZalcxydE4dGG7UpmfezDC+odrKSIiIiIi6o6YyFC7KSrL\nx6a//g0RoqLM3NgKT41/HRKBpxoRERERtR/eXVK7kMtl+PnAVyitKFKUCYIEz0xcAlMjcy1GRkRE\nRETdERMZahd/XdiGuNRrSmUTB8+Bj0ugliIiIiIiou6MiQy1WVzqNRw4v0WprKdLb0wY+JiWIiIi\nIiKi7o6JDLVJSXkRNh74EqIoV5SZGprj6YmLIZHoaDEyIiIiIurOmMhQq8lFOTYd/DeKywoUZQIE\nPD1hMcyNrbQYGRERERF1d0xkqNWOXNyFW8nRSmXjBs6Er3tfLUVERERERA+L/8/efYdXUaZtAL/n\nTNpJJZ2QRsAAQkRKIPTeI6CCqBRFUcTCIljBAuyyoLAoNhRcQBT9EFdBBUQ6oUmVSE8glYT03pOZ\n+f4IjAwlnIQcJie5f9fFtdzvzJx5yL6bzZOZd4aNDNVITPI5bDqwRjPWrMm9GNrlcZ0qIiIiIqKG\nhI0MVVthST5W//YfyNesi3Gwc8KTQ16ByHUxRERERHQXsJGhalEUBd9u+wTZBRma8fGDpsHVyUOn\nqoiIiIiooWEjQ9Wy689fcCrmsGasX4eRaBMUqlNFRERERNQQsZEhk0VfOoVf9q3WjAV6B+OBbuN1\nqoiIiIiIGio2MmSSnIJMfLV5kWZdjNHGHhOHvgor0VrHyoiIiIioIWIjQ7dVIZVj5eaFyC/O1YxP\nGDwd7i7eOlVFRERERA0ZGxm6rQ17VyHu8nnN2JDOjyKkWSedKiIiIiKiho6NDFXpyLndiIjcrBm7\nN7ADhoSN0akiIiIiIiI2MlSFpPRYrN2xVDPm5uyFJ4ZMh4HviyEiIiIiHbGRoZsqKinAfze9h/KK\nMnXMWrTBpPA34WDnpGNlRERERERsZOgmZEXGN78vQWZuqmZ8TL/n4O/VTKeqiIiIiIj+ZjGNzIIF\nC9CpUye4uLjAy8sLI0aMwOnTp/Uuq17aevgHnI47qhnrft8QhLXur1NFRERERERaFtPI7NmzBy+9\n9BIOHjyInTt3wsrKCgMGDEB2drbepdUrZ+KO4bc/1mrGAhu3wMO9JulUERERERHRjaz0LsBUW7Zs\n0eRvvvkGLi4uOHDgAMLDw3Wqqn7JzE3F11s+hAJFHXM0uuDpYa/D2oovvSQiIiKiusNirshcLy8v\nD7Isw9XVVe9S6oWyilL8d9N7KCotUMcEwYCJQ1+Bq5OHjpUREREREd1IUBRFuf1ut3bgwAHk5uai\nV69ecHBwqK26bmvMmDG4ePEijh49CkEQAAC5uX+/eT46Ovqu1WLpFEXBgQu/4mLaX5rxDoH9EeLX\nVaeqiIiIiKi+Cw4OVv/u4uJSrWNNviIzb948DB06VDM2YsQI9OjRA+Hh4WjZsiXi4+OrdfKamjFj\nBg4cOIAff/xRbWKo5qJSjt/QxAS4t0Ib3y46VUREREREVDWT18h89913GDJkiJp//fVXbNy4EW+8\n8QbatWuHqVOnYu7cuVi5cqVZCr1q+vTpWLduHXbt2oWmTZvecr/Q0FCz1lFfxKVE4duD2zRj3q5+\nePGRd2G0tdepqrrl6NHKJ7hxTlFt49wic+C8InPgvCJzufaOquoyuZG5dOkSWrVqpeYff/wR99xz\nDxYsWAAAOH/+vNmbmGnTpuGHH37Arl270KJFC7OeqyHIL8rByk3vQ5Ir1DFbaztMeuANNjFERERE\nVKeZ3MgIggBJktS8fft2PPzww2r29fVFSkpK7VZ3jRdffBFr1qzBhg0b4OLiop7Lycnprq7NqS8k\nWcJXvy1GTkGmZnzswKlo7OavU1VERERERKYxeY1MixYtsH79eiiKgi1btiA5OVmzZubSpUtmfYLY\n559/joKCAvTv3x9NmjRR/yxevNhs56zPNh5Yg+hLJzVj/To8iPbB3XWqiIiIiIjIdCZfkXnttdfw\n2GOPwc3NDQUFBWjdujUGDBigbt+xYwfat29vliIBQJZls312Q3My5jB2HFuvGbvHLwTDu0/QqSIi\nIiIiouoxuZEZM2YM3NzcsGnTJjRq1AgvvPACrK0rX5KYlZUFd3d3TJjAH4TrurLyUvxv13LNmIuj\nOyYOeRWiQdSpKiIiIiKi6jGpkSkrK8Mff/yBgIAAfPjhhzdsd3Nzw/r1629yJNU124/9hOyCDDUb\nDCKeHvYanB0a6VgVEREREVH1mLRGRhRF9O/fH9u2bbv9zlRnZeWlY8dRbcPZp91wBPm0usURRERE\nRER1k8mNTNOmTZGfn2/uesiMftm/GuVSmZqdjC4Y3PkRHSsiIiIiIqoZk59aNm3aNCxbtgypqanm\nrIfM5GLSaRyP2qcZe6DbeBht+ehqIiIiIrI8Ji/2LywshIODA4KDg/Hggw+iefPmMBqNN+z3+uuv\n12qBdOdkWcKPe1Zoxvy8miGsdT+dKiIiIiIiujMmNzIzZ85U/75mzZpb7sdGpu7548xOXEqP0YyN\n6vUMDHxKGRERERFZKJMbmZiYmNvvRHVOcWkhNh7QNp4dWvREc9/WOlVERERERHTnTG5kmjZtasYy\nyFx+P7wOBcW5ara2ssGI7k/oWBERERER0Z0zuZG5KioqCrt370Z6ejrGjh2LoKAglJWVISUlBd7e\n3rC1tTVHnVQDqdlJ2H1io2ZsQMeH4ebsqVNFRERERES1w+SnlsmyjGeffRatWrXClClT8O677yI2\nNhYAUFpaipCQEHzyySdmK5Sqb0PEKsiypGZXRw/07/iQjhUREREREdUOkxuZ+fPnY9WqVZg3bx4O\nHjwIRVHUbU5OThg9ejTWr19fxSfQ3XQm7hhOxx3VjI3sORE21rxiRkRERESWz+RGZtWqVXjqqacw\na9YsNG/e/IbtISEhiIqKqtXiqGYkqQI/RazUjDVv0hrtg7vrVBERERERUe0yuZG5dOkSwsLCbrnd\naDQiPz+/VoqiOxMRuRlp2UlqFiDg4d7PQBAEHasiIiIiIqo9Jjcy3t7eiIuLu+X248ePIzAwsDZq\nojuQX5SDLYfWasa6hgyAv1cznSoiIiIiIqp9Jjcyo0ePxhdffIGoqKgbfrP/22+/YfXq1RgzZkyt\nF0jVs+ngdyguK1KznY09wruO07EiIiIiIqLaZ3IjM3v2bAQEBKB9+/YYN67yB+MFCxYgLCwM4eHh\naNeuHWbOnGm2Qun2LqXH4OCpbZqxIWGPwsm+kU4VERERERGZh8mNjIuLC/bv34+33noLKSkpsLOz\nw759+1BYWIi5c+ciIiIC9vb25qyVqqAoCn7cswIK/n6anFejJuh1/zAdqyIiIiIiMo9qvRDTaDRi\n1qxZmDVrlrnqoRo6ceEALiad1ow91OtpWInWOlVERERERGQ+Jl+R6du3L3bs2HHL7bt27UK/fv1q\npSiqnrKKUmzY+5VmrHVgB7QJCtWnICIiIiIiMzO5kdmzZw9SU1NvuT01NRW7d++ujZqomnYe24Ds\n/HQ1GwwiHur1tI4VERERERGZl8mNzO0kJSXBwcGhtj6OTJSdn45tR3/UjPW6Pxzebn46VURERERE\nZH5VrpH5+eef8fPPP0NRKheQL1++HNu3b79hv6ysLGzfvr3KF2aSefyy/xuUV5Sp2cHojCFhfAw2\nEREREdVvVTYyp0+fxrp169T3xhw6dAjHjh3T7CMIAhwcHNC3b198+OGH5quUbhCTfBbHzkdoxh7o\nOg72to46VUREREREdHdU2chc+4Qyg8GA//73v+o7ZEhfsiLjxz3/1Yz5ejRF1zYDdKqIiIiIiOju\nMfnxy7Ism7MOqqaDp7YhMe2iZuzh3s/AYBB1qoiIiIiI6O6p9mL/bdu2YdasWXj22Wdx7tw5AEBB\nQQEiIiKQnZ1d6wXSjZLS4/BTxArNWLvgbgj2C9GpIiIiIiKiu8vkRqa4uBiDBw/G4MGD8f7772Pl\nypVITk4GAFhbW2P06NH4+OOPzVYoVSoqLcCKTe9pFvhbW9ngwR4T9SuKiIiIiOguM7mReeutt7Bn\nzx6sWbMG8fHx6pPMAMDW1haPPPIINm7caJYiqZKsyFiz9WNk5KZoxsf0fQ5uzl46VUVEREREdPeZ\n3MisW7cOL7zwAsaOHQs7O7sbtrds2RIXL168yZFUW7Yf/QmnYg5rxrqFDEJY6/46VUREREREpA+T\nG5mMjAy0bt36ltsFQUBxcXGtFEU3Op8QiU0Hv9OMBXjdg1G9n9GpIiIiIiIi/ZjcyPj7++PMmTO3\n3L5//34EBwfXSlGklZ2fjq+2LIai/P3kOHs7Jzwd/jqsrWx0rIyIiIiISB8mNzLjx4/H8uXLsXfv\nXvUFmVd9/vnnWLduHZ588slaL7ChK68ox8rNi1BYnKeOCRDw5JAZXBdDRERERA2Wye+RefPNN3Ho\n0CH06dMHLVq0AABMmzYNGRkZSE1NxfDhw/Hyyy+brdCGav3elYhPidKMDe3yGO4NbK9TRURERERE\n+jP5ioytrS02bdqEb775Bi1btkSrVq1QXl6ODh06YPXq1diwYQNEkS9jrE1Hzu3Gvr9+04y1aRqK\nQZ0f0akiIiIiIqK6weQrMkDlgv6xY8di7Nix5qqHrkhKj8PaHUs1Y+7O3pgw+GUYhGq/x5SIiIiI\nqF6pViOza9curFy5ErGxscjOzta8S0ZRFAiCUOUDAcg0RaUFWLnpfe1LL0UbPB3+BuztHHWsjIiI\niIiobjC5kfnPf/6D119/HUajES1btoSnp+cN+1z/EACqPlmR8e3Wj5Gee1kz/kjf5+Dv1UynqoiI\niIiI6pZqNTLdu3fHxo0b4eLiYs6aGrQdR9fj5A0vvRyILm340ksiIiIioqtMXmxRXFyM8ePHs4kx\no/MJkdh48FvNmL9Xc4zq/axOFRERERER1U0mNzJ9+vRBZGSkOWupUkREBEaMGAE/Pz8YDAasXr1a\nt1rMITs/A6u3fHDDSy8nhb/Bl14SEREREV3H5Ebm008/xfbt27FgwQKkpaWZs6abKiwsRNu2bfHR\nRx/BaDTWq/U4FVI5Vm1ehILiXHWML70kIiIiIro1kxsZf39/PPPMM3jrrbfg4+MDOzs7GI1GGI1G\n2Nvbq/9pLkOHDsW8efMwatQoGAz16/HD6yNWIS7lvGZsCF96SURERER0SyYv9n/rrbewYMEC+Pn5\noWPHjjddK1OfrpLcLUfO7cHevzZrxlo37YjBfOklEREREdEtCcq1L4OpgqenJ7p27YoNGzbofkXE\nyckJn332GZ544gnNeG7u37dmRUdH3+2yqi27MA2b/1oJSa5QxxxtXRB+/zOwtTbqWBkRERERkfkF\nBwerf6/uQ8VM7kjKy8sRHh6uexNTX5RVlGLPuf9pmhiDIKJ3q9FsYoiIiIiIbsPkW8seeOAB7Nmz\nB88995w566k1oaGhepdwS4qiYPWWxcgrydKMP9r/eXRtM0CnquhWjh49CqBuzymyTJxbZA6cV2QO\nnFdkLtfeUVVdJl9eefvtt3H27Fk8++yzOHToEC5fvoy0tLQb/tQVJt4xp4u9f/2G41H7NGNdWvdn\nE0NEREREZCKTr8i0bt0aABAZGYkVK1bcdB9BECBJUu1Udp3CwkJ13Yssy4iPj8eJEyfg7u4Of3//\nG/aX5UtYuzYCgwcPhoeHh1lqqon4lGisj1ipGWvi0RSj+07WqSIiIiIiIstjciPz7rvv3nYfcz61\n7MiRI+jXr596ntmzZ2P27NmYOHEiVq5cecP+//vfp5g1aw169OhRZxqZopICrNq8ULMuxtbGiKeH\nvQ4bK1sdKyMiIiIisiwmNzJz5swxYxm316dPH8iyfPsdr+jVqzV+//1t+PmVQlEU3R8NLSsy1mz9\nCFn56ZrxsQNegpdrE52qIiIiIiKyTPX2EWQ+Pm5o1coPBsN5FBWdwGOPPYrY2Fjd6tl5bANOxR7R\njPW6Pxztg7vrVBERERERkeWqt43MVYIALFnyAWQ5B/7+vrrUcDHpNDYeWKMZC/QOxoM9J+pSDxER\nERGRpTP51jJL9tprDwEABOEkZPl+FBWVwNHR8a6cO78oB1/9thiy8vdtcfa2jnhq2GuwEq3vSg1E\nRERERPVNvb8iAwA2NtawsbGGKCbj1Kkf0KpVK6SkpJj9vLIsYfWWD5BbqH1fzITBL8PN2cvs5yci\nIiIiqq8aRCNzrd9/34oFCybBy8vF7OfacngdohL/0owNCB2FNkF8mRQRERER0Z1oELeWXeu11x4G\nAMjyEchyB+zdewy9evWq9aeanY3/E78fWqcZa+7bBuFdx9bqeYiIiIiIGqIGd0XmKoMhF0uXzsIz\nzzyNvLy8Wv3s7PwMfP37h1CgqGNORhdMHPoKRINYq+ciIiIiImqIGmwjAwCBgS74/fe5cHSUau0z\nJakCX/32HxQW/90cCYIBTw59BS4ObrV2HiIiIiKihqxBNzLDh3dGs2YuMBiOIC8vFu+8884df+av\nB9Yg9vI5zdiwLo+hhX/bO/5sIiIiIiKq1KAbmasEoQxTpjyFjIyLkOV8KIqCy5cvIysr6/YHX+Ov\ni4ew8/gGzVirwPYY2Gl0bZZLRERERNTgNbjF/reycOGTkGUFghABWfbGP//5CRo3DsLs2XNMOj4j\nNwXfbv1IM9bI0R1PDJ4Og8B+kYiIiIioNvEn7Cv8/DwQEOAJQZAhipeRnR2Lp566F5J0HrKcjxkz\nZuDkyZM3Pba8ogwrNy9EcVmROmYwiJg49DU4Gp3v1j+BiIiIiKjBYCNzC2vXvoaAAHuIYhRSUjZg\n1ar/wt/fFrJc+WCAI0eOQFEqn0q2PmIlLqXFaI4f0f0JNGvS6q7XTURERETUEPDWMhN4ejpi165/\nwcXlPBTlEiIjC/Dgg1MQExODPZG/Yt/JLZr92zbvgr7tR+hULRERERFR/cdGxgTW1lZo164ZAEAQ\nCpGUdAwvTB2ApT+/htjLibgUnY60xFx06HcP3F28MXbgS7X+gk0iIiIiIvobby2rJkVR0CjAEdnO\nRYi9nAgAOLk/DgaDACvRChOHvICPP/wUn3zyiXpMaWmpXuUSEREREdVLbGSqIa+wCMt/2Ya1O/aj\nrLxCHe8xMgRtuwZhUnhfBHgnYs+en+DrWwpJioYkpWLKlMlYsWKFun9iYiJKSkr0+CcQEREREdUL\nbGRM9Gd0LBas+Qmn4xJv2BbWLhj/fmEs2gQFQBAU/N//TcfQoU0hiucgiodx9uwhtG8vQJJOQZIS\n8MQT47Bjxw71YQF79+5FTk7O3f4nERERERFZLDYyt1FUUoqvt+zGqs07UViivUXMxsoKj/brjudG\nDoKLo4M63qiRI4xGWzUfOPA+2rVzhyjGwmA4gdLSdISFFUOWj0GSovDkk+ORlhYHWS6DoigYNWoU\nEhP/bpgOHz7MKzhERERERNdgI1OFc/FJWPDtTzh6/uIN24J8vPDGuIfQ/b5Wt13YbzAYYDBUfqkF\nQcCBAwvh4WELUbyMiopTCA31R9OmsRCE7ZCkHdi8eRNcXJIhSdGoqLiEQYMGIj8/A7IsQ1EUjBs3\nDrm5uernHz58GJIk1e4/noiIiIioDmMjcxNl5RX43+6DWLphC3ILijTbRIMBw7uHYtrocHg2uvOX\nXdraWmPdujdgY2MFQZBgMBRi7975cHZOgyieQ3n5HwgLaw539xMAtqOgYCd++ulH2NsnQ5LiUVKS\nhO7du0OWiyDL5aioqECLFi1QUVG5hkdRFMyePVu9jU1RFJw7d07NRERERESWiI3MdeJS0rDwuw2I\niDxzw7Ym7q549bERGBh6v3qFpbYZDAaEhgar2Wi0xe+/z4XBoMBgKIW1dQ5+/fUtWFtfgCj+heLi\nCPTvfx+srCIgCNuQkbEeWVlpEIQ/IUmRyMg4iI8++hCynAhJSkFubgJCQ0OhKOWQZRl5eXm4//77\n1camqKgIzz//vHr+0tJSfP3112qWJAkXLlwwy7+diIiIiMhUbGSukCQZmw4ew4frNiItJ1ezTQAw\noGNbvPLYSPh6uutT4BV2djYYMKCdml1dHbFly1wIggxBkODhYY1jxxZDFFMgigmwto7HP//5GEQx\nEqJ4BAUFuxAW1hyCsB3ANmRn/4bMzMuQ5cOQpGNIT9+Hn3/+EZJ0HpJ0EWlpJ/DGG69BklIhSRlI\nSbmI7t27QZZLIcvlSEpKQmBgIBRFgaIoSEtLw8CBA9XGKDs7Gy+++KJab0FBAT7++GM1FxYW4ocf\nflBzSUkJ9u/fr+by8nLExsaqWZZlFBcXm+NLS0REREQWhI0MgOz8Aixe9wt+P3zihluu3F2c8I/R\n4RjRoxOsrUSdKjSdlZWIwEAvNTdq5Ih//GO4mv383LFjx7wrt7GVoUkTG+zfvwCimAZRTIarazY+\n+WQSRDEKongGtrZRmDixJ0TxMETxIMrL96JtW18IwnYIwjYUFf0OUSyDouyCokQgN3c3Ll48c+VB\nBn8iM/MgNm/+GZJ0BpJ0HqmpR/DBBwshSXGQpASkpPyF116bAUm6DElKRVLSaYwd+xgkKRuynIvE\nxHPo3bsXZLkYslyKuLgLaNWqFWRZgizLiI2NRatWrdRGKiEhAd26dVNzUlISwsPD1Xz58mWMGzdO\n/XqkpqZiypQpak5PT8err76q5szMTCxfvlzNWVlZWLhwoZqzs7M17wzKzc3Fl19+qea8vDysWbNG\nzfn5+Vi3bp0mb9iwQc0FBQXYvHmzmgsLC7F9+3Y1FxUVYc+ePZp8beNXXFyMQ4cOqbmkpATHjh3T\n5D///FOTT548qebS0lKcOXNGk8+dO6fmsrIyREVFafK1V+jKyso0jWd5eTni4uI0OSEhQZOvfbBF\neXllc3xtTk5OVnNFRcUNOSUlRZNTU1OrzGlpaZqcnp6uyRkZGVXmzMxMNUuSdNuclZVVZb52vZsk\nScjOzq5WvvaJh7WRr69H75yXl8fMzFxHckFBQZ2qh7nuZL2wkQGwdsd+XErLvGG8W0hLvDH2QTT3\nbaxDVXeHtbWVpvFxdrbHqFHd1Ozl1QgLFjyp5qZNvbBt2z/VK0D33OOBM2c+hcFQCIMhD/7+In79\ndRZE8TJE8RK8vPLx0UcTIYoXIYpRcHFJxtSpgyCKJyGKkXB0jMaYMZ0gikchiodha/sXevZsDoNh\nHwQhAoJwGMHBbhCEnRCEHZDlvXByEgBsBbAVZWW7UFGRD0XZCUXZjeLiCKSlJUBR9kFRDqCgYD/O\nnYuELB+BLB9DXt4hHDoUAUk6Dkn6Ezk5h7Bt2yZI0l+QpJPIyjqC9eu/hySdhiSdQUbGEWzZ8isc\nHVMgSVHIyDiOZcs+ReU7gi4gPf1PLFnyH0hSLCQpFqmpf+K99+ahslGLR0pKJGbPfguSlAhJuoTL\nlyMxc+brkKQkSFISLl/+C6+88jIkKRmSdBnJyScxdeoLkKQUSFIqLl06ieeeewaSlAZJSkdi4kk8\n/fSTkKR0NT/xxHhIUgYkKRMJCaeuNIJZkKQsxMefwpgxoyFJ2ZCkbMTHn8bo0Q9DknIgSTmIjz+L\nBx8cAVnOhSznIj7+DIYPD1dzQsJZhIcPhSznQZbzEB9/BkOHDoYs50OW8xEffxaDBw/U5AED+kOW\nCyDLBYiLO4v+/ftdk8+hb98+kOVCyHIh4uLOoU+f3lfWeBUhLu48evXqqck9e/ZQc2zsuWtyMWJj\nz1+5Qlis5m7dulaZu3btAlkugSyXIDY2Cl26hGlyWFjnKnPnzp2uXJEsRUzM+dvmTp1Cb5nT0pIx\nceKTmu2hoR1NzGWIiYlCx44dIMtltZY7dGhfp3L79u2Yq5mtrBRYWSl1ph7m+pHT0pIxYcL4OlMP\nc93KslwBPVjpctY6pEKSEH3psmbM2d6Ixwf0RJsgf52qshyCIMDOzkbNdnY2aNMmQM3OzvYYbxk6\nagAAIABJREFUMSJMzR4eznjllYfU7O3tioULn1Kzn58H1qx5Rc1BQV7YsWMeABkAcM89Xjh16hMA\nlf+DCQ52x8mTH8FgqHwoQ7NmDoiImAeDofK3zIGBIn75ZSZEsfK38v7+Ffj666kQxcrf+vv6luDz\nz5+FKMYDAHx8irBo0XiIYsyV+grw0kt9r1yhUuDhkY9XXw2HKFZepXB3z8NLLw2EKJ4CALi55eGZ\nZ3pDFCuvcjRqlINx47pCFE8AAFxcsvHII6EQxeNXvj7ZGDmyHUSx8qqJk1MWhg5tA1E8ciVnon//\nlhDFQ2ru3fseiOIfAABHx0x07x4EUTwIAHBwyEDnzv4wGCqv0tjbZ6BjR18YDPsAAEZjOtq184HB\nsFfN993nDUGIAADY2qajdWtPCMJeNbds6a5ut7FJu9JY7lFzs2aNNLlpUycIwm4AgLV1GgIDr83p\n8Pd30Gz383OAIOxSc5MmRk328fk7W1ml3pC9vW0hCDvV7OVlU2X29LSBIOxQs4eHtSa7u1tVmd3c\nrK7cmgmIYsqVvOOW2dVVvGV2dIxEo0YGzfbqZhcXg6aeO83OzkKdyk5OYK5mdnSs/P5gMDjUiXqY\n60d2dIyEo2PdqYe5bmVZbgygA+42QalHj6+69pYEF5cIk45JTMvAov/7Wc1ORjvMnDAKjka7Wq+P\nLFN0dDQAIDg4+DZ7ElUP5xaZA+cVmQPnFVVFkppAFDvW6Fjtz+8u1Tq2wd9alpCaoclNfbzYxBAR\nERER1XENvpGJT03X5ABvD50qISIiIiIiUzX4Rub6KzIB3p46VUJERERERKZq0I1MWXkFUjKzNWMB\nXrwiQ0RERERU1zXoRuZSeibka5514O7iBAeujyEiIiIiqvMadCOTcN36mECujyEiIiIisggNvJHh\n+hgiIiIiIkvERuYafGIZEREREZFlaLCNTFFpKdJy/n4BjwDA35ONDBERERGRJWiwjUxiaqYme7s1\ngq2NtU7VEBERERFRdTTYRub6hf5cH0NEREREZDkacCPD9TFERERERJaq4TYyadc/eplXZIiIiIiI\nLIVFNTJLly5FUFAQjEYjQkNDsW/fvhp9Tn5RMbLzC9UsGgxo4uFWW2USEREREZGZWUwj8/333+Pl\nl1/G22+/jRMnTqBbt24YOnQoEhMTq/1Z16+PaeLhBmsrsbZKJSIiIiIiM7OYRuaDDz7AU089hUmT\nJqFly5b4+OOP4ePjg88//7zanxXP9TFERERERBbNIhqZsrIyHD9+HIMGDdKMDxo0CAcOHKj25/GJ\nZUREREREls1K7wJMkZGRAUmS4O3trRn38vJCSkrKTY+Jjo6+6biiKIhNTtUOlhTdcn+iqzhHyFw4\nt8gcOK/IHDiv6GYUpRh5eUqNjg0ODq7xeS3iikxtyi8pRXFZuZqtDAa4OdrrWBEREREREVWXRVyR\n8fDwgCiKSE3VXklJTU2Fj4/PTY+5VXf3Z3SsJgd4e6Jlyxa1UyjVS1d/+3QnvzEguhnOLTIHzisy\nB84rqookNYEodqzRsbm5uTU+r0VckbGxsUHHjh2xdetWzfi2bdvQrVu3an1WIhf6ExERERFZPIu4\nIgMAM2bMwIQJE9C5c2d069YNX3zxBVJSUjBlypRqfQ4X+hMRERERWT6LaWTGjBmDzMxMzJs3D5cv\nX8Z9992HzZs3w9/f3+TPkBUFCWm8IkNEREREZOksppEBgOeffx7PP/98jY9Pz8lFyTUL/Y22NvBs\n5FwbpRERERER0V1kEWtkakvC9etjvDwgCIJO1RARERERUU01sEaG62OIiIiIiOqDBtXIxPOJZURE\nRERE9UKDaWQkSUZSWqZmjI0MEREREZFlajCNTEpWNsolSc1O9kY0cnTQsSIiIiIiIqqpBtPI3Oy2\nMi70JyIiIiKyTA2mkeFCfyIiIiKi+qMBNTLaKzKBXB9DRERERGSxGkQjU15RgeTMLM0Yr8gQERER\nEVmuBtHIXErPgiwranZzdoSj0U7HioiIiIiI6E40iEbmhvUxXrytjIiIiIjIkjWQRub6J5bxtjIi\nIiIiIkvWMBqZtBsfvUxERERERJar3jcyJWVlSMvKUbMAwJ+3lpGFUhQF0jUvdlUUBaWl5WqWZRmF\nhSVqliQJeXlFmpyVla/migoJGRl5mpySkq3m8vIKJCdnavKlSxmanJCQrslxcalqLisrR0xMiiZf\nvHhZk6OjkzU5KipJzaWl5Th//pImnzunzWfPJmrymTMJmnz6tDafOhWvySdPxqm5pKTstvmvv2Kr\nzJGRVecTJ2KuqzfplttLSsrw558X7ygfP167+dixC/U2FxeXMjMz3yKXlJTj1KnEGh/PXL+zXup9\nI5OYlgnlmuzl6gKjrY1u9VDVZFlGcXGpmq//QbioqBR//HFOzfn5Rdi8+aiac3IK8O23u9WcmZmH\nTz/dqOb09Fz8+9/r1Jyamo2ZM1er+fLlLEydukzNSUmZePPNtWpOTMzAo48uhKIAigIkJKRjxIh5\nUBQBiiIgLi4dgwa9eyUbEBubjp4934SiGKAoBsTEpCEs7FUoighFEXHhQho6dJiu5ujoVISETIWi\nWEGWrRAVlYYWLaZAlitzdHQGWrR4HrJsDVm2QXR0Jlq3fgmybAdZtsOFCzlo23YaZNkIWbbHxYt5\naN9+OmTZAbLsgIsX89Gp06uQZUfIsiNiYgoQFvbaleyEmJhCdO8+E7LsDFl2RlxcMXr2fOtKdkFc\nXAl6934bsuyi5r5934EsN4IsN0JcXCn6958NWXaFLLsiPr4CAwfOgSy7QZbdEB9fgUGD5l7J7oiP\nr8CQIf+ELLureejQf13JHkhIkDBs2DzIsoeaw8OvzTIeeGA+ZNkTsuyJhAQZw4cv0OQRI7R55Mj3\nIMtekGUvJCQoePDB9yFJXpAkLyQk4Lb5oYcWVpkffvhm2RuS5I2EBAGjRi1Sc2qqLaZOXXPL7QkJ\nAkaP/s8d5UceuVluDElqjIQEQ7XzmDGL621OTBTrRQZ8AfjWmXqY60dOS7PDtGnf1Zl6mOtWVhTn\nGv/sdyesdDnrXcQXYdau8vIKJCVlomlTbwBAQUEx9u8/i8GDOwCobBzWrt2LF18MB1DZGCxatB4f\nfDAJABAXl4apU5fhl1/eBSAgNjYFY8a8hyNHPoKiCIiOTkZ4+LuIivoGgAGxsckYNmwOoqP/B0UR\ncelSMsaN+whRUb8AEJCcfAlTp67E4MGPAADS0i7hnXfW4bHHJgMQkJmZiA8+2Iznn38DgIDs7ASs\nXBmBN9/8NwABubnx+P77I5g37yMAAvLz47Fp00ksWdIZgICiongcOnQJZWWdIUn3org4DkeOJEKW\newAQUFoaj1OnUqEoPQEIqKiIw4ULOVCUPgAESFIckpKKoCj9AACSFIv09DIoSn8AgKLEIDdXhqIM\nvPIVvojiYvFKFgBcgCTZARgMABCEixAEBwCDAACiGAtra2cIwgAAgJVVLIxGNwhCfzU7OXlBEPoC\nAKyt49CokQ8EoY+a3d391GxjEw8vrwAIQq8r2+Ph4xOkyb6+zSEIPa/snwA/v3sgCD3UHBjYEoLQ\nXc1BQfdCELqpuVmz1mq2tU1E8+ZtIAhd1e3Bwfep2dY2ES1atIUgdFFzy5b3a3KrVvdDEMKu5Ca4\n9952mty6dXtNbtOmAwSh85Xsg5CQjjAYKrPR2OS2+b77QqvMbdt2uknudCX74P77O6u5pCQdzZu3\nvuV2o9EH7dqF3VFu377LTXLoldy42rlDh671Ntvb+9SLnJvbHADQuHH9/Pcx65NLS9PRosV9daYe\n5rqV9SIoiqLcfjfLkJubq/7dxSUCALBy806ciP771o5Rvbugd7s2d722uqKiQkJychYCAiobutzc\nQqxf/wcmTqz8wTc1NRv//Of3+OyzKVAUID4+HY8++j7++GMJFEXExYtpGDz4dURHrwcgIi4uBf36\nTUZMzNYr+TL69ZuAmJh9AAxISEhB794PIzb2TwAGJCZeRq9ewxAXdwaAiISES+jZsz/i42OubL+E\ngQMH4vz58wCA5ORkjB07Frt3775SXypefvllrF1beZUkPT0ds2fPxtKlSwEAmZmZ+OCDD/Dvf/8b\nAJCTk4MVK1bglVdeufLvzcX//vc/TJpU2Vjl5+dj8+bNePTRRwEAhYWF2LNnD4YNGwYAKC4uxjff\nfIMOHTogNDQUJSUlOHXqFEJDr35jL0V0dDRCQkIAAGVlZUhMTETz5s2vfL0rkJqaCl9fXzXn5OTA\nw6Py9kZJklBYWAhn58rfZMiyjLKyMtjZVT4eXFEUyLIMURRr5b9/qluOHq28mnh1PhHVBs4rMgfO\nKzIX7c/vLtU6tt43MnNWfY+svAJ1fPqY4Qjy8brrtZmLoijIySmEq6sjgMorJOvW7cPTT1f+hj81\nNRvPPvsZfv75XQAGxMdno0ePlxEfvwmANS5fzkZo6BgkJR0EYIXU1Gy0azcQly+fA2CFjIxstGnT\nCWlpKRAEEVlZWRgyZAgOHz4MQRCQk5ODGTNmYOXKlQAqG4PPPvsMb775JoDKRuC3337Dww8/DAAo\nLy/H+fPn1R/8JUlCbm4u3Nzc7uaXrVr4zZvMhXOLzIHzisyB84rM5U4amXq9Ria/qFjTxBgMAnw9\n6+4PzLdy7eLtvLwivPHGV1fWaBiQkVGCZs0mQ5bdIUlNUFbmh2nTVkCSQiBJ7WE09sS2bX9BlvtA\nUQagceOH4eTkDkHoCFFsBw+PrpgwYSJE8R6IYlN4eoZg2bIvIYoeEMVG8PQMxOnTp2EwWEEQBLi7\nu+PIkSMQBAEA0KhRI7WJAQAnJye1iQEAo9GoNjEAYG1trTYxACCKYp1uYoiIiIiobqrXjUzidY9d\n9nF3hY1V3VsWdO1FsYoKCf/851ooigJFAYqKyuHhMR7l5a6QpADY2t6HJUs2ori4PRSlD1xdH4Kt\nrQMqKkJhMHSAq2tXTJr0LIAAiKIfnJ2DsHv3bhgM9jAYrGFnZ4ezZ8/CYKj8r97Ozg6LFi1Sz29t\nbY2HHnpIzQaDAd7e3nfta0FEREREZIp63chc/yLMwDqw0F9RFCQkpKvNS0lJOVxdxyI/X4QkNQbQ\nHB988CvS0oIgyz1gZzcMvr7+SE9vBlG8H7a2rfHll18CcIPB4AArK2ukpKTAxsYGgiBAEAQsWbJE\ns6YiLCxMvYJCRERERFQfNKhGRq8XYf7xxzkUFVU+UlhRDOjS5XVcvGgFSQqBtXUfNG/eArGxfjAY\nQmFldR/mz38PougDUXSFwWCH6OhoNGnSRP28J554Avb29rr8W4iIiIiI6oJ628goiqLbo5c3bTqC\npKRMKAogyzaYPv0bHDhQCEnqCKAvhg4dicREI0QxCKLohgMHDqJt27bqVZMXXnhBfaoVAF5NISIi\nIiK6Tt1bMFJLcgqKkFdUrGZrUYSPm6tZzrV2bQRatPBF+/bBUBQHrFlzBCkpTpg4cQQEwRljxjyF\n8nIviGLlVZUVK1Zojre1tTVLXURERERE9VW9bWSuvxrj6+UOUay9C1AlJWWws7OBoljj8OE0nD4t\noV27yRAEI8aOzYcoihDFyqdxTZ8+vdbOS0RERERE9bqRuX6hf+2tj1m5cjv27InCypVLIQg+eOGF\nexAdHQ2DoXLdyvDhw2vtXEREREREdKN6u0amNtfHpKfnYsmSn6Eo1pCkAAwbNgX790dDlv1gMNjh\nnnvuwdChQ++0ZCIiIiIiMlH9bWSue4dMgFf1rsjk5xep73Kxt2+MefN+QkxMUxgMbdG48b04f/48\nrK2ta7NkIiIiIiIyUb1tZIpLy9S/29lYw9PVpVrHd+/+Jg4dKoAsd4W9fX+sWLEKRqOz+gSxa9/T\nQkREREREd1e9bWSu5e/lAcNtHmH8448HsHv3KciyKyQpBGPHPoM9exIhih4QBAEjR47UvMuFiIiI\niIj0U28X+1/LlBdhnj+fif37j6F37zdhMAh4441ZfH8LEREREVEd1UAamaoX+suyG954Ywl27z6o\nNi9sYoiIiIiI6q4GcWvZrR69/NZb32D9+nMAQiGK9ujfv//dLYyIiIiIiGqk3jcyjkY7uDo53nTb\niBHD8fLLnyI/v+QuV0VERERERHei3jcyAd4emtvEiopKUV4uQZIC0bnzWJw5cwYuLtV7ohkRERER\nEemr3q+RuX59zOzZ3yEzU8B//7sOgiDCwcFBp8qIiIiIiKim6v8VmWtehKkowDvvvIvCQiukp2dU\ncRQREREREdVlDeKKzMWLl2EwiAgI6Acnp6b4/vvv9S6LiIiIiIjuQL2+IuPq6ABnByN27DiFQYPm\nIT3dyMcqExERERHVA/X6ikyAtycUxQqTJs2EnV0o18MQEREREdUT9baRSTifBod8O8hDQ2EweOCJ\nJ57QuyQiIiIiIqolFnFr2fLly9G3b180atQIBoMBCQkJtz3GwdkOXy7Zir/+usTbyYiIiIiI6hmL\naGSKi4sxZMgQzJ071+Rj3H2cEbEvAu3atTNjZUREREREpAeLuLVs2rRpAICjR4+afIxXoyZo3SrE\nXCUREREREZGOLOKKTE34e9+jdwlERERERGQmFnFFpiaEMttqXcEhuh3OJzIXzi0yB84rMgfOK6pt\nwcHBNT5Wtysyb7/9NgwGQ5V/IiIiavz5Ho5NarFaIiIiIiKqSwRFURQ9TpyZmYnMzMwq9/H394fR\naFTz0aNH0blzZ8TFxSEgIOCG/XNzc9W/Gx3sYGNlW3sFU4N19bdPoaGhOldC9Q3nFpkD5xWZA+cV\nmcu1P7+7uLhU61jdbi1zd3eHu7u72T6fTQwRERERUf1lEWtkUlJSkJKSgqioKADA6dOnkZWVhcDA\nQLi6uupcHRERERER3W0W8dSyL774Ah06dMD48eMhCALCw8PRsWNH/Prrr3qXRkREREREOrCIRmbO\nnDmQZRmyLEOSJPU/n3jiCb1LIyIiIiIiHVhEI0NERERERHQtNjJERERERGRx2MgQEREREZHFYSND\nREREREQWh40MERERERFZHDYyRERERERkcdjIEBERERGRxWEjQ0REREREFoeNDBERERERWRw2MkRE\nREREZHHYyBARERERkcVhI0NERERERBaHjQwREREREVkcNjJERERERGRx2MgQEREREZHFYSNDRERE\nREQWh40MERERERFZHDYyRERERERkcdjIEBERERGRxWEjQ0REREREFoeNDBERERERWRw2MkRERERE\nZHHYyBARERERkcVhI0NERERERBaHjQwREREREVkcNjJERERERGRx2MgQEREREZHFYSNDREREREQW\nh40MERERERFZHDYyRERERERkcdjIEBERERGRxWEjQ0REREREFoeNDBERERERWRw2MkREREREZHHY\nyBARERERkcVhI0NERERERBaHjQwREREREVkcNjJERERERGRx2MgQEREREZHFYSNDREREREQWp843\nMtnZ2Zg6dSruvfde2NvbIyAgAC+88AKysrL0Lo2IiIiIiHRS5xuZ5ORkJCcnY9GiRTh16hTWrFmD\niIgIPP7443qXRkREREREOrHSu4DbadOmDX788Uc1N2vWDIsWLcIDDzyAgoICODo66lgdERERERHp\noc5fkbmZ3Nxc2Nrawt7eXu9SiIiIiIhIB4KiKIreRVRHTk4OOnXqhPDwcCxZskSzLTc3V6eqiIiI\niIjoTri4uFRrf92uyLz99tswGAxV/omIiNAcU1BQgOHDh8Pf3x8LFy7UqXIiIiIiItKbbldkMjMz\nkZmZWeU+/v7+MBqNACqbmGHDhkEQBPz22283va2MV2SIiIiIiCxTda/IWMStZfn5+Rg6dCgEQcCW\nLVvg4OCgd0lERERERKSjOt/I5OfnY9CgQcjPz8eGDRs0Tylzd3eHtbW1jtUREREREZEe6nwjs3v3\nbvTr1w+CIODaUgVBwK5du9CrVy8dqyMiIiIiIj3U+UaGiIiIiIjoehb5HplbWbp0KYKCgmA0GhEa\nGop9+/bpXRJZkIiICIwYMQJ+fn4wGAxYvXr1DfvMmTMHvr6+sLe3R9++fXHmzBkdKiVLsmDBAnTq\n1AkuLi7w8vLCiBEjcPr06Rv249yi6vjss89w//33w8XFBS4uLujWrRs2b96s2Ydziu7UggULYDAY\nMHXqVM045xZV15w5c254OnGTJk1u2Ke686reNDLff/89Xn75Zbz99ts4ceIEunXrhqFDhyIxMVHv\n0shCFBYWom3btvjoo49gNBohCIJm+/vvv48PPvgAn376KY4cOQIvLy8MHDgQBQUFOlVMlmDPnj14\n6aWXcPDgQezcuRNWVlYYMGAAsrOz1X04t6i6rr6G4M8//8SxY8fQr18/PPjgg4iMjATAOUV37o8/\n/sCXX36Jtm3bav7/kHOLaqpVq1ZISUlR/5w8eVLdVuN5pdQTnTt3ViZPnqwZCw4OVmbOnKlTRWTJ\nHB0dldWrV6tZlmWlcePGyvz589Wx4uJixcnJSVm2bJkeJZKFKigoUERRVDZu3KgoCucW1R43Nzdl\n+fLlnFN0x3JycpTmzZsru3fvVvr06aNMnTpVURR+v6Kamz17thISEnLTbXcyr+rFFZmysjIcP34c\ngwYN0owPGjQIBw4c0Kkqqk9iY2ORmpqqmWN2dnbo1asX5xhVS15eHmRZhqurKwDOLbpzkiRh7dq1\nKCkpQa9evTin6I5NnjwZjzzyCHr37q150BLnFt2JmJgY+Pr6olmzZnj88ccRGxsL4M7mlZVZK75L\nMjIyIEkSvL29NeNeXl5ISUnRqSqqT67Oo5vNseTkZD1KIgs1bdo0tG/fHl27dgXAuUU1d/LkSXTt\n2hWlpaUwGo1Yt24dWrZsqf4fP+cU1cSXX36JmJgYfPfddwCgua2M36+oprp06YLVq1ejVatWSE1N\nxbx589CtWzecPn36juZVvWhkiPR0/VoaoluZMWMGDhw4gH379pk0bzi3qCqtWrXCX3/9hdzcXPzw\nww947LHHsGvXriqP4Zyiqpw/fx5vvfUW9u3bB1EUAQCKomiuytwK5xZVZciQIerfQ0JC0LVrVwQF\nBWH16tUICwu75XG3m1f14tYyDw8PiKKI1NRUzXhqaip8fHx0qorqk8aNGwPATefY1W1EVZk+fTq+\n//577Ny5E02bNlXHObeopqytrdGsWTO0b98e8+fPR5cuXfDZZ5+p/7/HOUXVdfDgQWRkZKBNmzaw\ntraGtbU1IiIisHTpUtjY2MDDwwMA5xbdOXt7e7Rp0wYXLly4o+9Z9aKRsbGxQceOHbF161bN+LZt\n29CtWzedqqL6JCgoCI0bN9bMsZKSEuzbt49zjG5r2rRpahPTokULzTbOLaotkiRBlmXOKaqxhx56\nCKdOnUJkZCQiIyNx4sQJhIaG4vHHH8eJEycQHBzMuUW1oqSkBGfPnoWPj88dfc8S58yZM8fMtd4V\nzs7OmD17Npo0aQKj0Yh58+Zh3759WLVqFVxcXPQujyxAYWEhzpw5g5SUFKxYsQL33XcfXFxcUF5e\nDhcXF0iShPfeew8tW7aEJEmYMWMGUlNTsXz5ctjY2OhdPtVRL774Ir7++mv88MMP8PPzQ0FBAQoK\nCiAIAmxsbCAIAucWVdubb74JOzs7yLKMxMRELFmyBN999x0WLlyI5s2bc05RjdjZ2cHT01P94+Xl\nhW+//RaBgYF48skn+f2KauzVV19Vv2dFRUXhpZdeQkxMDJYtW3ZnP2PV3oPV9Ld06VKladOmiq2t\nrRIaGqrs3btX75LIguzatUsRBEERBEExGAzq35966il1nzlz5ig+Pj6KnZ2d0qdPH+X06dM6VkyW\n4Pr5dPXP3LlzNftxblF1TJw4UQkMDFRsbW0VLy8vZeDAgcrWrVs1+3BOUW249vHLV3FuUXU99thj\nSpMmTRQbGxvF19dXGT16tHL27FnNPjWZV4KimLCCi4iIiIiIqA6pF2tkiIiIiIioYWEjQ0RERERE\nFoeNDBERERERWRw2MkREREREZHHYyBARERERkcVhI0NERERERBaHjQwREREREVkcNjJERFSlPn36\noG/fvnqXcYOkpCQYjUbs2rVLtxo+++wzBAYGoqysTLcaiIgaKjYyRESEAwcOYO7cucjNzb1hmyAI\nEARBh6qqNnfuXLRr107XJmvSpEkoLS3FsmXLdKuBiKihYiNDRERVNjLbtm3D1q1bdajq1tLT07F6\n9WpMmTJF1zrs7Ozw5JNPYvHixVAURddaiIgaGjYyRESkutkP41ZWVrCystKhmltbs2YNAOChhx7S\nuRLg0UcfRUJCAnbu3Kl3KUREDQobGSKiBm7OnDl4/fXXAQBBQUEwGAwwGAyIiIgAcOMambi4OBgM\nBrz//vtYunQpmjVrBgcHBwwYMAAJCQmQZRn/+te/4OfnB3t7e4wcORKZmZk3nHfr1q3o3bs3nJyc\n4OTkhKFDhyIyMtKkmjds2IBOnTrB2dlZM56amopnnnkG/v7+sLOzQ+PGjTFs2DCcOXOmRueOiorC\n448/Di8vLxiNRrRo0QLTp0/X7NOhQwe4ublh/fr1JtVORES1o279io2IiO66UaNGITo6Gv/3f/+H\nJUuWwMPDAwBw7733qvvcbI3M2rVrUVpain/84x/IysrCwoUL8cgjj6BPnz7Yu3cvZs6ciQsXLuDj\njz/GjBkzsHr1avXY7777DhMmTMCgQYPw3nvvoaSkBMuXL0fPnj1x5MgRtGzZ8pb1lpeX48iRI5g8\nefIN20aPHo1Tp05h6tSpCAoKQlpaGiIiIhAdHY3WrVtX69ynT59G9+7dYWVlhcmTJ6NZs2aIjY3F\nunXr8OGHH2rO26FDB+zfv78aX3UiIrpjChERNXiLFi1SBEFQ4uPjb9jWu3dvpW/fvmqOjY1VBEFQ\nPD09ldzcXHV81qxZiiAIyn333adUVFSo42PHjlVsbGyUkpISRVEUpaCgQHF1dVUmTZpVbc//AAAE\nFElEQVSkOU92drbi5eWljB07tspaL1y4oAiCoHz00Uc3HC8IgrJ48eJbHludc/fu3VtxcnJS4uLi\nqqxHURRl8uTJiq2t7W33IyKi2sNby4iIqEZGjRqlubWrc+fOAIDx48dDFEXNeHl5ORITEwFUPjwg\nJycHjz/+ODIyMtQ/FRUV6NGjx20fp3z1NjVXV1fNuNFohI2NDXbt2oXs7OybHmvqudPT0xEREYGJ\nEyciMDDwtl8LV1dXlJWVoaCg4Lb7EhFR7eCtZUREVCMBAQGa7OLiAgDw9/e/6fjV5iIqKgoAMHDg\nwJt+7rVNUFWU6x5MYGtri/fffx+vvvoqvL29ERYWhmHDhmHChAnw8/Or1rljYmIAACEhIdWqpS4+\nppqIqL5iI0NERDVyq4bjVuNXf9iXZRkAsHr1avj6+lb7vFfX8Nzsqsu0adMwcuRI/Pzzz9i2bRv+\n9a9/Yf78+di4cSN69+59x+e+lezsbNja2sLBwaHWPpOIiKrGRoaIiO7qlYTmzZsDqGxI+vXrV+3j\nAwICYG9vj9jY2Jtub9q0KaZNm4Zp06YhKSkJ7dq1w7///W/07t3b5HNf3e/kyZMm1RQbG6t5OAIR\nEZkf18gQEZF6JSErK8vs5xoyZAgaNWqE+fPno7y8/IbtGRkZVR5vZWWFsLAwHDlyRDNeXFyM4uJi\nzZivry88PT3VF30OHjy4ynOnp6cDqGx0evfuja+++gpxcXGafa6/pQ0Ajh8/jm7dulVZNxER1S5e\nkSEiInTq1AkAMHPmTDz++OOwsbFB//794enpCeDmP7zXlJOTE7744guMGzcO7du3V9/TkpCQgC1b\ntiAkJASrVq2q8jNGjhyJ1157Dbm5ueoanPPnz6Nfv34YM2YMWrduDVtbW2zevBnnzp3D4sWLAQDO\nzs4mn/uTTz5Bjx490LFjRzz33HMICgpCQkICvv/+e3WtDQAcO3YM2dnZePDBB2vta0RERLfHRoaI\niNCxY0csWLAAS5cuxdNPPw1FUbBr1y54enpCEASTbz271X7Xj48ZMwZNmjTB/PnzsXjxYpSUlMDX\n1xfdu3fHlClTbnuecePG4fXXX8f69esxceJEAJW3nI0fPx47duzAd999B0EQ0LJlS6xcuVLdpzrn\nDgkJwR9//IF33nkHy5YtQ3FxMQICAjBixAhNLevWrUNAQAAGDBhg0teIiIhqh6DU5q/ZiIiI7pIp\nU6YgMjISBw8e1K2GkpISNG3aFLNmzcI//vEP3eogImqIuEaGiIgs0rvvvovIyMjbvnfGnFasWAE7\nOzs8//zzutVARNRQ8YoMERER/X97dkACAAAAIOj/63YE+iIC2HFkAACAHSEDAADsCBkAAGBHyAAA\nADtCBgAA2BEyAADAjpABAAB2AkogIQPIN5uXAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c48550>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the filter diverges almost immediately. After the first second the residual exceeds the bounds of three standard deviations. It is important to understand that the covariance matrix $\\mathbf{P}$ is only reporting the *theoretical* performance of the filter *assuming* all of the inputs are correct. In other words, this Kalman filter is diverging, but $\\mathbf{P}$ implies that the Kalman filter's estimates are getting better and better with time because the variance is getting smaller. The filter has no way to know that you are lying to it about the system.\n",
      "\n",
      "In this system the divergence is immediate and striking. In many systems it will only be gradual, and/or slight. It is important to look at charts like these for your systems to ensure that the performance of the filter is within the bounds of its theoretical performance."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try a third order system. This might strike you as a good thing to do. After all, we know there is a bit of noise in the movement of the simulated object, which implies there is some acceleration. Why not model the acceleration with a second order model. If there is no acceleration, the acceleration should just be estimated to be 0. But is that what happens? Think about it before going on."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf2 = SecondOrderKF(R, Q, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs)\n",
      "\n",
      "plot_kf_output(xs, fxs2, zs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QUEaNGoWjoyOff/45bdu2Zc2aNYSHh9uM0aNHD6pVq8aECRP47rvvePvtt/Hx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       "text": [
        "<matplotlib.figure.Figure at 0x7fe1589ed668>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Did this perform as you expected? We can see that even though the system does have a slight amount of acceleration in it the seond order filter performs poorly compared to the first order filter. Why does this? The system believes that there is acceleration in the system, and so the large changes in the measurement gets interpreted as acceleration instead of noise. Thus you can see that the filter tracks the noise in the system quite closely. Not only that, but it *overshoots* the noise in places if the noise is consistantly above or below the track because the filter incorrectly assumes an acceleration that does not exist, and so it's prediction goes further and further away from the track on each measurement. This is not a good state of affairs.\n",
      "\n",
      "Still, the track doesn't look *horrible*. Let's see the story that the residuals tell. I will add a wrinkle here. The residuals for the order 2 system do not look terrible in that they do not diverge or exceed three standard deviations. However, it is very telling to look at the residuals for the first order vs the second order filter, so I have plotted both on the same graph."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res = xs[:,0] - fxs2[:,0]\n",
      "res1 = xs[:,0] - fxs1[:,0]\n",
      "\n",
      "plt.plot(res1, ls=\"--\", label='order 1')\n",
      "plt.plot(res, label='order 2')\n",
      "bp.plot_residual_limits(ps2[:,0])\n",
      "plt.title('Second Order Position Residuals')\n",
      "plt.legend()\n",
      "plt.ylabel('meters')\n",
      "plt.xlabel('time (sec)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sCACYOnUqunTpgrlz5+LSpUui+nK5HCdOnADPVw7uev/99+Ho6IizZ8+qe4UG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\nw8Ph7u6Ol19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       "text": [
        "<matplotlib.figure.Figure at 0x7fe1589a3390>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the residuals for the second order filter fall nicely within the theoretical limits of the filter. When we compare them against the first order residuals we may conclude that the second order is slight worse, but the difference is not large. There is nothing very alarming here.\n",
      "\n",
      "Now let's look at the residuals for the velocity."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res = xs[:,1] - fxs2[:,1]\n",
      "res1 = xs[:,1] - fxs1[:,1]\n",
      "plt.plot(res, label='order 2')\n",
      "plt.plot(res1, ls='--', label='order 1')\n",
      "bp.plot_residual_limits(ps2[:,1])\n",
      "plt.title('Second Order Velocity Residuals')\n",
      "plt.legend()\n",
      "plt.ylabel('meters/sec')\n",
      "plt.xlabel('time (sec)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PnorkBwBatGiBNm3a4Pz585V9S6oNe4CIiIiI6L43+9PRVr3+v1/aWG3XOn/+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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165a123c8>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the story is very different. While the residuals of the second order system fall within the theoretical bounds of the filter's performance, we can see that the residuals are *far* worse than for the first order filter. This is the usual result this scenerio. The filter is assuming that there is acceleration that does not exist. It mistakes noise in the measurement as acceleration and this gets added into the velocity estimate on every predict cycle. Of course the acceleration is not actually there and so the residual for the velocity is much larger than it optimum."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have one more trick up my sleeve. We have a first order system; i.e. the velocity is more-or-less constant. Real world systems are never perfect, so of course the velocity is never exactly the same between time periods. When we use a first order filter we account for that slight variation in velocity with the *process noise*. The matrix $\\mathbf{Q}$ is computed to account for this slight variation. If we move to a second order filter we are now accounting for the changes in velocity. Perhaps now we have no process noise, and we can set $\\mathbf{Q}$ to zero! "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf2 = SecondOrderKF(R, 0, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs)\n",
      "\n",
      "plot_kf_output(xs, fxs2, zs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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94ORJ+PxzrnbvzI+b57Nh968YGFw6m0xUxFEORp4kKzMbgOCQarz84isMGjTI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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1589e08d0>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To my eye that looks quite good! The filter quickly converges to the actual track. Success!\n",
      "\n",
      "Or, maybe not. Setting the process noise to 0 tells the filter that the process model is perfect. I've yet to hear of a perfect physical system. Let's look at the performance of the filter over a longer period of time.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(25944)\n",
      "xs500, zs500 = simulate_system(Q=Q, count=500)\n",
      "\n",
      "kf2 = SecondOrderKF(R, 0, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs500)\n",
      "\n",
      "plot_kf_output(xs500, fxs2, zs500)\n",
      "plot_residuals(xs500[:,0], fxs2[:,0], ps2[:,0], \n",
      "               'Zero Order Position Residuals',\n",
      "               'meters') "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9//7pZ8+eTbVq1bL/HYqqK1eu4Orqausy8sXt/H8gIiJS2I4fP878jz7i4xUr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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1659095c0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5uXrSgv79+2ts13ZjeMXzp6ena31MbfGKY958882HnqubN2/WKIfaVJFbdYvCajvvlpaW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\nh/Ycr+TYt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MePH9fq1at19913Kzk5+aL/LSIjI3X27FlVVFRc9FgAQMtgCRwAoEV16dLF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\n7QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165a081d0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the performance of the filter is abysmal. We can see that in the track plot where the filter diverges from the track for an extended period of time. The divergence may or may not seem large to you. The residual plot makes the problem more apparent. Just before the 100th update the filter diverges sharply from the theoretical performance. It *might* be converging at the end, but I doubt it.\n",
      "\n",
      "Why is this happening? Recall that if we set the process noise to zero we are telling the filter to use only the process model. The measurements end up getting ignored. The pysical system is *not* perfect, and so the filter is unable to adapt to this nonperfect behavior. \n",
      "\n",
      "Maybe just a really low process noise? Let's try that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(32594)\n",
      "xs2000, zs2000 = simulate_system(Q=0.0001, count=2000)\n",
      "\n",
      "kf2 = SecondOrderKF(R, 0, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs2000)\n",
      "\n",
      "plot_kf_output(xs2000, fxs2, zs2000)\n",
      "plot_residuals(xs2000[:,0], fxs2[:,0], ps2[:,0], \n",
      "               'Seceond Order Position Residuals',\n",
      "               'meters') "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mp4qS1HrasyTVtG7dmtDQUBYsWMAtt9wCQGJiIkePHmXSpEn897//rTb/wQcf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\nFAZ1UVl5AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe158975748>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UimI3fZQkCZmZmQCgLsqgbz2LtuTkZADA/v37sX//foPXzsrKUj9OS0uDs7OzznoLFU9P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dKuk1SNsVKB3rCv2Y/GwkZZtzNJPTu2xYWr15GedQvRoSFVKnaQl6eGSqXQlmD+8cejCA8Pho9P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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1658ae940>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, the residual plot tells the story. The track looks very good, but the residual plot shows that the filter is diverging for significant periods of time.\n",
      "\n",
      "How should you think about all of this? You might argue that the last plot is 'good enough' for your application, and perhaps it is. I warn you however that a diverging filter doesn't always converge. With a different data set, or a physical system that performs differently you can end up with a filter that never converges. \n",
      "\n",
      "Also, let's think about this in a data fitting sense. Suppose I give you two points, and tell you to fit a straight line to the points. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter([1,2], [1,1],s=100,c='r')\n",
      "plt.plot([0,3], [1,1])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2p59+av/lL3+xT58+bc+YMcMODg62CwsLA3EKP3i7d++2g4OD7a1b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\nEFexpgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c316a0>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is only one possible answer, to draw a line between the two points. Furthermore, the answer is optimal. If I gave you more points you could use a least squares fit to find the best line, and the answer would still be optimal (in a least squares sense).\n",
      "\n",
      "But suppose I told you to fit a higher order polynomial to those two points. There is now an infinite number of answers to the problem. For example, for a second order system any parabola that passes through those two points would 'fit' the data, and there are an infinite number of parabolas that do that. When the Kalman filter is of higher order than your physical process it also has an infinite number of solutions to choose from. The answer is not just non-optimal, it often diverges and never reacquires the signal. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So this is the story of Godilocks. You don't want a filter too big, or too small, but one that is just right. In many cases that will be easy to do - if you are designing a Kalman filter to read the thermometer of a freezer it seems clear that a zero order filter is the right choice. But what order should we use if we are tracking a car? Order one will work well while the car is moving in a straight line at a constant speed, but cars turn, speed up, and slow down, in which case a second order filter will perform better. That is the problem addressed in the Adaptive Filters chapter. There we will learn how to design a filter that *adapts* to changing order in the tracked object's behavior.\n",
      "\n",
      "With that said, a lower order filter can track a higher order process so long as you add enough process noise. The results will not be optimal, but they can still be very good, and I always reach for this tool first before trying an adaptive filter. Let's look at an example with acceleration. First, the simulation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class ConstantAccelerationObject(object):\n",
      "    def __init__(self, x0=0, vel=1., acc=0.1, acc_noise_scale=.1):\n",
      "        self.x = x0\n",
      "        self.vel = vel\n",
      "        self.acc = acc\n",
      "        self.acc_noise_scale = acc_noise_scale\n",
      "    \n",
      "    def update(self):\n",
      "        self.acc += randn()*self.acc_noise_scale       \n",
      "        self.vel += self.acc\n",
      "        self.x += self.vel\n",
      "        return (self.x, self.vel, self.acc)\n",
      "\n",
      "   \n",
      "R = 6.\n",
      "Q = 0.02\n",
      "def simulate_acc_system(R, Q, count):\n",
      "    obj = ConstantAccelerationObject(acc_noise_scale=Q)\n",
      "    zs = []\n",
      "    xs = []\n",
      "    for i in range(count):\n",
      "        x = obj.update()\n",
      "        z = sense(x, R)\n",
      "        xs.append(x)\n",
      "        zs.append(z)\n",
      "    return np.asarray(xs), zs\n",
      "\n",
      "np.random.seed(124)\n",
      "xs,zs = simulate_acc_system(R=R, Q=Q, count=80)\n",
      "plt.plot(xs[:,0])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IIgAAAMB1sNltWrDmDZ3MOmyoR4X217DbHzGpq4aDIAIAAABUk8Ph0Efr39G+E9sN9W7t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\nnPe+AWmSyG4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c862b0>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we will filter the data using a second order filter. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf2 = SecondOrderKF(R, Q, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs)\n",
      "\n",
      "plot_kf_output(xs, fxs2, zs)\n",
      "plot_residuals(xs[:,0], fxs2[:,0], ps2[:,0], \n",
      "               'Second Order Position Residuals',\n",
      "               'meters') "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6pUqVwmw263eLg23ZsoWRI0dy5coVR4eSLkpiREQecYZhsGD1VCLPH7Urb1Sl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\n0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++OEydO4LPPPsPGjRtRXFwMZ2dnjBgxQqMvu3fvhrOzM4YMGfJUMSIiIu2QCG3+iY2I\niKgJTJs2DcnJyTh+/Hiz9aGkpASurq6YP38+Zs2a1Wz9ICLSR1wTQ0RELc7f//53JCcnP3FfGV36\n7rvvYGJigvfff7/Z+kBEpK84EkNERERERC0KR2KIiIiIiKhFYRJDREREREQtCpMYIiIiIiJqUZjE\nEBERERFRi8IkhoiIiIiIWhQmMURERERE1KIwiSEiIiIiohbl/wPRU63n5gUuXQAAAABJRU5ErkJg\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe158975080>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cRQ6CGSIiIiLSkoQXzS6eNWsWXnvtNfj4+MBsNmP27Nn45z//aXu8sLDQ9u8z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\nCUgUzBBCCCGEEEIC0v8HZoC7p7Jzed4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe16595b048>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the filter is perfoming within the theoretical limits of the filter. \n",
      "\n",
      "Now let's use a lower order filter. As already demonstrated the lower order filter will lag the signal because it is not modelling the acceleration. However, we can account for that (to an extent) by increasing the size of the process noise. The filter will treat the acceration as noise in the process model. The result will be suboptimal, but if designed well it will not diverge. Choosing the amount of extra process noise is not an exact science. You will have to experiment with representative data. Here, I've multiplied it by 10, and am getting good results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf2 = FirstOrderKF(R, Q*10, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs)\n",
      "\n",
      "plot_kf_output(xs, fxs2, zs)\n",
      "plot_residuals(xs[:,0], fxs2[:,0], ps2[:,0], \n",
      "               'Second Order Position Residuals',\n",
      "               'meters') "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KCmLcuHGOClFEsjF3d3cWLFiQonzLli0cOXIENzc3TCaTAyKTG5TEiIhIthId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\nERERERF1KP8PMFEsYdLOHtcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c7ada0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nXH/99fj222+DPDJqy0y1RtU+ppkRERERhYawSTMbPXo0Nm7ciMOHDwMADhw4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LNuRtBjJhmZCZ1ga2a8ebKDufgTdGRGIpLEGWmphK6/neOCqhkCpHsOpAydyhdInxmLzYZ+qvif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\nREREFJP+P8ySpCDdbcGOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1589b7c50>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Think about what will happen if you make the process noise many times larger than it needs to be. A large process noise tells the filter to favor the measurements, so we would expect the filter to closely mimic the noise in the measurements. Let's find out."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf2 = FirstOrderKF(R, Q*10000, dt=1)\n",
      "fxs2, ps2 = filter_data(kf2, zs)\n",
      "\n",
      "plot_kf_output(xs, fxs2, zs)\n",
      "plot_residuals(xs[:,0], fxs2[:,0], ps2[:,0], \n",
      "               'Second Order Position Residuals',\n",
      "               'meters') "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uvvs8iIiIFDb9thERkes6n3IWj5gjAByr7IvZ3Y0qQTVIS0tjwIABAIwbN46I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\nEV1XmMQQEREREdF15f8DDiWcttnDkGoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15899b9e8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7drwOwMwOERERkR4GO0Rd1NR2TLXcZmuO22vZdJoTAICdDQqIiIiINBjsEHVR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wAAAg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\nIiIiIiJKSv8fSxmu2CCEF1gAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15899b9b0>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Sensor Fusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Early in the g-h filter chapter we discussed designing a filter for two scales, one that was accurate and one that was very inaccurate. We determined that we should always include the information from the inaccurate filter - we should never discard any information that is available to us. If you do not recall this discussion, consider this edge case. You have two scales, one accurate to 1 lb, the second to 10 lbs. You way yourself on each scale, and the first reads 170 lbs, and the second reads 181. If we only used the data from the first scale we would only know that our weight is in the range of 169 to 171 lbs. However, when we incorporate the measurement from the second scale we can decide that the correct weight can only be 171 lbs, since 171 lbs is exactly at the outside range of the second measurement, which would be 171 to 191 lbs. Of course most measurements don't offer such a exact answer, but the principle applies to any measurement.\n",
      "\n",
      "So consider a situation where we have two sensors measuring the same value at each time. How shall we incorporate that into our Kalman filter? \n",
      "\n",
      "Suppose we have a train or cart on a railway. It has a sensor attached to the wheels counting revolutions, which can be converted to a distance along the track. Then, suppose we have a GPS-like sensor which I'll call a 'PS' mounted to the train which reports position. Thus, we have two measurements, both reporting position along the track. Suppose further that the accuracy of the wheel sensor is 1m, and the accuracy of the PS is 10m. How do we combine these two measurements into one filter? This may seem quite contrived, but aircraft use sensor fusion to fuse the measurements from sensors such as a GPS, INS, doppler radar, VOR, the airspeed indicator, and more.\n",
      "\n",
      "Kalman filters for inertial filters are very difficult, but fusing data from two or more sensors providing measurements of the same state variable (such as position) is actually quite easy. The relevant matrix is the measurement matrix $\\mathbf{H}$. Recall that this matrix tells us how to convert from the Kalman filter's state $\\mathbf{X}$ to a measurement ${Z}$. Suppose that we decide that our Kalman filter state should contain the position and velocity of the train, so that\n",
      "\n",
      "$$ \\mathbf{X} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "We have two measurements for position, so we will define the measurement vector to be a vector of the measurements from the wheel and the PS.\n",
      "\n",
      "$$ \\mathbf{Z} = \\begin{bmatrix}x_{wheel} \\\\ x_{ps}\\end{bmatrix}$$\n",
      "\n",
      "So we have to design the matrix $\\mathbf{H}$ to convert $\\mathbf{X}$ to $\\mathbf{Z}$ . They are both positions, so the conversion is nothing more than multiplying by one:\n",
      "\n",
      "$$ \\begin{bmatrix}x_{wheel} \\\\ x_{ps}\\end{bmatrix} = \\begin{bmatrix}1 &0 \\\\ 1& 0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "To make it clearer, suppose that the wheel reports not position but the number of rotations of the wheels, where 1 revolution yields 2m of travel. In that case we would write\n",
      "\n",
      "$$ \\begin{bmatrix}x_{wheel} \\\\ x_{ps}\\end{bmatrix} = \\begin{bmatrix}0.5 &0 \\\\ 1& 0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "Now we have to design the measurement noise matrix $\\mathbf{R}$. Suppose that the measurement variance for the PS is twice the variance of the wheel, and the standard deviation of the wheel is 1.5m. That gives us\n",
      "\n",
      "$$\\sigma_{wheel} =  1.5\\\\\n",
      "\\sigma^2_{wheel} = 2.25 \\\\ \n",
      "\\sigma_{ps} = 1.5*2 = 3 \\\\\n",
      "\\sigma^2_{ps} = 9.\n",
      "$$\n",
      "\n",
      "That is pretty much our Kalman filter design. We need to design for Q, but that is invariant to whether we are doing sensor fusion or not, so I will just choose some arbitrary value for Q.\n",
      "\n",
      "So let's run a simulation of this design. I will assume a velocity of 10m/s with an update rate of 0.1 seconds."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "from numpy.random import randn\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from filterpy.kalman import KalmanFilter\n",
      "from numpy import array, asarray\n",
      "\n",
      "def fusion_test(wheel_sigma, ps_sigma, do_plot=True):\n",
      "    dt = 0.1\n",
      "    kf = KalmanFilter(dim_x=2, dim_z=2)\n",
      "\n",
      "    kf.F = array([[1., dt], [0., 1.]])\n",
      "    kf.H = array([[1., 0.], [1., 0.]])\n",
      "    kf.x = array([[0.], [1.]])\n",
      "    kf.Q *= array([[(dt**3)/3, (dt**2)/2],\n",
      "                   [(dt**2)/2,  dt      ]]) * 0.02\n",
      "    kf.P *= 100\n",
      "    kf.R[0,0] = wheel_sigma**2\n",
      "    kf.R[1,1] = ps_sigma**2 \n",
      "\n",
      "    random.seed(1123)\n",
      "    xs = []\n",
      "    zs = []\n",
      "    nom = []\n",
      "    for i in range(1, 100):\n",
      "        m0 = i + randn()*wheel_sigma\n",
      "        m1 = i + randn()*ps_sigma\n",
      "        z = array([[m0], [m1]])\n",
      "\n",
      "        kf.predict()\n",
      "        kf.update(z)\n",
      "\n",
      "        xs.append(kf.x.T[0])\n",
      "        zs.append(z.T[0])\n",
      "        nom.append(i)\n",
      "\n",
      "    xs = asarray(xs)\n",
      "    zs = asarray(zs)\n",
      "    nom = asarray(nom)\n",
      "\n",
      "\n",
      "    res = nom-xs[:,0]\n",
      "    print('fusion std: {:.3f}'.format (np.std(res)))\n",
      "    if do_plot:\n",
      "        bp.plot_measurements(zs[:,0], label='Wheel')\n",
      "        plt.plot(zs[:,1], linestyle='--', label='Pos Sensor')\n",
      "        bp.plot_filter(xs[:,0], label='Kalman filter')\n",
      "        plt.legend(loc=4)\n",
      "        plt.ylim(0,100)\n",
      "        plt.show()\n",
      "\n",
      "fusion_test(1.5, 3.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fusion std: 0.391\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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x4sXp06cP77333rWaAQMGcOXKFfr27cv58+dp2LAh0dHReHt75/bwIiIiIneV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n5+fsyZM4egoKAitVlVZ6ZBfX98vVrQoFZTqjs4F1NvhRBCCCGEEEVRKonGmjVrGDt2LAsXLiQo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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1659e25f8>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see the result of the Kalman filter in blue.\n",
      "\n",
      "It may be somewhat difficult to understand the previous example at an intuitive level. Let's look at a different problem. Suppose we are tracking an object in 2D space, and have two radar systems at different positions. Each radar system gives us a range and bearing to the target. How do the readings from each data affect the results?\n",
      "\n",
      "This is a nonlinear problem because we need to use a trigonometry  to compute coordinates from a range and bearing, and we have not yet learned how to solve nonlinear problems with Kalman filters. So for this problem ignore the code that I used and just concentrate on the charts that the code outputs. We will revisit this problem in subsequent chapters and learn how to write this code.\n",
      "\n",
      "I will position the target at (100,100). The first radar will be at (50,50), and the second radar at (150, 50). This will cause the first radar to measure a bearing of 45 degrees, and the second will report 135 dgrees.\n",
      "\n",
      "I will create the Kalman filter first, and then plot its initial covariance matrix. I am using what is called an Unscented Kalman filter, which is the subject of a later chapter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import  UnscentedKalmanFilter as UKF\n",
      "\n",
      "def hx(x):\n",
      "    \"\"\" compute measurements corresponding to state x\"\"\"\n",
      "    dx = x[0] - hx.radar_pos[0]\n",
      "    dy = x[1] - hx.radar_pos[1]    \n",
      "    return np.array([atan2(dy,dx), (dx**2 + dy**2)**.5])\n",
      "    \n",
      "def fx(x,dt):\n",
      "    \"\"\" predict state x at 'dt' time in the future\"\"\"\n",
      "    return x\n",
      "\n",
      "# create unscented Kalman filter with large initial uncertainty\n",
      "kf = UKF(2, 2, dt=0.1, hx=hx, fx=fx, kappa=2.)\n",
      "kf.x = np.array([100, 100.])\n",
      "kf.P *= 40\n",
      "\n",
      "x0 = kf.x.copy()\n",
      "p0 = kf.P.copy()\n",
      "\n",
      "stats.plot_covariance_ellipse(\n",
      "       x0, cov=p0,\n",
      "       facecolor='y', edgecolor=None, alpha=0.6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9/f3j1xUKBT399NO6+uqrx68bGhrSzTffrCRJ9I//+I/MZgANZuwkfUFwRGH4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\n8+aFrfH5fDp79ix5jLCbfa38/vvvFQwGyeMcQP5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       "text": [
        "<matplotlib.figure.Figure at 0x7fe165bfa470>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We are equally uncertain about the position in x and y, so the covariance is circular.\n",
      "\n",
      "Now we will update the Kalman filter with a reading from the first radar. I will set the standard deviation of the bearing error at 0.5$^\\circ$, and the standard deviation of the distance error at 3."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import radians, atan2\n",
      "\n",
      "# set the error of the radar's bearing and distance\n",
      "kf.R[0,0] = radians (.5)**2\n",
      "kf.R[1,1] = 3.**2\n",
      "\n",
      "# compute position and covariance from first radar station\n",
      "hx.radar_pos = (50, 50)\n",
      "dist = (50**2 + 50**2) ** 0.5\n",
      "kf.predict()\n",
      "kf.update([radians(45), dist])\n",
      "\n",
      "\n",
      "# plot the results\n",
      "x1 = kf.x.copy()\n",
      "p1 = kf.P.copy()\n",
      "\n",
      "stats.plot_covariance_ellipse(\n",
      "       x0, cov=p0,\n",
      "       facecolor='y', edgecolor=None, alpha=0.6)\n",
      "\n",
      "stats.plot_covariance_ellipse(\n",
      "       x1, cov=p1,\n",
      "       facecolor='g', edgecolor='k', alpha=0.6)\n",
      "\n",
      "plt.scatter([100], [100], c='y', label='Initial')\n",
      "plt.scatter([100], [100], c='g', label='1st station')\n",
      "plt.legend(scatterpoints=1, markerscale=3)\n",
      "plt.plot([92,100],[92,100], c='g', lw=2, ls='--')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VlJeP7uxi5e0e05Ercu29kc26zkVRUVGaK5FcUlRUdNz3d3t7e6/37XPQmDhxIlVVVaxe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\nY9AgIiIiIiLLMWgQEREREZHl/j+AT35583vKUAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe16593f5c0>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see the effect of the errors on the geometry of the problem. The radar station is to the lower left of the target. The bearing measurement is extremely accurate at $\\sigma=0.5^\\circ$, but the distance error is inaccurate at $\\sigma=3$. I've shown the radar reading with the dotted green line. We can easily see the effect of the accurate bearing and inaccurate distance in the shape of the covariance ellipse. \n",
      "\n",
      "Now we can incorporate the second radar station's measurement. The second radar is at (150,50), which is below and to the right of the target. Before you go on, think about how you think the covariance will change when we incorporate this new reading."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute position and covariance from first radar station\n",
      "hx.radar_pos = (150, 50)\n",
      "kf.predict()\n",
      "kf.update([radians(135), dist])\n",
      "\n",
      "stats.plot_covariance_ellipse(\n",
      "       x0, cov=p0,\n",
      "       facecolor='y', edgecolor='k', alpha=0.6)\n",
      "\n",
      "stats.plot_covariance_ellipse(\n",
      "       x1, cov=p1,\n",
      "       facecolor='g', edgecolor='k', alpha=0.6)\n",
      "\n",
      "stats.plot_covariance_ellipse(\n",
      "       kf.x, cov=kf.P,\n",
      "       facecolor='b', edgecolor='k', alpha=0.6)\n",
      "\n",
      "plt.scatter([100], [100], c='y', label='Initial')\n",
      "plt.scatter([100], [100], c='g', label='1st station')\n",
      "plt.scatter([100], [100], c='b', label='2nd station')\n",
      "plt.legend(scatterpoints=1, markerscale=3)\n",
      "plt.plot([92,100],[92,100], c='g', lw=2, ls='--')\n",
      "plt.plot([108,100],[92,100], c='b', lw=2, ls='--')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZZyxYsICPP/6YDz74gPDwcF599VX7xH9X44jPFZXiJPW1l/bC9/HxcWAknceB\nAwcAGDp0qIMjESDXw9m09/XYt28fH330IeXlJ9FqC5k0SWoxrqS4uBigVZ0yu4LqasuPtRu1uLnF\nEBs7jF/84hdNRpdpK/JZ5Tyu91qYTCb0en2bxGK1WjledJy0gjQ2HNmA0WTE382fGQNnEB8ST9+g\nvlfsYCxubM29z652/y41GkIIcQ1sNhv//Oc/+eqrLdTWpksthrhuP63d+P57I6+8UsjcuXMJCwtz\ndHiii9BoNAwMHciAkAFMj5uO2WrGVeOKVquVByii1STREEKIFqqtreXdd9/lhx92YzZnMGlSOEOH\nBsuXsGgTF/tufPxxOufO7WXJkkpmz/4lQ4YMcXRoogtRqVS4uLjg4uIcM3+Lzs15hg0QQggnVlRU\nxGuvvcbBg0lABjNn9iMhIUSSDNGmPD11zJoVx8CBGsrKUnnnnZVs2bJFRqUSQnRKUqMhhBBXcfTo\nUdas+RtlZUfo1q2ahx++CT+/tmkXLcRPabVq7r47muDgfJKSDvHFF2by8vKYPXt2m7XHF0KIjiCJ\nhhBCXIGiKCQnJ/Pppx9TXX2UPn10TJs2CJ1OOkSK9qVSqbj11u4EBrrzySfH2bevjuLiYp566ikC\nAgIcHZ4QQrSINJ0SQojLqK+vZ926dfz97+uorDzI8OF+PPhgP0kyRIfq3duPOXMG4eFxjlOnUvjT\nn/5ERkaGo8MSQogWkURDCCF+ory8nGXLlrFrVyJm8xHuvz+KMWPCpT+GcAh/fzfmzLmJ8PA6zp//\njj//+Q127twp/TaEEE5Pmk4JIcQl8vLyWLFiBYWFh9Drz/PYY7EEB3s6OizRxen1WqZPH0By8hn2\n7j3Ihg0m8vPzeeihhyQBFkI4LUk0hBDiR7m5ufz5z3+muDiN0FALDz54k8yPIZyGWq1i/PhIgoI8\n2LLlCMnJDVgsFmbMmIFaLQ0UhBDORxINIYQAsrKyWLFiOaWl3xMVpfDAA7G4uMjNm3A+gwYZ8PLS\nsXFjOjt32qivr2f27Nkya7MQwunIt6gQosvLzMxk+fI/U1qaRnQ0PPhgP0kyhFOLivJlxoz+NDRk\nsHfvdtasWUNDQ4OjwxJCiEbkm1QI0aWdOHGCFSsuJBn9+ml54IF+aLXy0SicX3i4D4891h+b7ST7\n9yfzzjvvUF9f7+iwhOh01q1bh1qtJjc319GhNOvMmTOo1WrWr1/v6FBaTL5NhRBd1smTJ1m1aiVG\n40FiY10dF9vDAAAgAElEQVSZNi0GtVo61orOo0cPb2bNGgic4uDBr/nb3/4mNRviuiiKgtVqtf84\nanSz1NRUnn76aQYMGICnpyfh4eE8+OCDZGZmOiSeltq4cSMrVqy4rjJWr159xWRCpVJ1qgEgpI+G\nEKJLOn36NG+9tRKj8XsGDXJj6tToTvXhLcRFISGezJo1kLVrj5CWpua997Q8/vjj0kFcXBObzUZO\nTj2HDtnYsUNDUZGK4GCF8eMtxMWpCQ/Xdehn5JIlS/j222+5//77iYuLo6CggFWrVhEfH8+3337L\nwIEDOyyWa7Fx40aOHTvGs88+2+oyVq9eTWBgII899lij5REREdTV1aHVdp7b984TqRBCtJGcnBxW\nrlyB0fg9AwbomDJFkgzRuQUFeTBz5kDWrTvKvn0qtFots2fPlmRDtIjJZOXLLy08/bQr+fmN3zNv\nvw3du9tYvdrEnXfqcHXtmEEHnn/+eRISEhrdVD/44IPExsbyyiuvsHHjxg6JozXa8/tEp+tcIyHK\nJ5AQoks5d+7cjx2/D9Knj4Z77pHmUuLGEBrq+WMH8ZPs2ZPEhg0bZFI/cVUNDTY+/9zCvffqmyQZ\nF+XlqbnnHj1bt1qwWm0dEtett97a5Ml979696d+/P8ePH2+0PCIigokTJ7J7926GDRuGm5sbvXr1\nYsOGDU3KPXbsGGPGjMHd3Z2wsDD+9Kc/YbO17Jyqq6v5r//6LyIjI9Hr9RgMBkaPHs2uXbsAGDVq\nFNu2bbP3pbj4c9GyZcsYPnw4gYGBuLm5ERcXx3vvvdfkXNLT09m5c6d9/8jISODKfTQOHTrEpEmT\n8PHxwdPTk9GjR7N79+5G21zsh5KSksLvfvc7AgMD8fT0ZNq0aZSUlLTo/FtDajSEEF1GSUnJj/Nk\nHKR3bxX33SdJhrixhIV588gj/fjww3RSUlS4ubnxwAMPODos4cSOHLEwa5YeRWn+s9BmUzFjhp5v\nvzUzaJC+g6JrTFEUioqK6NevX6PlKpWK7Oxs7r//fn71q18xe/Zs3nvvPWbNmsWQIUPo378/AIWF\nhYwePRqbzcZ///d/4+npyd/+9jdcXV1bdPwnn3ySTz75xN53pKysjP3793P48GHuuOMO/vCHPzBv\n3rwfH2gtb7L/8uXLmTJlin2izc8//5zHH3+choYGfv3rXwOwYsUKfvOb3+Dl5cVLL70EgKdn40lj\nL60xOX78OHfccQdeXl7MmzcPV1dX1qxZw9ixY9mxYwd33HFHo32fe+45/P39WbRoEdnZ2Sxfvpyn\nn36ajz/+uEWvwbVqNtFISUlh6dKlHDx4kPz8fNauXdukvdjChQtZs2YNRqORm2++mbffftt+QS+l\nKAqTJk1i+/btfPLJJ9x7771teyZCCNEMk8nE6tWrKS4+RHh4A/ffPwCNRip1xY0nIsKH6dMvJBtJ\nSTpCQ0MZPny4o8MSTkhRFPbuBbO5ZQ9c6upU7NsHcXGKQ5qbfvTRR+Tn57No0aJGyxVF4eTJk6Sk\npNjf6/fffz9hYWGsXbuWN954A7jQ76OkpIT9+/czdOhQAGbNmkXv3r1bdD5bt25lzpw5LF269LLr\nx44dS2hoKOXl5UyfPr3J+szMTPT6/0/S5s6dy5133snSpUvticbPf/5zXnrpJQwGw2XL+KmXXnoJ\ni8VCSkoKvXr1AmD27Nn07duX3/3ud6SmpjbaPiAggKSkJPvvNpuNlStXUlVVhZeX11WPd62a/Zat\nqakhLi6OFStW4Obm1uQiLFmyhDfffJNVq1aRmpqKwWBg3LhxVFdXNylr2bJl9smEpC20EKIjKYrC\n2rVryco6gJeXUYawFTe8qChfJk+OpLb2GB999AGnTp1ydEjCCZ0/X8/KlS7XtM9bb7lQWtrxwyif\nOHGCuXPncuutt/KLX/yiyfqYmJhGCXVAQAAxMTFkZ2fbl23bto1hw4bZkwyAbt268cgjj7SomaGv\nry/fffcd+fn5rTqHi0lGfX09ZWVllJSUMGrUKE6fPk1VVdU1l2e1Wtm+fTtTpkyxJxkA/v7+zJo1\ni7S0NIqLixvt88tf/rLR78OHD8dqtZKTk9OKM7q6Zr9pJ06cyOLFi7n33nubdChTFIXly5czf/58\n7rnnHgYMGMD69eupqqpq0kEnNTWVlStXsnbt2rY/AyGEuIrExEQOHNgJ5PDIIwPQ66XVqLjxxccH\nM2yYH1VVx/jLX/5CWVmZo0MSTqa6WqGg4NoeuuTnq6iu7ti+P4WFhdx11134+fnxj3/847IPrHv2\n7Nlkma+vL0aj0f57Tk4O0dHRTba73LLLeeONNzh27Bg9e/YkISGBP/7xj5w8ebLF5/HFF18wdOhQ\n3N3dCQgIwGAw8NJLL6FSqaioqGhxORcVFxdTV1dHTExMk3V9+/YFLvTruNRPXyc/Pz+ARq9TW2r1\nI73s7GyKiooYP368fZler2fEiBHs3bvXvqyqqorp06ezZs0aAgMDry9aIYS4RmlpaSQm/pO6uhPc\nf38M/v5ujg5JiA5z551R9OypUFx8mNWrV2M2mx0dknAiGg3odNeWNLi6gkbTcS1TKioqmDhxIpWV\nlXz11VcEBwdfdruLrWZ+6tKaiuttUXPfffeRlZXF6tWrCQ8PZ+XKlcTGxrJp06ar7rt7927uuece\nPD09+etf/8q2bdtITk7mt7/9LYqitLhD+vVqyevUllr9WK+wsBCAoKCgRssNBkOjKqUnnniCSZMm\nceedd7a47AMHDrQ2rC5JXi/nItfDeRQWFvLBB+uwWNIZNaobPj4NTaqRRceR194xRo8O4KOPTpKW\nlsyiRbXcc889qFQq+axyIq29FuHh4Y3a/F8rg0HD+PFWNm1q+XPnO+9swGDomCFuTSYTU6ZM4dSp\nUyQnJ9uf0rdWeHj4ZWsgrqVWIigoiDlz5jBnzhwqKiq45ZZbWLBgAQ8//DBw5WTm008/xd3dnaSk\npEZD1P773/9usm1LE6LAwEDc3d05ceJEk3UXl0VERLSorOZUVVVx9OjRy667Wm1QuzRSvvgCbdiw\ngcOHD/P6668D/58tyXB7Qoj2Vl1dzaefforFcpoBA9wYMkRqVEXX5Oam5e67o9Bq8zh+PK1RqwPR\ntbm5aZg589pmkp8+3dohc2lYrVYefPBB9u3bxyeffMLNN9983WVOmjSJ1NTURh2kS0tL2bhx41Vv\n7m02W5PmTT4+PkRERDRa7uHhcdlmSBdrEqxWq32Z0Wjk/fffb3JsDw+PFjV11Gg0TJgwgcTERLKy\nsuzLy8rKWL9+PQkJCQ5vTdTqGo2LVVdFRUX06NHDvryoqMi+7uuvvyY9Pb3JsFwPPvggt912Gykp\nKZct+9JOOuLKLj4BkdfLOcj1cB4NDQ08//zzlJefJDpax/TpcdL524Eu1mQ4+guvKwsMhBkz3Pn4\n41Ps3JlMYGBgi0a0Ee3rer83TCbTdR1fpVIRF6dh3LgGduy4+i3hXXc1EBfXcRP2JSYmMmXKFEpK\nSvjwww8brX/00UdbVM6lD7fnzZvHhg0bmDBhAs8++yweHh6sWbOGnj17cvjw4WbLqayspHv37tx3\n333ExcXh7e3Nnj172L59O7/5zW/s2yUkJLB582aee+45hg0bhlqt5qGHHmLq1Kn8+c9/Zty4cTz6\n6KOUlZXx7rvvEhISQlFRUaNjJSQksHr1al5++WWio6Px9PRkypQpl41r8eLFJCUlMXz4cObOnWsf\n3rayspJly5a16DW6Gi8vryu+R6/Wt6TViUZkZCTBwcEkJSUxZMgQ4MIbfteuXfYT+9Of/sQLL7xg\n30dRFGJjY1m2bBk///nPW3toIYS4IkVR2LRpE7m5R/D0LOWhh26TJEMIICbGnzFjatm6NYstW75g\n5MiRdO/e3dFhCQcLCXFhxQozv/417Np15dvCMWMaWLasgaCgjplD49ChQ6hUKhITE0lMTGy0TqVS\nNUo0rlQboVKpGq0LDg7mm2++4Te/+Q2vvfYaAQEBPPHEE4SEhPCrX/2q2Xg8PDx4+umn2bFjB1u2\nbKG+vp6oqCiWLVvGs88+a9/uqaee4siRI3z44Ye89dZbADz00EOMHDmS9evX8+qrr/Lb3/6WsLAw\nnnnmGXx9fZuMBPU///M/nD17ljfffJPKykoiIiKumGj07duX3bt3M3/+fJYsWYLNZiMhIYH33nuv\nybDWzb1O7UWlNNOOqaamhszMTABuv/12/vu//5spU6bg7+9PWFgYr7/+Oq+88gpr164lOjqaxYsX\ns3v3bjIyMvDw8LhsmWq1mk8//ZRp06Y1Wn5pRuTj49MW53bDkyfozkWuh3P45ptv+Oij9zAa9/Hw\nw72IjQ13dEhdntRoOA9FUVi37gAnTsCAAROZP39+k1YHouO0RY3G9fTRuEhRFLKzLezdq7BkiQtH\nj/5/rcVNN1n5r/+q57bbVERE6GSKgi6ouffZ1e7fm63RSE1NZcyYMcCFbGfBggUsWLCAWbNm8f77\n7zNv3jzq6uqYO3cuRqORW265haSkpCsmGUII0Z7Onj3L5s2bqKk5xoQJPQgOdnd0SEI4FZVKxYQJ\nPTEaM8nL+4EPPviAJ598Um4euziVSkVUlCuRkQpjx9Zz5kw9JhPo9RAZqcZgcJX3iGiVZhONUaNG\nXXW4rYvJR0t11PBdQoiupaGhgXXr1lFdfZJhw/zp18/b0SEJ4ZS0WjU//3kkf//7WQ4e3Etq6lCG\nDRvm6LCEE1CpVAQH67jCCLJCXDNpuCyEuCFs27aN7OxDeHpWMnZshKPDEcKpeXvrmDAhgtraDDZt\n2kRlZaWjQxJC3IAk0RBCdHq5ubls25ZIXV0md9/dB52uY0ZFEaIzGzw4iKgoHWVlJ/joo49k6Hkh\nRJuTREMI0ak1NDSwfv16amoyGTYskIgIGUxCiJZQqVRMnRoN5JOWtqfR3AJCCNEWJNEQQnRq0mRK\niNbz8XGVJlRCiHYjiYYQotOSJlNCXD9pQiWEaC+SaAghOqWLo0xJkykhro80oercJDEU7el631+S\naAghOqVt27Zx5sxhaTIlRBuQJlSdk06nw2QySbIh2oXVasVkMqHT6VpdRrPzaAghhDO62GTKZDrF\ngw/2lSZTQrSBwYODOHashLNnLzSheuKJJ2SSNienVqtxdXXFbDY7OpQbQlVVFQBeXl4OjsQ5qFQq\n9Hr9dX0OSKIhhOhUFEXhgw8+oKYmk4SEAGkyJUQbudiE6u23vyctbQ/ff38z8fHxjg5LXIVarUav\n1zs6jBvC0aNHARg6dKiDI7lxSNMpIUSnsn//frKzj+HmViFNpoRoYz4+rowd25O6uiw+++wzrFar\no0MSQnRikmgIITqNhoYGtmzZgsmUzZgx4dJkSoh2MHRoCL6+ZvLyMtizZ4+jwxFCdGKSaAghOo1d\nu3ZRUHCSbt0aGDTI4OhwhLghqdUqxowJx2TKJjExEYvF4uiQhBCdlCQaQohOwWQysXXrVkymM4wd\nG4FaLZ1UhWgvAwYEEBysoqTkNF9//bWjwxFCdFKSaAghOoXk5GTKyrLo3l1NTEw3R4cjxA1NpVIx\nblwkZnMOX375JTU1NY4OSQjRCUmiIYRwelVVVSQlbf+xNiNShtwUogNERfkSEeFKRUU2X331laPD\nEUJ0QpJoCCGc3pdffkll5Rl693aX4WyF6EBjx0ZgNufw9dfJGI1GR4cjhOhkJNEQQji10tJS/vOf\nr7FYzspwtkJ0sO7dvejf34fq6hy2bt3q6HCEEJ2MJBpCCKeWmJhITU0OAwf6EBzs6ehwhOhyxowJ\np77+HHv27KSwsNDR4QghOhFJNIQQTisvL4+9e3fR0JDHmDERjg5HiC4pIMCd+PgAamtz+eKLLxwd\njhCiE5FEQwjhtP71r39hMuUyZEggfn56R4cjRJc1cmRPFKWQAwe+5ezZs44ORwjRSUiiIYRwSkaj\nkYMHD2C1FnHHHWGODkeILs3b25X4eANmcwE7d+50dDhCiE5CEg0hhFPavXs3JlMBMTG+eHu7Ojoc\nIbq8YcNCqK8v5LvvvqW2ttbR4QghOgFJNIQQTsdqtbJr1y4slgKGDQtxdDhCCC701YiM9KCmpoDv\nvvvO0eEIIToBSTSEEE7nhx9+oLQ0l27dFJk3QwgnkpAQgsWSz86dO1EUxdHhCCGcnCQaQgins3Pn\nTszmfBISQmUWcCGcSN++/ri7m8jLO01GRoajwxFCODlJNIQQTqWgoIDjx4+gVpdz000GR4cjhLiE\nWq1i6NAQLBbpFC6EuDpJNIQQTmXnzp1YLIXExQWg12sdHY4Q4ifi44OwWov5/vs0ysvLHR2OEMKJ\nSaIhhHAaZrOZvXv3YrEUkJAgncCFcEbe3q7ExPhiMhWwa9cuR4cjhHBikmgIIZzGvn37qK7OIyxM\nT3Cwp6PDEUJcwbBhF5pP7dq1C6vV6uhwhBBO6qqJRkpKClOnTqVHjx6o1WrWr1/fZJuFCxfSvXt3\n3N3dGT16NOnp6fZ1RqOR3/zmN/Tr1w93d3d69uzJU089RVlZWdueiRCiU1MU5cdO4DKkrRDOLiLC\nh27dFEpLczl06JCjwxFCOKmrNoCuqakhLi6Oxx57jJkzZzYZAWbJkiW8+eabrF+/nj59+vDyyy8z\nbtw4MjIy8PT0JD8/n/z8fN544w369+/PuXPneOqpp3j44YfZvn17u52YEKJzycrKIicnE72+hn79\nAhwdjnBi1dUWzp+vpaiohspKM2azFYvlwo+rqwY3Nxfc3V3o1k1PWJg3vr6uMnpZG1OpVCQkhLJj\nRz7/+c9/iI+Pd3RIQggndNVEY+LEiUycOBGAWbNmNVqnKArLly9n/vz53HPPPQCsX78eg8HAxo0b\nmTNnDgMGDOAf//iHfZ+oqCjeeOMNJk+eTHV1NZ6e0jxCCAEHDhygvv48Q4YY0GqlVae4oL7exunT\nRs6cqeD8+RoKC2uoqDJT21BPXUMDFpsVq03BqtiwKaBRq9CqVGjVavQaLZ4uOrr56OnVy49hw0Lo\n3t1Lko42ctNNBpKSzpCRcZzKykq8vb0dHZIQwslc15Au2dnZFBUVMX78ePsyvV7PiBEj2Lt3L3Pm\nzLnsfhUVFbi6uuLu7n49hxdC3CAUReHw4cPU15fQv3+0o8MRDmY2N3DyZBnp6aWczCyjrKaOSouZ\n2oYG6hrqsWoU3Py0uAVpcfXSoHPRoHFRodaqsDUoNJhsNJhslBjryDlfgaZcTXphKfvS8okM82H0\n6HBiYvwdfZqdnl6vJTLSm/z8Uo4cOcLtt9/u6JCEEE7muhKNwsJCAIKCghotNxgM5OfnX3af8vJy\n/vjHPzJnzhzU6ss/tTxw4MD1hNXlyOvlXOR6XLvi4mKOHz+Eq2sFOp2J4mJzm5YtnENz10JRFHJz\nqzl6tJSMjHLKTGYq6i1U1lvQ+anxjtDh3U1LkJ8OFw91M7USKkADaPDHBUXRY66wUpZl5ujpKk4f\nLuV4ZhGDYwMYM6YHbm5ddwjltvjbCA7WcPRoDomJibi6urZBVF2TfG84F7keLRcd3fzDwXb7hL3c\nl0B1dTVTpkwhLCyM119/vb0OLYToZE6ePInNVkFUlDdqtTRr6Urq6ho4eLCYo0fLKDLWUmYxY7SY\n0Qdo8AnXEdzDB52nptXlq1Qq9L5aQuO1BMe5U3rSRObhCiq/t5CbW8399/cmIEDfhmfUtfTq5c2O\nHQVkZWXR0NCAVtt1EzchRFPX9YkQHBwMQFFRET169LAvLyoqsq+7qLq6mkmTJqFWq9m6dSs6ne6K\n5Q4dOvR6wuoyLmbc8no5B7kerZecnIyHh5WEhAgCA9umI/jFp7WBgYFtUp5ovctdi7q6Br799hx7\n9+aRV1FFsamWBr1CwEA9PaJ9cPVqnxtW9yFuBPb2IntXBZnGKj7/4hy/+uUgAgO7TlPetvzbCAyE\nqKgiKivVeHh4EBsbe91ldiXyveFc5Hpcu4qKimbXX1ePy8jISIKDg0lKSrIvM5lM7N69m9tuu82+\nrKqqigkTJqAoCtu2bZO+GUIIu8rKSrKyMlGpqujVy8/R4Yh2ZjY3sHNnLn/+834+/SqDtMJCyn1N\n9BjrRez9AYTGe7VbknGR3kdLnwndqPe3kV5UwoYNRzGbG9r1mDeymBh/6utLZZhbIUQTLRreNjMz\nEwCbzUZOTg4//PAD/v7+hIWF8dxzz/HKK6/Qt29foqOjWbx4MV5eXkyfPh24kGSMHz+eqqoqPv/8\nc6qqqqiqqgLA398fFxeXdjw9IYSzO3LkCPX1RiIjvdHpWt9ERji3+nobe/acY9eus5wzVpFfU42L\nQU3kCB88g65cw91eNFoVvX7mR8a/SjlVaCQp6QxTpvTu8DhuBH37+pOScpzDhw+jKIqM6iWEsLtq\nopGamsqYMWOAC21dFyxYwIIFC5g1axbvv/8+8+bNo66ujrlz52I0GrnllltISkrCw8MDgLS0NPbt\n24dKpaJPnz72clUqFd988w0jRoxop1MTQnQGhw4doqGhlL59ZRSgG1F9vY20tGL27SukpLaB/Npq\nNN1U9LzNC+9Qx3Ye1mhVRI7wIWOLkT37zjFwYACRkb4OjakzCg72wNPTRllZATk5OURERDg6JCGE\nk7hqojFq1ChsNluz21xMPlq7vxCia7JYLKSnp1Nfb6RPn0hHhyPaWGZmGVu2nOLkufMUmWrRBmjp\ncbMX3j10TvPU283PBUOsG3knqti9+5wkGq2gUqmIifHnyJFSDh8+LImGEMJOZsUSQjjMiRMnqKsr\nJjRUj7e3DI15ozCZGvjii5O8t+4Qqbn5FLrUEjTcjX5T/PEJc75Zug39PShvMHE8o4SysjpHh9Mp\nxcR0o76+TPppCCEakURDCOEwhw4dor6+VCZPu4FkZpbx9ttpfLU7i/TKUrzidPSZ5OOUCcZFWr0a\nv0g9JaY60tIKHR1OpxQZ6YtGU0NubjalpaWODkcI4SQk0RBCOISiKD92BC+jb99ujg5HXCez+dJa\njAJK9HXETPEjJM4TVSeYG6VblJ5yi5msrHJHh9IpabVqevXypaGhjCNHjjg6HCGEk5BEQwjhEGVl\nZRiN59HrGwgK8nB0OOI6nDplZNWqg41qMfpO7oabX+cZVdAj0IVaaz35BdVYLFZHh9Mp9erlR0ND\nBVlZWY4ORQjhJGQKTyGEQ+Tm5mK1VhMa6uW0TWrElSmKQnW1hW3bTvNdaj45VRUoPtDnLl/c/Tt+\nuNrrpdGp0ftqqDZbyM+vJiLCx9EhdTohIZ5YrQXk5uY6OhQhhJOQREMI4RA5OTk/Jhqejg5FtEBl\npZlTp4ycOmXkzJkKiotrycwsp7ymgdoGG66+Otwb1KR/UYbOQ43eV4u7vwvu/i64drOh0Tl/Bbre\nV4u5xEplpdnRoXRKF2om6ygoyMdkMqHX6x0dkhDCwSTREEI4xP8nGkGODkVcgcVi5dtv8zh6tJi8\nPBOVle5UVrpz/nwQZWU2LNYIFI0WVy9XGupcKD9rQbHWoNaa0ehMaPW1uOhr0LiX491dS1CMgk+Y\nKxoX50w6tK5qGmw2amvrHR1Kp+TiosZgcKOqqpqzZ88SHR3t6JCEEA4miYYQosMpivJj06kqQkJ6\nOToc8ROKonD0aDFJSWfIznahqKgbJpMXnp49aWgwYLV1Q+2pw8tbi2eQDtUleYNis2JrqKbBXEaD\nuYzasgLq889SXWDEeKocvXcxvuGuBES74RXqPPNpAGhdVZJoXKfQUE/S06vJzc2VREMIIYmGEKLj\nlZWVUVlZhl6v4Osr82c4k/z8arZtO8WJE2Zycw3YbOF07347Hh5h5ObWUGqsocpqRh9woWnUT6nU\nGjQ6HzQ6H1y9LkzCWG+qxFx9htqSbKoK8qnMM3L+xHn8wmvoPsQTT4Nz9OlQa1U0oGCxyCSzrRUa\n6sWRI1Xk5OQ4OhQhhBOQREMI0eEu1mZIR3Dncvx4CR9/fJLsbH8qKyMJDb0Df/8B1NcrnDxppKzK\nRI3VgleoDp2npsXlqrUeuPkOQBMQh7W+CnPlKSpyj1BXlkfF2Xy6RanpPtQLN1/HfiVZGxQ0KhWu\nri0/N9GYdAgXQlxKEg0hRIeTjuDO59Ch82zefIqMjFDc3YcyYMAoNBpXamosnDpVTnmdCbPKik+4\nHq2u9cmhxsULd//B6H37U1d2GGP2YWrLCjCeKSQwxoUeCV5o9Y7pw2GrV9CqNJJoXIdLO4SbzWZc\nXaXGUoiuTBINIUSHk47gzuXkyTI++eQUx493p1u3kYSE3IZKpaK0tI7sM+VUmM0oevANdUWtaZsa\nKLXGFY/ABNz8BlBbepCyrHRMFeeozC8hapQvnkEd35zKWn+xRkO+Glvrpx3Ce/fu7eiQhBAO5JxD\nfwghbliNO4JLjYajlZbWsWnTCTIyQvDzu4PQ0NtRqVTk51dxKsuI0WRC463Gp0fbJRmXUmvd8Qwa\njm/PBzFXDqHkZCTHEyspOFyNoihtfrzmmCoacNVopN/QdQoN9cRqrZbmU0IISTSEEB1LOoI7lx07\nssnN9UWniyM0dDgAZ89WknuuinKLCTeDFs8gF9q7K41G54NP2GTULiMwZvfjTApkJhmpr+uYWboV\nRaHO2ICbVisz1V+n0FAvrFbpEC6EkKZTQogOJh3BnceZMxV8/30FxcW96N9/NCqVipycSgqKqqio\nN+MZosPVq+P6K6jUGjwNN2NxD6Uy/xvq67KpLS0ierwfHgFNR7hqS5YaG5oGFT6eejw9nWMUrM7q\nYodwSTSEEFKjIYToUMXFxdhsJgID3RwdSpemKArbt2eRl+ePwXAzLi5enDlTQf6PSYZXaMcmGZfS\neYbhG34vlpohlJ2OJGObkapCS7ses66sHr3WheBgqc24XgaDOzZbHSUlJR3e/E0I4Vwk0RBCdKiK\nigpsNjNeXtJsypGOHSvh5Ml6qqtDMBiGcuZMOQXnq6lsMOPV/dqGr20PGhcPfHpMBFU8Zdm9yfiy\nnP9tYKwAACAASURBVIpz5nY7Xl15A+5aLQaDe7sdo6vQ6TTodCosljrq6uocHY4QwoEk0RBCdKiK\nigoUxYKXlzRPcaTjx0spLvYhKCiBc+fqKCyuobLBjHd3V3QezjG8q0qtwStkNBqXoZSfiSZzRwWV\n+e2TbNSW1OOudZH+GW3Ey0uHzWahvLzc0aEIIRxIEg0hRIe6UKMhiYYjKYpCVlY5lZXuVFUF2Gsy\nvLu74uLuXF8LKpUaz6A70LgmUJ7Tm8ykCqqL2rYZla1B4f/Yu/P4qOt73+Ov2Zfs6yQhISEQSGST\nrYpgWERZXBBbpLZu9Vi1tSrtqdbtXryneh/22vZYi8e29vhQ0aLtkaL0tlfQgmxHBASRJRB2spJ9\nncxklvtHTGTfsswkeT8fDx7E5Dfz+4Qx+c379/ku9cVeoi1WsrNju/S5+6v2oFFXVxfqUkQkhMLr\niiIifV57R0MTbkOnvLyJqqog9fURVFSZqP9qTka4hYx2BoOBSNckTJax1B4ZTOGqWrxNXbcaVX2x\nBycWMjNiiI21d9nz9mdRUVaCQQUNkf4uPK8qItJntXc0oqMVNELlwIFaDh400OJNpN7nJSrNGjbD\npc7GYDAQmZIPhuHUF6dycHUtgUDXTDSuOdJCnM3OZZcldsnzCURGKmiIiIKGiPSglpYW3O4mzOYg\nNlt4v7HtyzZsKKKk1ITHkEhkaugnfl8og8FIVMpUWuoHU33QSfGWhk4/Z8AfpO6Yl1ibnby8hC6o\nUqB96JRHQUOkn1PQEJEec+L8DO2hERpFRfVs/bwMd6sBZ0JMyJawvVRGs53otOk0lGVTss1H7ZGW\nTj1f3TEPjoCZgWnRJCZqxamuEh2tyeAioqAhIj1IK06FVn29hz/9aTcVTc0Y7SbsvXRndosjBUf8\nRBpKsjm4th5Pg++Sn6uy0E2i3cGYMa4urFDahk61qqMh0s8paIhIj2nvaGgieM9rbQ2wdOlu9pZX\n4bcHsTgtGIzmUJd1yRxxIzGaL6O+OI0jG+sv6Tm8zX6ailtJcDgYOTKpiyvs39omg2volEh/p6Ah\nIj2mvaOhieA9KxgMsnz5PnYcrKDa1EJshg2CRgyG3jVs6kTtk8M99enUHDJQV3zx+2tU73cTa7WR\nl5uo8NvFTlzeVruDi/RfChoi0mNqa2vV0QiBdeuO8ennxRxrqWfIjFgwAEED9OKgAWA02XHEjaGp\nYgDFmxsu6g2t3xfk+K5mkh0RjB2b0o1V9k82mxmLBTwe7Q4u0p8paIhIj2lsbCQYbCUiwhLqUvqN\ngoIq/rHyIAcaasjKj8YRZ8FsNWIw+Qn6OzeROhw44obja8mgrthG9YEL/34q9jQTEbAyZGAsQ4fG\ndWOF/VdEhIVAwEtjY2OoSxGREFHQEJEe4/f7gSBms3719ITy8ib+/Jc97K+rIWmMk9iBbZvR2aJN\nmCwe/K2dXx421AxGM87E8TQdT6d4awMB3/m7Gn5vgPIvm0iLiGT69CytgNZNTCYjEPzq515E+qNz\nXu3Xrl3LTTfdRHp6OkajkTfeeOO0Y5555hkGDBiA0+lk2rRp7N69+6SvezweHnroIZKSkoiMjGTu\n3LkUFxd37XchIr1CIBAgGAzojV0P8Hr9LF26m31V1dgyTaSMjOj4mi3KhMnagt/bNybq2qIHEwxm\n0lAWTcXe5vMef3xPM1FBK8MGxZOTo25GdzEaDUCQQCAQ6lJEJETOGTSampoYNWoUv/nNb3A4HKe9\nOfjFL37Br3/9axYvXszmzZtJTk7m2muvPalNunDhQpYtW8Y777zDunXrqK+v54YbbtAvHpF+qP3n\nvu0NiHSnDz88xL6SaloifGRNijnp97cjzozJ5sbnqQxhhV3HYDDiTBiDuyaZyn3nng/g8wQo39ms\nbkYPMJkUNET6u3MGjdmzZ/Pss8/yzW9+E6Px5EODwSAvvvgiTzzxBPPmzWP48OG88cYbNDQ08Kc/\n/QloW2Hmtdde45e//CXXXHMNY8aMYcmSJezYsYOPPvqo+74rEQlLbUMoAl+9AZHucvBgLRs2FVHU\n3EBWfgxG88n/3s5ECxZ7E76Wqh6pJ2gwEOzmN/TWiIH4vYk0HjfSXN161uOO72oi1mAjb0gigwbF\ndGtN/Z3RaCAY1NApkf7skgdKHzp0iPLycq677rqOz9ntdvLz89m4cSMAW7dupbW19aRj0tPTycvL\n6zhGRPqP9jka6mh0H4/Hx/Ll+zjSUEfyaCfO+NMn3jtizVicXoKBKvzeS9uD4kK1tgZpajTS1Gik\ntbX7ljk1GE3YorLx1MefdVK4ryXA8V1uUp2RTJ+eqW5GN9PQKRG55N2aysrKAHC5Tt5NNTk5mZKS\nko5jTCYTCQkJJx3jcrkoLy8/63Nv2bLlUsvql/TvFV70epzd4cOHaWxsoLa2hoqKnrnLWVFR0SPn\nCRerVh1j15Ey3HYP6Tl2WtxnftMdmWqk9lgV7tpCHPGXd0stQYOB5mYjwa/eZzY3G4iIDGDopn0V\nzM5BNFXEcnxfKQnDzacFidJtTUQGjGSlO3A6vf3u/41Tdff339zcRHV1Fdu3b6e6urpbz9Xb6boR\nXvR6XLicnJxzfr1bln7RXSIROZO2IZgGtH9X9zhypIHNnx+nzNNMxlWRGM7ROYodZMMaVYWnYX/P\nbqjWjacy210EA8m4q200Hfed9LXWZj9Vez247E4mTdK+GT2h7X8rw2lDr0Wk/7jkjkZKStsv6vLy\nctLT0zs+X15e3vG1lJQU/H4/VVVVJ3U1ysrKyM/PP+tzjx8//lLL6lfaE7f+vcKDXo/z27RpE6Wl\nUcTExJKUlHD+B3RC+93apKSkbj1PuPB4fKxde4iyVg+p46KJS4s85/G2bBsliRU0H68Afy0me2KX\n1uN1FNMcWUhEyRSam9sCj9MZxBC001A6iJiMvXTHPSlHzBB87v24j9eSmNW2nG8wGOTY+loGOKO5\nYvxARo3K6voT9yI99bPhcBQRH5/A5ZdfTlZWVreeq7fSdSO86PW4eHV151698JJvMwwaNIiUlBRW\nrlzZ8bmWlhbWr1/PVVddBcC4ceOwWCwnHVNUVERBQUHHMSLSf5hMJsBAIKCWRldbufIw+8tqaI3y\nkzIq4rzHG4wG4rPt2KKraanf36W1eB3FlF7+b1Rf9ju8KVuJiAwQERHAbDZQtuNqqg9cTlXhmG7p\nbFkcKfjcETRXfj0hvGp/C62lfgbFxzJnzuCuP6mcUSAQxGBQR0OkPztnR6OpqYnCwkKgbVnKI0eO\nsH37dhISEsjIyGDhwoX87//9v8nNzSUnJ4dnn32WqKgovvOd7wAQExPDv/zLv/DYY4+RnJxMfHw8\nP/nJTxg9ejQzZszo/u9ORMJK+9ApBY2udeIqU0Ovibvgyfbx2XZKt1dRe3Q/EYnjMRgvucndweso\npmT0vxGw1mE+PgJDyUgCgMkUxGCAuKzdlH05ifrioQAk5Gzr0s6G2Z6Ir8VJc5WPYDBIa3OAok0N\nDIuKZ86cwURH27ruZHJObT/nhq9uMIhIf3TO2wybN29m7NixjB07lpaWFhYtWsTYsWNZtGgRAI89\n9hg//vGPefDBB5kwYQLl5eWsXLmSiIiv76a9+OKLzJs3jwULFjB58mSio6NZsWKF5nGI9EMmkwmD\nQUGjK/n9AT74oPCcq0ydTUSShahUPxZHCe6aXZ2upb2TEbDV4agZQeL2R3HabJhMX7/ezoRSUkZu\nAIOf+uKhXd7ZMJqdYIii1W3G2+jnyMZ6XBYnY0a4GD06uetOJOfl97cFDXU0RPqvc96+mjp16nmX\npVu0aFFH8DgTq9XKSy+9xEsvvXRpFYpIn9E+dKrtDYh0hW3byjlcVofH4WPwqNiLeqzBYCB9fBQN\npcXUHt2GPWYYRrP9kuoIEuD4Zb/Bb20LGa6djxIwnbl70B422jsb9phKIl3HLum8Z2KyROP32ijf\n1dw2ZCo1iRtuGKIbXD2svaOhoCHSf+mnX0R6jMPhwGAw43affUM1uXCtrQE++eQoxU0NpI2JvKT9\nSaIH2IgbFMQWVUxz9bZLrsWAkaSCB4k4fiWunY9iDNgwn+NWVnvYiB5QSERy14UMAJM1mtYWK8Wb\nGxgUFashUyHidrdiNJpxOp2hLkVEQkRBQ0R6TGxsLEajjYYGb6hL6RO2bi3jaEU9gaggcYMurRMB\nkD4hCmdiKZ66Lzu1gZ+tKRPXnoUYAxf2pt6ZUEri0M+7fPUpg9FMc1WAWJNdQ6ZCpLU1QEtLALPZ\nTmTkuVdAE5G+S0FDRHpMTEwMBoNVQaMLeL1+1q79qpsxNrJTw4Kc8RaShplxxJfQVPFZz+6r0Q28\nTa0EPX7SYyO58cYcDZkKgcZGLwaD9aufef37i/RXChoi0mMUNLrO5s2lHKuqh1iIHdj5YUEDxkUR\nkXQcv3c3nrp95z0+YGru9DnP+tw+8yVPEPd7g3jqPESYTUyePJCoKGvXFicXpKHBi9HYFjREpP9S\n0BCRHhMTE4PRqKDRWR6Pj3XrjlHS3MiAMVFdcsfYGmEia3IUUQMO0lS5Dl9L1VmP9TqKOTbhX6lL\n+3+dPu+p/F4bxZ9fc0mrUQUCQeqKPVgNQeJireTlde+mkHJ2DQ1eDAabgoZIP6egISI9pj1oNDYq\naHTGp5+WUFTTgCneQHR6192xTxjiIGWEgYjkg9SXfEzAf/rr5HUUUzr65/htNTQnbiHIuVcmvFje\nphham6MufunbIDSUeLH6TThsRtLTI7BYdIkLlYYGD0ajhdjYi1sJTUT6Fv0WFpEe43Q6sVodeDxB\nvF5/qMvpldxuHxs2FFHS1NjpuRlnMvDKaOKy6rE699NYvu6k+Rpfh4xa7DXDce18FEMXX0Yccccv\naZ+NxopWcEOM3UpkpBuHw69hUyGkjoaIgIKGiPQgg8GgeRqdtGVLKcW1DViSjUSndf2SrUazgcHT\nYolOL8Lv3Ym7ZidweshI2fnYBa8udbEudlO/ljo/3lo/MVYbGRkGzOY64uODuFwRZ3+QdCvN0RAR\nUNAQkR6meRqXLhgMsm1bORUtzbhGdN/eBPYYM1mTo4gecICWmrW01O4FA2AIdnvIaHdi2Gg7+Zm1\nugM0lXuJttrIzIwhECglOrqZ7OxYrXYUQieuOiUi/dc5dwYXEelq6mhcumPHGigqr8dj9hMzoHvf\n6MdnO8iaFOBwcB+1R41EGK8lLfC/MHnjuj1ktHMmlJI+fhWWiLoz7rUR8AVpKPYQZbGS5ookKcnJ\n/v1HiI9vZvDg1B6pUc6svl4dDRFR0BCRHqYJ4Zdu27YyqlrcJAxxYLiEXcAvlmtEBAFfkCB7qTsK\nEYFpWGJTuv28J7JG1p3x88FAkLoiDw6DhcRYJxkZUfh8Hhobj5CZ6SY7W5OQQ6mhwYvFYtVkcJF+\nTkFDRHqUhk5dmtbWAF/urKCqxU1OTnyPnTf18kigkaMUUHcsQCDQijN+ZI+d/2waSlsx+4zERto7\nhkmVlW0iNraSIUMiiIu79J3SpXN8vgAtLX4cDpt2BRfp5zRHQ0R6VEJCAkajnepqd6hL6VUOHKih\nqtGNOd6II7Z77xHVez0U1tV0/Hfq5ZFkXW0lNrMAT91qGkrXEAy0dmsN51JXZKapbDjRVhtDhsRh\nNhvxeOqorNzMgAFVzJyZHbLaBKqq3BiNduLj4zVPRqSfU0dDRHpURkYGRmMkxcWHQl1Kr7J7dyU1\nnhbihnTvnfp6r4c1JUdp8fuxmUwMjIwGwDU8ArPdyOF1e6kvaaLm8HGi06Zjtid2az2naij3UXv4\nWvyt8bTGJmK3HwaguHgdyclVjBsXT3p6VI/WJCcrLW3EaIxk4MCBoS5FREJMHQ0R6VEulwunM5b6\nep/maVwgvz9AQUEVtZ4W4jK7L2icGDKSHU7SnCcPe0kY7OCym+NIzismInEbdUV/xV2z66S9NrpT\nU0UrvjofSQlfYjAEOHp0INu2Daa6upDGxp2kp9cxY0ZWj9QiZ1dS0ojZrKAhIgoaItLDjEYjGRkZ\nmEyRlJY2hrqcXuHw4TqqGtyYoo3YY7qnEX1qyJicko7ZePolwhFrJu/GBNIntBA7cCctdR/RUPIR\n/taGbqmrXXNVK94aP7E2OyNHepg8eRdGY4D9+wewZUsK2dmlXHNNBrGxmpsRaiUlDZhMChoioqAh\nIiGQmZmJyRRFSYmCxoU4cqSe+lYPMRnds9N1MBhk0/HS84aMdkazgcxJMeTMdJAwZC9m20ZqD79D\n4/FPCfi6fu5Nc1UrLVVtIWNwdixxcXZSU2sYM+afGAyt1NZeT2LiDUyenN7l55aLEwgEKS1twmSK\nJDMzM9TliEiIaY6GiPS4gQMHftXRqAh1Kb1CeXkTzT4fcQnds3+FwWDgyuQ0dtdUMi4p5Zwh40Tx\ng+xEJFoo3lpD5b4KmquOU3NoD4640djjRmA0dT4YNVW0dTLibHayB8USH+8gEPBx/Pg2Gho+Ydy4\n5TidE/nZz8o18TgMVFQ0EwhYSUx0acUpEVHQEJGe19bR0ITwC1Ve3oTb5yMtLqLbzhFltXKFK+2i\nH2eLMpE9NZaUka0Uby2n+lA5TZXl1BzahT0mF1tUNphiLikENB5vpbX25E5Gbe1+jh1bg8NRTF5e\nJVOmNDN7tlchI0y0TQSPUjdDRAAFDREJAZfLhcMRQ0VF24TwyMjuGRLUF3i9fiqr3HiDPmzdND+j\nKzgTLORcF09DqZfircXUFpXhqTtMfUkcwWAy1shBOOJyMFsvbAO3xvJWfHUB4mx2srIcwFEKC3fQ\n2lpIZmYF2dkwe/bQHt1TRM5PE8FF5EThe9USkT7LaDQycOBAqqvbJoTrzeLZHT/ehNvfii3WjLGL\ndgP3fLV0bXeISrUy7Pp4GstaqT5UTc3hEhor9+NtKKDu2GYMxiTM9kTMtgRM1hhMliiM5rZOTTDQ\nSsDnpbG8mUBzK3ZDDSZTFceOHScyson4+EYyMtxMmzaQCRNSMZnOPsSrttZJTEwzanT0rLaJ4AkK\nGiICKGiISIhkZmby5ZdtE8IVNM6uvLyZFp8PR3LX/LpuX11qcHQcw+O7Zw8Mg8FAVKqVqFQrGVdG\nU3mogdrDx2kqKcXTYMfnceLzOGhttuNvtRHwWb56pB9voxdTMIDDYiA13Uhqqpfo6BYyM6PJyUlg\n3LgUnE7LOc9fVhbLnXf+K1dfvYunn35HYaOHtE8Edzo1EVxE2ihoiEhIaEL4hWlo8OIN+LFFdb4D\nceISthUtzQSCQYzd/C7caDQQnWYlOs2K1WrDXd1Kc3Ur7mo3LfU+vI1+vE0BfC1+6ou9xCVbSYmL\nZPz4FAYNimXIkAEMGhSDzXbhl6uDB1MoLY3j7benAShs9JD2ieAJCcmaCC4igIKGiISIJoRfGI/H\nhz8YxGzu3DvlM+2T0d0h41RGk4GIJCsRSSfPyanc10zRfzcyYVQCY/NSuPXWPByOS788XXVVAS+/\n/AoPPvgDhY0e1D4RPCsrK9SliEiY0D4aIhISLpeLiIg46usD1NS0hLqcsOX1+vEHghgtl/7r+kI3\n4+tpwUCQY5vqKfvvZnJj4pmZn80dd4zoVMhol5+/i5dffgWLpZW3357Gs89+mx7awLzfOny4DrNZ\nK06JyNdCf6URkX7JaDQyfPhwLJZ49u6tDnU5Ycvr9RMgiLETHQ2TwYDRYAirkOHzBChcVYO70Mfw\nhEQW3HIZc+YM7rIJ73By2IiM7PqNBOVrwWCQffuqMZsTGDFiRKjLEZEwoaFTIhIyo0eP5tNPP2Tv\n3lKuvPLi93DoD2w2MyaDgUBr4JKfI8JiZfqATKxGU1iEjJY6H/s/qiHGa2NYWgLfXnAZWVkx3XKu\n/PxdvP/+zxk0qFxDp7pRUVEDbreFrKwBDBgwINTliEiYUNAQkZAZMWIEVmsChw/vo6XFh92uX0mn\ncjrNmA1GfC2XHjQAnOZzr9TUE4LBIJX73BR/1ki6PYoRQ5K47bbLiIuzd+t5s7PLu/X5Bfbubetm\njB49WpsnikiHTt/aamhoYOHChWRlZeF0Opk0aRJbtmzp+Hp9fT0//OEPycjIwOl0kpuby4svvtjZ\n04pIHxAREUFOzjCMxhgKC2tCXU5YcjotmI1GWjsZNELN2+SncGUNlZvcDIuKZ+r4gdx77+huDxnS\nMwoKqrBY4hk1alSoSxGRMNLpoHHvvfeyatUq3nzzTXbu3Ml1113HjBkzKCkpAWDhwoV8+OGHvPXW\nWxQUFPDUU0/x+OOP89Zbb3W6eBHp/UaNGoXZHM/evVWhLiUsxcc7cJjNuGt8F3R8vddDQU0VwTCZ\n+RwMBqkqbKHwb3VE19oYOyCFO789kvnzc7Fau2fTwAtRVJTAyy9frwniXaCmpoXKylYiI5PJyckJ\ndTkiEkY6FTTcbjfLli3j+eefJz8/n+zsbBYtWsSQIUN45ZVXANi8eTN33nknU6ZMYeDAgdxxxx1c\neeWVfPbZZ13yDYhI7zZ69GgslngKC2vw+3v3XfvukJERTYTZgrvKR8B/7nfF7atL7aiu4HBDXQ9V\neHaexrYuRtWWFgbbo5k+PpOHfjSOkSOTQjq8xucz8v3vP8xvf3uTVqPqAnv3VmE2xzNixAjMZg1/\nFJGvdSpo+Hw+/H4/NpvtpM/b7XY2bNgAwOzZs/nggw8oKioCYOPGjWzfvp1Zs2Z15tQi0kckJyeT\nlpaJ12vn6NH6UJcTdhwOMymuSGyYaKpsPetxpy5hmxEZ3YNVniwYDFKxt5k9f60iutbGqKQEvjV3\nCAsW5BEZaT3/E3QzsznA44//RUvfdpG2YVNt8zNERE5kCHayvz5p0iRMJhPvvPMOLpeLpUuXcvfd\nd5OTk8OePXsIBoPceeedvP322x13OhYvXsx999130vPU1X19962wsLAzJYlIL/PPf/6TjRuXM26c\nn2nTtGLNqVavLubv64/gGeAnY+LpOy43tHrZWFWGJxAg0WrnG/HJIVtdytvkp+jTJnzHAwx0RjIy\nN5Frr00nIiL0k9FP9d//PZannvoZra0Wbrnl7yxc+EetTHWRWlp8vPzyLozG0Sxc+GMcDkeoSxKR\nHnTicMmYmNNXD+z0lWjJkiUYjUbS09Ox2+0sXryY2267DeNXF7mf/vSnbNq0iRUrVvD555/z7//+\n7/zrv/4rH374YWdPLSJ9RE5ODgZDNPv314XN3IJwMnp0AvFWG3WHvfg8Jw8vCwaDfFFXFfKQ0eoO\nULyliX0f1BFZY2HkV12MuXOzwjJkAEyc+DnPPfcLLJZWli2bw2efjQl1Sb3OoUMNBIORDByYqZAh\nIqfpdEejndvtpr6+HpfLxYIFC2hububdd98lKiqK5cuXc+ONN3Yc+/3vf5/Dhw+zatWqjs+d2NE4\nUyKS07Wv7jV+/PgQVyKg16MzAoEAjz76KCUl/+SHPxxBcrKz089ZUVEBQFJSUqefKxy8+eaXrNp2\nGMtQI+njo076WlNrK7tqKhmb6OrxkOFrCVC2s4nKPc3Emx2kOiMZM8rFnDmDO4ZJhftr8cknI9iz\nJ4MHHvhHqEvpEV35evzlLwXs3x/D7bc/zIwZMzr9fP2NrhvhRa/HxTvf+/cum7XlcDhwOBzU1NSw\ncuVKXnjhBQKBtjtvxlMufEajUXctRaSD0Whk5MiRVFRsZ+/eqi4JGn3NtGmZFBRWsWtXJXFZdiIS\nv+4SRFgsfCM5tUfr8XkCHN/VxPFdbuJMdi6LTmLUZUlMm5ZJaurpw7vC2ZQpO5kyZWeoy+h1fL4A\nhYXVWK3Zmp8hImfU6aCxcuVK/H4/ubm57N+/n0cffZS8vDy+973vYTKZuOaaa3j88ceJjIxk4MCB\nfPLJJyxZsoQXXnihK+oXkT5izJgxrFv3Idu27WPy5HRt+nWKjIxo8icNpH61l0Of1JJ7fQJme88P\nkfK3Bji+u5nync3EGmzkRSUwfFgS06dnkp4edf4nkD5jz54qfL5IhgzJDttulYiEVqeDRl1dHU88\n8QRFRUXEx8fzrW99i+eeew6TqW199LfffpsnnniC22+/naqqKrKysnj22Wd58MEHO128iPQdI0eO\nJCkpk6NH93PwYC2DB8eFuqSwM316JjsOHKfpoJfClTXkXBfXY2HD0+Cnar+bij3NRAWt5EbEkzs4\nkWuuySQzs28Od62qiiI+vkETxM9i8+ZSbLZU8vPzQ12KiISpTgeN+fPnM3/+/LN+PSkpiT/+8Y+d\nPY2I9HFGo5H8/Hz+/OfdbN5cqqBxBkUtDbyfVki6LYqoPRb2rKgia3IMUands2Ss3xek9nALlYVu\n3OU+4m12hjrjGTYonunTsxg0KKbPdp6OHEnirrt+wowZ23nqqXcVNk5RXt7E0aPNJCWlc8UVV4S6\nHBEJU9pZR0TCxuTJk1mx4n327j1MXZ2HmBjb+R/UTxysr+Wuf66gyuNmUGYMY1pT2H+khkMf1hIz\n1EbKyEhsUZ3fadvvDVBX5KHmsIf6Yg+RBivJdieJLifDL0tk7NiUPh0w2h07lkhVVRRvvTUdQGHj\nFJs3l2K1pjJx4kTsdnuoyxGRMKWgISJhIzo6mrFjx7Nu3QG2bi1l+vSsUJcUFtpDRkWLmyuT03gl\nfxaWaUbWrj3G6k+OUHS0gT37KokYYCVhsJ1IlxVrxPlDRzAQpKXej7u6FXe1j6aqVprKWok0WYmz\n2cmMjiZrYCxjxrgYMSIJh6P/XDImT97D4sW/40c/ekBh4xQej48vvqjAZhvLlClTQl2OiISx/nPV\nEJFeYerUqWzatJYtW3aQnz8Qszk0G8+FizOFDMdXm59On57J8OGJrF9/jB1fVlBR20z1xhaO+how\nOsARZ8ZkM2KxGzGaDQR8QfytQfzeIJ56H556P5agCYfZjMNkJtnsJDrexqDMWC67LJHc3ATi4vrv\n3eopU3YqbJzBF18cJxCIJTd3JGlpaaEuR0TCmIKGiISVIUOGkJExhH379rNnTxUjR/bv1WwinkC9\ncgAAIABJREFULBYiLFYGR8edFDLauVwRfPObucycmc22beUcOlRLUVEDtU0teBr8+OoC+IIBAsEg\nZoMJk8GAyWDAajThiDWTEO/A5YogJSWC5OQIsrJiOva/kJPDhstV2+9DRjAY/GrY1GB1M0TkvBQ0\nRCSsGAwGpk6dypEjX7B5c2m/DxouRwRLpt9IpMV6Wsg4UWSklauvzuDqqzMIBIJUVDRTW9tCc7OP\n5uZWWlsDWK1GbDYzVquJ2FgbyclObDZdBs5nypSd/P3vz5CRURnqUkLuyJF6KiuDDBgwkMsvvzzU\n5YhImNMVRkTCzhVXXMF776Vz9OgBysubcLkiQl1SSCU5Lm4DQ6PRgMsV0e//3bqSQkab9kngV199\nNeZzBF8REYD+PfhZRMKS3W7nyiuvxGpNZfPm0lCXIyJAY6OXPXuqsdvbgoaIyPkoaIhIWJoyZQpW\nawpffFGBx+MLdTk94mB9LS99uYVgMBjqUuQCHDzo4qWXbqS/vFxbt5ZhNCYxevRY4uK0z42InJ/6\nniISlgYMGMCwYSPYvv0Qn31WytVXZ4S6pG514upSiXYH38kZHuqS5By8XjP33vswJSWJ1NVF8PTT\n7/TpieJer59Nm0qw2UYyderUUJcjIr2EOhoiErauv/567PZM1q8vxu3uu12NU5ewnTdoWKhLkvOw\nWn0sWrQUi6WVt9+exrPPfrtPdzY2bizG640lJ2ckubm5oS5HRHoJBQ0RCVt5eXmMGDEWvz+BdeuO\nhbqcbnGufTIkvLUvfdvXw0ZTUysbNhRjs2Uyb968Pr8rvIh0HQUNEQlrN998M3b7QDZtKqOuzhPq\ncrrcs1s3KGT0YqeGjU2bhoa6pC7XFvKTGD16AkOH9r3vT0S6j4KGiIS1rKwsJky4CqMxhU8+ORrq\ncrrcCxOn8+0heQoZvVh72HjyyXe48sp9oS6nS9XUtPDZZ+XYbAO5+eabQ12OiPQyChoiEvbmzp2L\n05nJtm2VVFY2h7qcLpVgd/DM+KsVMnq5KVN2cuedq0NdRpdbs+YoZnMaV145mYyMvr0gg4h0PQUN\nEQl7LpeLyZOnYLWm8/HHR0Jdjki/UF7exI4d1Tidmdx0002hLkdEeiEFDRHpFW644QYiIrLYs6ee\noqKGUJdzScqbmwj0xdnCclbl5bG9doL4xx8fxmrNID9/KklJSaEuR0R6IQUNEekVYmNjmTHjWmy2\ngXz00aFet6ndwfpavrVyGc9sWaew0U/s25fGvHlP9crVqI4erWffviaiorK4/vrrQ12OiPRSChoi\n0mvMnDmT2NhsjhzxcvBgbajLuWAnLmF7tKGe1oA/1CVJDygvj6WhwdHrlr4NBoOsWnUIuz2Ta6+9\njujo6FCXJCK9lIKGiPQaTqeT2bNnY7dnsmpV7+hqnGmfDJtJE7/7g6uv3s3LL7/S6/bZ2LevhqIi\nH3Fx2Vx77bWhLkdEejEFDRHpVaZNm0Zi4hCOHzexaVNJqMs5p0PajK/fy8/fdVLYeO65BaEu6Zw8\nHh//9//ux27PZs6cOTgcjlCXJCK9mIKGiPQqVquV7373uzgcQ/noo6NUVblDXdJZxdrsJNidChn9\nXHvYsFpbGTy4NNTlnNPKlYdpbo5l8ODRTJs2LdTliEgvp6ueiPQ6o0eP5qqrprJ2bTXLl+/jnntG\nYTAYQl3WaeJsdl6fdj02k1kho5/Lz9/FypVPk5ISvnOLDh6sZevWKmJjv8Fdd92FyWQKdUki0sup\noyEivdKCBQtITMyluJiwHkIVa7MrZAhAWIcMj8fH8uX7cDhyuOGGuaSnp4e6JBHpAxQ0RKRXioiI\n4I477ugVQ6hEwt3XQ6YuZ9asWaEuR0T6CAUNEem12odQmUwDWb58X0hXoTpYX8vz2/4bfyAQshqk\n99m9O4Nf//rmkK5G1T5kKjIyR0OmRKRLqZ8vIr3aggUL2LNnD8XF69i0qYQrrxzQ4zUcrK/lzn+u\noLLFTbIjgntyR/V4DdL7tLRYuP/+H1FREUtTk52nn36Hnp5qpCFTItKd1NEQkV4tIiKC22+/PWRD\nqE4MGRNdA7htyGU9en7pvez2Vp577s2Q7rOhIVMi0p0UNESk1wvVEKpTQ8Z/XD1TE7/lopy6z0ZP\nhg0NmRKR7qagISJ9woIFC0hKyuvRVaj+z/ZPFTKk004MG3/60xS2b8/u9nN6PH4NmRKRbtfpoNHQ\n0MDChQvJysrC6XQyadIktmzZctIx+/bt45ZbbiEuLo6IiAjGjRtHQUFBZ08tItLhxCFUq1Ydo7S0\nqdvP+Ysrp3Hn0BEKGdJp7WHj2WeXMGbMwW49VzAY5MMPj9LcHKchUyLSrTodNO69915WrVrFm2++\nyc6dO7nuuuuYMWMGJSVtdxQPHTrEpEmTGDx4MKtXr2bXrl0899xzREZGdrp4EZETjR49munTZ2G1\n5vDXvx6mocHbreeLsdp4cuxVChnSJfLzd/HNb27s9vN8+mk5+/Z5iYsbzj333KMhUyLSbToVNNxu\nN8uWLeP5558nPz+f7OxsFi1axJAhQ3jllVcAeOqpp5g1axYvvPACl19+OVlZWcyaNUttWhHpFrfe\neivDh0+kuTmB5csP0dqq5WZF2hUUVLF+fSVG42Duvff7pKamhrokEenDOhU0fD4ffr8fm8120uft\ndjsbNmwgGAzyt7/9jby8PGbNmkVycjLf+MY3+POf/9ypokVEzsZsNnPfffcRH59LebmNDz7omsnh\nJU2N+LRHhoRAUVFCl0wQLy9v4r33CjEas5k27VpGjdIyzCLSvQzBTl6BJ02ahMlk4p133sHlcrF0\n6VLuvvtucnJyWLNmDampqTidTp599lmmT5/Oxx9/zGOPPcb777/PnDlzOp6nrq6u4+PCwsLOlCQi\nQnl5OW+++QYezy6mTIljwoTkS36uI00NPPz5OsbFJfHkZeMwG7WOhvSMPXuG8JOfLGLmzDU88sh/\nXvI+G83NPt56ay8NDWmMGDGZm266CUNPb9ohIn1OTk5Ox8cxMTGnfb3TV8slS5ZgNBpJT0/Hbrez\nePFibrvtNoxGI4Gv7v7dfPPNLFy4kFGjRvHjH/+YW2+9lcWLF3f21CIiZ+VyubjpprkYjYP45JPj\nHDxYf0nP0x4yqr0eqrwe/KHcwln6nbq6KDweK++9dz2/+c2/XFJnw+8P8sEHh6ivjyMt7TKuv/56\nhQwR6RGdnsGYnZ3NmjVrcLvd1NfX43K5WLBgAdnZ2SQmJmI2m7nsspM3sMrNzeXdd98963OOHz++\ns2X1C+2re+nfKzzo9QgvW7ZsYdiwYfzLv/yAZcve4uOPd5OdnUpSkvOCn+NgfS0/3rCBaq+HK5PT\neCV/liZ+X4KKigoAkpKSQlxJ73PjjUVER/+OH/3oAd5773ocDgdPPfXuRXU2/va3/dTWxpCTM5En\nn3ySAwcOAPpdFQ503Qgvej0u3okjks6ky/r/DocDl8tFTU0NK1euZO7cuVgsFiZMmHDaUrb79u0j\nKyurq04tInJWc+bM4YorpmE0DmLp0t243b4Letzhhjru+ucKKlrcChkSUlOm7GTx4t9hsbTy1lvT\nef75+Rf82M2bS9m6tZbo6BH84Ac/IC4urhsrFRE5WaeDxsqVK/nHP/7BoUOHWLVqFdOmTSMvL4/v\nfe97ADz22GO8++67vPrqq+zfv59XX32Vd999lwcffLDTxYuInI/BYOCuu+5i8ODxNDTE8Ze/FBAI\nnH/8SaLdQVpElEKGhIX2sGG3exk+/OgFPebw4Tr+8Y8jOJ3DueOOu8jO7v6NAEVETtTpoFFXV8dD\nDz1EXl4ed911F/n5+Xz44Ycd63LPnTuXP/zhD/zyl79k1KhRvPzyyyxZsoTZs2d3ungRkQths9n4\nwQ9+QFLSaI4cCfL//t/B865EFWmx8p9T5yhkSNiYMmUnq1Y9xU03bTrvsVVVbt59dw822zBmzbqJ\niRMn9kCFIiIn6/TVc/78+cyff+427l133cVdd93V2VOJiFyyhIQEHnjgAX796wY2b96GzXaEa67J\nOudjIi3WnilO5AIlJZ1/UYOamhZef/1LgsEsxoyZzC233NIDlYmInE5rNIpIv5GTk8N99/2AqKjR\nrF9fxSefXNgQFJHeoq7OwxtvfInXm05e3iTuv/9+jFqOWURCRL99RKRfGTNmDPfeez9RUaNZs+Y4\nGzYUcbC+lme2rKNVG/JJL/T559n86lfzaGjw8sYbX+J2pzJs2FU89NBDp22oKyLSkzTwWET6nQkT\nJuDz+Xjttd/z3iefsaHkIHV+DymOCB4YPjbU5YlcsKYmGw8++ENqaqLYtKmW0aPLGDp0Ig8//DAO\nhyPU5YlIP6eOhoj0SxMnTiT/lmtYnXmYOr+HPHsCdw0bFeqyRC5KRISHRYv+iNHoZceOb7N37zM8\n/PAjREREhLo0EREFDRHpnwoqC3hs92O4TW7SWlIY/kU6W/67NNRliVyU+noP+/a9xdSpP8dk8vHZ\nZ1fw9NNRl7SDuIhIV1PQEJF+adGaRZQ1ljF90HRen/kmcZFj+Oc/y1mz5uh5l74VCQe1tS289toO\nmppcTJli4Z13vFit8B//Adu2hbo6ERHN0RCRfuo/b/pPsmKyWDR1EU6Lk0hbJK+//kc++eQLfL4A\n11yTicFgCHWZImdUXe3m9de/xOMZQE7ORBYuXEhEhBOnExobYaymGolIGFDQEJF+KdIayS+u/UXH\nf0+cOBGLxcIf//g7Nmz4Arfbx5w52ZhMavxKeCkubmDp0t20tg4kL28SDz30EE6nE4A5c0JcnIjI\nCXQFFRH5yvjx47n//geJjR3H9u0e3nxzJ01NraEuS6TDl18e57XXduL3D2bkyCk88sgjHSFDRCTc\nKGiISJ93qOYQHp/ngo4dM2YMP/3pY6SmTqSkJIo//GEb5eVN3VyhyLkFg0E++ugw7713GLt9FFOn\nzuWRRx7Bbrdf0OP37UMTxEWkxyloiEifVlBZwFWvXcX8v8y/4LCRnZ3Nk08+SW7uVDyeLP74xy8p\nKKjq5kpFzszj8bF06W42bqwnOnoc3/nOPdxxxx2YzRc2+vmTT2DMGHj4YYUNEelZChoi0mcdbjzM\ntDemUdZYRlNrE/6g/4IfGxcXx6OPPsrkyTdgsQznnXf288knWpFKelZ1tZtXX/2CQ4esJCdfwcKF\n/8r06dMvaqGC5mbw+WDxYoUNEelZChoi0icdbjzMA58+0LGE7YrbVuC0XNxYdovFwj333MOtt95F\nVNRY1qyp5i9/KcDrvfDAInKpDh6s5Q9/+IKGhjSys/N54oknycvLu+jnmT0bli8Hq7UtbPzylxkK\nGyLSIxQ0RKTPOVB9gAc+fYAqT9Ulh4x2BoOBmTNn8qMfLSQx8Rvs22fktde+oK7uwoZhiVysYDDI\np5+WsGRJAUZjHuPHX8fjjz9OcnLyJT/niWHjz3928eKL6V1YsYjImSloiEifkxqVyuCowYxPGN+p\nkHGiUaNG8cQTT5KZOZmammR+//vtHD1a3wXVinzN5wvwwQeFfPhhKU7n5dxwwwJ++MMfXvCk73Np\nDxtOp5+xYxu7oFoRkXPTPhoi0uc4LU5+Nf5XHR93ldTUVJ544gleffVVduzYyOuv72bKlDQmT07X\nfhvSaeXlTSxfvo/jx23ExU3g7rvvYcKECV16jtmz4f33dxAbq+F/ItL9FDREpE+ymzp/B/hMIiIi\nePjhh/mv/0pj1aq/s3ZtIXv2bGfevGG4XBHdck7p2wKBIBs2FLF6dREWSxYZGcN54IEHyMzM7Jbz\nKWSISE9R0BARuUhGo5Fbb72VkSNH8uabb1JWtpvf/34HU6YMUHdDLsrXXQwzTudYpkyZwbe+9a0u\nGSolIhJquhqKSK9WUFnAnX+9kxZfS4+fOy8vj0WLFjFjxq04nWNZu7aeV1/drg3+5LwCgSDr1h3j\n97/fQXV1ChkZU/jxjx/j9ttvD0nIWLUKfvpTLX0rIl1LHQ0R6bUKKguY+vpUypvKyYzJ5OfTf97j\nNdjtdr773e8yduxYdTfkgoRbF6O2Fm69te1vjwdeegkuYpsOEZGz0hVQRHqlE0PGNYOu4Ymrnwhp\nPepuyPmEWxejXWws/OlPX++zoU39RKSrqKMhIr3OqSHjg9s+6NLVpS6VuhtyNuHWxThV+9K3N9/c\nFjZAnQ0R6Txd9USk13l+/fNhFzJOdHp3o4HFi7fy5ZcVBHWruF+pr/fwwQeF/O534dXFOJMTN/X7\nwx9g165QVyQivZ06GiLS6/zuht+RGZPJzyb/LOxCRrsTuxtLly6lqGgvy5YdYsOGY8yYMYjBg2Mx\n6HZxn+V2+1i//hibNpVhMKQQHX0F+fnTuOWWW8IuYJyoPWwAjBgR2lpEpPdT0BCRXsdutvO/pv2v\nUJdxQdq7Gxs3buSDDz6gquoAb799gMxMKzNmDCI9PSrUJUoX8nr9bNpUwvr1Rfj9idjtYxk/fiJz\n584lJSUl1OVdkNmzQ12BiPQVChoiIt3MZDJx9dVXc8UVV7B69Wr+8Y9/UFp6kD/+cTe5uVHMmJFF\nYmJ4dmbkwgQCQbZtK2f16iO43dHY7ZczatTl3HLLLWRlZYW6PBGRkFDQEJGwdqD6AKlRqWE7ROpi\nWK1WZs6cydVXX82HH37IRx+t4tChw7z88g7GjElg6tSBREfbQl2mXIRgMMju3VV8/PFhamut2O2X\nkZc3nHnz5pGXl9enhsd9+WXbcKo+9C2JSDdT0BCRsNW+utTw5OGsuG1FnwgbAE6nk3nz5jFt2jT+\n9re/sX79J3z55RG++OJzvvENFxMnDlDgCHPBYJDCwhpWrz5CWVkQu30w2dnDmDt3LuPGjetTAQPg\n73+HefPg/vvhN79R2BCRC6OgISJh6cQlbIczPNTldIvY2Fhuv/12rr32Wt5//302b97Ili3H+PTT\nz8nNjWXChFQGDYrpc29ae7Pm5la2bStn8+ZS6upM2GwZDBgwmBtuuIHJkydjMplCXWK3+u1v2/5W\n2BCRC9Hp5W0bGhpYuHAhWVlZOJ1OJk2axJYtW8547P3334/RaORXv/pVZ08rIn3YiSFj+qDpfaqb\ncSYul4v77ruPp556hkmTbiU6+koOHoxhyZIDLF68lU8/LaGlxRfqMvutYDBIUVEDy5bt5Ve/2sLq\n1U14vblkZs7g29++n2effZYpU6b06ZAxZw789a9tS9/+9rfwyCPa1E9Ezq/THY17772XnTt38uab\nb5Kens6SJUuYMWMGu3fvJi0treO4//qv/2Lz5s2kpaXp7pyInNWhmkP9KmScKCsri/vvv5/a2lrW\nrVvHunXrqKo6yqpVJXz88RFGjkzkG99IJSUlMtSl9gter5+dOyv47LNSysp82GypREQMZsSIy5ky\nZQojRozAaOw/21G1h41589rChs0GL7wQ6qpEJJx1Kmi43W6WLVvGsmXLyM/PB2DRokWsWLGCV155\nhZ///OcAHDlyhIULF/Lxxx8za9aszlctIn3WgOgBXJF+BY3exn4VMk4UGxvLjTfeyJw5c/jiiy9Y\ns2YNe/Z8yc6dZXz++S4yMuxMmJDKZZclYjb3nze6PaWqys3mzaVs21aOzxeN1ZpJSko6kydPJj8/\nn6SkpFCXGDLtYeO734WZM0NdjYiEu04FDZ/Ph9/vx2Y7edKi3W5n/fr1Hcfcdttt/I//8T8YNmxY\nZ04nIv2A1WTlL/P/gi/g65ch40Qmk4mxY8cyduxYSktLWbt2LRs3bqSysojly0v5xz8OMnJkEsOG\nxZOZGaPQ0Ql1dR727q1iz54qDh5swmp1YbONITc3j6lTpzJu3DgsFkuoywwLc+bAoUMQGxvqSkQk\n3BmCwc6Nspw0aRImk4l33nkHl8vF0qVLufvuu8nJyWHPnj089dRT7Nq1i+VfbTU6aNAgHnroIX7y\nk5+c9Dx1dXUdHxcWFnamJBGRPsvr9bJr1y4+//xzysqOEgzWAHVYrR6ysqIYMiSG7Oxo7Hat9XEu\nwWCQ48fd7N9fx4ED9ZSXezEYojEYYrBYEhgxYiRjxowhNTU11KWKiIStnJycjo9jYmJO+3qnr0RL\nlizhnnvuIT09HZPJxLhx47jtttvYunUra9as4Y033mD79u0nPaaT2UZEpN+yWq2MGTOGyy+/nNLS\nUvbt20dhYSEVFSUUFtazb18tBkMRAwY4GDIkhsGDY4iL01K5AD5fgKNHGzlwoI4DB+poaDBiMMRg\nMAzAbo8jOzubnJwchg4dit1uD3W5IiK9Xqc7Gu3cbjf19fW4XC4WLFhAU1MTEyZM4N/+7d9Omizn\n9/sxGo2kpaVx9OjRjs+f2NE4UyKS07Wv7jV+/PgQVyKg1+NSFFQW8D9X/09em/sakdauneDc316P\nyspKduzYwRdffMG+fXvxeCppba3G56siMdHCsGHxDBuWQFpaZI8PsaqoqAAIydyGxkYvhYU17N1b\nxYEDtfj9EVgsCZjNCSQkpDJ69GhGjRrFsGHD+s3QqO762Vi+HNatg1/+UkvfXqj+9nsq3On1uHjn\ne//eZb11h8OBw+GgpqaGlStX8sILLzB37lzmz5/fcUwwGGTmzJl85zvf4fvf/35XnVpEeqGCygKm\nvTGNssYysmKz+D/X/p9Ql9SrJSYmMn36dKZPn05zczO7du1ix44d7Nixg8bGCjZvrmLjxv0YDG6S\nk52kpUUyYEAUqamRJCc7+8T8jsZGL8XFjZSWNlJS0kBpaSP19QHM5lgslgTs9hwGDszuCBcDBw7U\nKohdpLIS7rgDGhuhtVX7bIhIm04HjZUrV+L3+8nNzWX//v08+uij5OXl8b3vfQ+TyXTaHSyLxUJK\nSspJY7pEpH85MWRMHzSdZ6Y+E+qS+hSn08mECROYMGECfr+fwsJCduzYwa5duygtLaa+vomamkZ2\n7KjH7y/GYGjpdeHj7KEiEqMxCrPZhck0GJcrlsGDBzN69GhGjhxJfHx8qEvvkxIT4d13v176FhQ2\nRKQLgkZdXR1PPPEERUVFxMfH861vfYvnnnuuT29cJCKX7tSQ0V+XsO0pJpOJ3NxccnNzAWhpaeHo\n0aMcPXqUI0eOcOTIEcrKSs4aPuLi7ERFWYmKshIZaSU6uu3vqCgrDoe5WzoCPl+AhgYvjY1eGhq8\nHR/X17d9XFHRdNZQMXDgQDIzMzv+Tk5OVteih5y6zwYobIj0d50OGvPnzz9peNT5HDp0qLOnFJFe\n7LebfquQEUJ2u52hQ4cydOjQjs+dPXw0U1fXQiDgJRDwEgw2f/V323+bTP6O0NEeRBwOM0ajoeOP\nyWSgvr4egwGio70EAkECgSB+f5BAIIDPF6Sx8eRQ4Xb7MRisGAxWjMa2P20fR2MwWDGZnAoVYerE\nsPGf/wkPPQQawCDSf2n9QxHpUS/OepEB0QNYeOVChYwwcbbwUVRURE1NDXV1dR1/amtrOz5ubm7C\n7/dSU+Oluro9jPiAIMFgAAgCQerrPUCQ6GgbYAAMGAzGrz42YTQ6O0KF2WwlNtZKbGwsMTExJ/2J\njY0lOjoal8ulUBHG2sNGZKRChkh/p6AhIj3KYrLw5NVPhroMOQ+73c6QIUPOeYzX6+0IH/X19dTW\n1tLS0kIgEMDv9+P3+wkEAhQWFhIMBsnJycFoNGIymTCZTB0fR0dHnxQoIiMjT1qtUHqfOXNCXYGI\nhAMFDRERuSRWq5WkpKTzLlurJSNFRPon3TISkW5TWFVIXUvd+Q8UkX5h61bQnr0i/YeChoh0i4LK\nAvJfz2fmWzMVNkSEP/8ZrrgCHn5YYUOkv1DQEJEud+ISthHWCCym/rHjsoicXVQUmEyweLHChkh/\noaAhIl1K+2SIyJnMng3Ll4PVqrAh0l8oaIhIlzlWd0whQ0TO6tSw8fjjoa5IRLqTgoaIdJm0qDSu\nGXSNQoaInFV72EhMhLlzQ12NiHQnLW8rIl3GZDTxxs1v4PV7cVgcoS5HRMLU7Nlw6FDbpn4i0ncp\naIhIlzIZTTiMChkicm4KGSJ9n4ZOiYiIiIhIl1PQEJFLUlBZwA1/uoFqd3WoSxGRPuKtt2DhQq1G\nJdJXaOiUiFy0E5ewfWbNM7w0+6VQlyQivVxZGdx3H7jd4PfDSy+BwRDqqkSkM9TREJGLcuo+Gc/P\neD7UJYlIH5CSAu+9p302RPoSBQ0RuWDajE9EupM29RPpWxQ0ROSCvbbtNYUMEelWJ4aNJUvgyJFQ\nVyQil0pzNETkgj0/43lSI1O5f/z9Chki0m1mz4b332/b1C8rK9TViMilUtAQkQtmNBj58cQfh7oM\nEekHZs0KdQUi0lkaOiUiIiIiIl1OQUNEzmhv5V4qmytDXYaIyEk2btQEcZHeQkFDRE5TUFnAlNen\nMP2N6VQ1V4W6HBERAF57DSZNgkceUdgQ6Q0UNETkJAWVBUx9fSrlTeUkRyTjsDhCXZKICNC214bV\nCr/9rcKGSG+goCEiHU4MGdcMuoYPbvtAq0uJSNiYMwf++leFDZHeQkFDRAAoaShRyBCRsHdq2Hj6\n6VBXJCJno6AhIgCkRKYwL3eeQoaIhL32sJGWBvPnh7oaETkb7aMhIkDbHhkvX/8yXr8Xu9ke6nJE\nRM5pzhzYvx8cmkYmErbU0RCRDkaDUSFDRHoNhQyR8KagISIiIiIiXa5LgkZDQwMLFy4kKysLp9PJ\npEmT2LJlCwA+n4+f/exnjB49msjISNLS0vjud7/LsWPHuuLUInIJCioLmPHmDMoby0NdiohIl/qP\n/9BqVCLhokuCxr333suqVat488032blzJ9dddx0zZsygpKSEpqYmtm3bxtNPP822bdt4//33OXbs\nGLNmzcLv93fF6UXkIhRUFjDtjWl8fOhjFq1ZFOpyRES6zLFj8JOfwEsvKWyIhINOTwZ3u90sW7aM\nZcuWkZ+fD8CiRYtYsWIFr7zyCj//+c9ZuXLlSY/5/e9/z/DhwykoKGD48OGdLUFELlDW1uuLAAAN\nHUlEQVR7yChrLGP6oOn8euavQ12SiEiXyciAZctg3ry2pW8BfvMbMBhCW5dIf9XpjobP58Pv92Oz\n2U76vN1uZ/369Wd8TF1dHQBxcXGdPb2IXKBTQ8aK21ZoCVsR6XO0qZ9I+DAEg53/8Zs0aRImk4l3\n3nkHl8vF0qVLufvuu8nJyWHPnj0nHev1epk2bRpJSUksX7684/Pt4QOgsLCwsyWJyCn+sO8PvFr4\nKuMTxvPvE/4du0mrS4lI37VhQwyPPjqYyEg/b721m+Tk1lCXJNLn5OTkdHwcExNz2te7JGgcPHiQ\ne+65h7Vr12IymRg3bhw5OTls3bqV3bt3dxzn8/n4zne+w549e1i7du1JHQ0FDZHuFQwGee/oe9yQ\nfoNChoj0Cxs3RuNyeRk8uCXUpYj0ST0SNNq53W7q6+txuVwsWLCA5uZmVqxYAbSFjNtuu41du3ax\nZs0akpOTT3rsiUHjTIXK6dpX9ho/fnyIKxHQ6xFu9HqED70W4UWvR/jQaxFe9HpcvPO9f+/SfTQc\nDgcul4uamhpWrlzJ3LlzAWhtbWXBggXs3LmT1atXnxYyRERERESkb+n0qlMAK1euxO/3k5uby/79\n+3n00UfJy8vje9/7Hj6fj/nz57NlyxZWrFhBMBikrKwMgNjYWOx2DeEQEREREelruqSjUVdXx0MP\nPUReXh533XUX+fn5fPjhh/+/vXsPqbv+4zj+Oue4eUkzknnbAY/HyRRXUUJUhrmYrkg2Rlu1FaVi\nY1SSLBbojIw2mxTSNisMarnBJvvDPwZFO4PcyokwZVEmWSNhO3MeJMx5m87j5/fHj9+h89uYpl+v\nPR8gzPP9nPP9HN68Drx2vucoh8Mhr9erU6dO6dq1a8rMzFRiYmLg5+TJk1acHgAAAMAiY8k7Gtu2\nbdO2bdtue8zlcmlyctKK0wAAAABYIiz9jAYAAAAASBQNAAAAAHOAogEAAADAchQNAAAAAJajaAAA\nAACwHEUDAAAAgOUoGgAAAAAsR9EAAAAAYDmKBgAAAADLUTQAAAAAWI6iAQAAAMByFA0AAAAAlqNo\nAAAAALAcRQMAAACA5SgaAAAAACxH0QAAAABgOYoGAAAAAMtRNAAAAABYjqIBAAAAwHIUDQAAAACW\no2gAAAAAsBxFAwAAAIDlKBoAAAAALEfRAAAAAGA5igYAAAAAy1E0AAAAAFiOogEAAADAchQNAAAA\nAJajaAAAAACwnCVFY3BwUKWlpXK5XIqIiFBWVpba2tqC1lRWVmr16tWKiIjQ+vXr1dnZacWpAQAA\nACxClhSN4uJinTlzRkePHlVHR4fy8vK0YcMG9fT0SJKqq6tVU1Oj2tpaXbhwQbGxscrNzdXQ0JAV\npwcAAACwyMy6aIyOjqqxsVEHDhxQdna23G633n33Xa1Zs0afffaZJOnjjz9WWVmZtmzZooyMDNXX\n12twcFDHjx+f9RMAAAAAsPjMumhMTEzI7/crNDQ06PawsDCdP39e3d3d8vl8ysvLCzqWnZ2tlpaW\n2Z4eAAAAwCJkM8aY2T5IVlaWHA6HGhoaFBcXpxMnTqigoECpqan68ssvlZWVpcuXL8vpdAbuU1RU\npJ6eHn377beSpIGBgdluAwAAAMACiI6OvuU2Sz6jcezYMdntdjmdToWFham2tlbbt2+XzWa74/2m\nOg4AAABgabKkaLjdbp09e1bDw8Pyer1qbW3V+Pi4UlJSFB8fL0ny+XxB9/H5fIFjAAAAAJaXECsf\nLDw8XOHh4erv75fH49GHH36o5ORkxcfHy+PxKDMzU5J048YNNTc366OPPgrc93ZvtwAAAABYmiwp\nGh6PR36/X2lpabp06ZL27Nmj9PR0FRYWSpJKS0tVVVWltLQ0paamat++fYqKitKOHTusOD0AAACA\nRcaSojEwMKCysjJ5vV7de++92rp1q/bv3y+HwyFJevvttzU6OqrXX39d/f39euSRR+TxeHTXXXdZ\ncXoAAAAAi4wl3zoFAAAAAH9nyYfBMbcmJiZUXl4ut9ut8PBwud1uvfPOO/L7/YE1BQUFstvtQT+P\nPfbYAu56+RocHFRpaalcLpciIiKUlZWltra2oDWVlZVavXq1IiIitH79enV2di7Qbpe/qeZBNubG\n999/r02bNsnpdMput6u+vv6WNVPlYGxsTCUlJVq1apUiIyO1efNmXb16db6ewrJixTxycnJuyQqX\nOP9zU82isbFRGzduVGxsrOx2u86dO3fLY5AN61gxD7IxcxSNJaCqqkp1dXU6fPiwurq6dPDgQX36\n6af64IMPAmtsNptyc3PV29sb+Pnmm28WcNfLV3Fxsc6cOaOjR4+qo6NDeXl52rBhg3p6eiRJ1dXV\nqqmpUW1trS5cuKDY2Fjl5uZqaGhogXe+PE01D7IxN4aHh3X//ffr4MGDCg8Pv+XryqeTg9LSUjU2\nNqqhoUE//PCDrl+/rvz8fE1OTs7301nyrJiHzWZTUVFRUFbq6urm+6kseVPNYmRkRI8//rhqamok\n3f6r/smGdayYB9mYBYNFLz8/3xQUFATd9vLLL5v8/PzA76+88krQ75gbIyMjJiQkxJw6dSro9szM\nTFNRUWGMMSY+Pt5UVVUFjo2OjpqoqChTV1c3r3v9N5jOPMjG3IuMjDT19fWB3ycnJ6fMwV9//WVW\nrlxpjh8/Hlhz5coVY7fbzenTp+dv88vQTOZhjDE5OTnmjTfemNe9Lnf/P4u/6+vrMzabzZw7dy7o\ndrIxd2YyD2PIxmzwjsYS8PTTT+u7775TV1eXJKmzs1NNTU165plnAmtsNpuam5sVFxentWvXaufO\nnerr61uoLS9bExMT8vv9Cg0NDbo9LCxM58+fV3d3t3w+n/Ly8oKOZWdnq6WlZb63u+xNNY//IRvz\nazo5aG9v182bN4PWOJ1OpaenkxWL/ZPXpYaGBq1atUrr1q3Tnj17eCd2AZCNxYlszIylf0cDc+O1\n116T1+tVenq6QkJCNDExoYqKCu3atSuw5qmnntKzzz6r5ORkdXd3q6KiQk8++aTa29u1cuXKBdz9\n8hIVFaVHH31U+/bt07p16xQXF6cTJ06otbVVqamp6u3tlSTFxcUF3S82NjZwKQ+sM9U8pP8W9a1b\nt5KNeTSdHPT29srhcCgmJiZoTVxc3C1/4BWzM93XpR07dsjlcikxMVEdHR0qKyvTTz/9pNOnT8/r\nfv/tyMbiQzZmjqKxBBw6dEhHjhxRQ0ODMjIydPHiRb355ptyuVwqKiqSJD3//POB9RkZGcrMzFRS\nUpK+/vprbdmyZaG2viwdO3ZMRUVFcjqdcjgcyszM1Pbt29Xe3n7H+93uuk/M3lTzIBuLCzlYXP4+\nj1dffTXw74yMDKWkpOjhhx/WxYsX9eCDDy7E9oBFgWzMHJdOLQH79+9XeXm5nnvuOWVkZOill17S\n7t27gz4M/v8SEhLkdDp16dKledzpv4Pb7dbZs2c1PDwsr9er1tZWjY+PKyUlRfHx8ZJ0y/86+Xy+\nwDFY607zuB2yMfemk4P4+Hj5/X79+eefQWt6e3vJisVm+rr00EMPyeFwkJV5RjYWP7IxfRSNJcAY\nI7s9eFR2u13mDn8Cpa+vT1evXlVCQsJcb+9fKzw8XHFxcerv75fH49HmzZuVnJys+Ph4eTyewLob\nN26oubmZr1SdY7ebx+2Qjbk3nRxkZmZqxYoVQWu8Xq9+/fVXsmKxmb4u/fzzz/L7/WRlnpGNxY9s\nTJ+jsrKycqE3gTv7/fff9dVXXyktLU0rVqxQU1OT9u7dqxdeeEF5eXkaHh5WeXm57r77bk1MTOjH\nH39UcXGxJicnVVtby3XoFvN4PPrtt98UEhKitrY2vfjii0pMTNShQ4dkt9vl9/t14MABrV27Vn6/\nX7t375bP59Pnn3/OLObAneYxMjJCNubI8PCwOjs71dvbqy+++EL33XefoqOjdfPmTUVHR0+Zg7Cw\nMF27dk2ffPKJHnjgAQ0MDGjXrl265557VF1dzSVW/9Bs5/HHH3/o8OHDioyM1Pj4uFpaWrRz504l\nJSXp/fffZx7/wFSz6O/vV1dXly5fvqz6+nplZWXJbrfLZrMpMjKSbFhstvMgG7O00F97hakNDQ2Z\nt956y7hcLhMeHm7cbrfZu3evGRsbM8b892sKN27caGJjY83KlStNUlKSKSwsNF6vd4F3vjydPHnS\npKSkmNDQUJOQkGBKSkrM9evXg9ZUVlaahIQEExYWZnJycswvv/yyQLtd/u40D7Ixd5qamozNZjM2\nm83Y7fbAvwsLCwNrpsrB2NiYKSkpMTExMSYiIsJs2rSJ2czQbOdx5coV88QTT5iYmBgTGhpq1qxZ\nY0pLS01/f/9CPJ0lbapZHDly5LbH33vvvcBjkA3rzHYeZGN2bMbc4fobAAAAAJgBPqMBAAAAwHIU\nDQAAAACWo2gAAAAAsBxFAwAAAIDlKBoAAAAALEfRAAAAAGA5igYAAAAAy1E0AAAAAFjuP3QAu37M\nYCOIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1588fd160>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see how the second radar measurement altered the covariance. The angle to the target is orthogonal to the first radar station, so the effects of the error in the bearing and range are swapped. So the angle of the covariance matrix switches to match the direction to the second station. It is important to note that the direction did not mearly change; the size of the covariance matrix became much smaller as well.\n",
      "\n",
      "The covariance will always incorporate all of the information available, including the effects of the geometry of the problem. This formulation makes it particularly easy to see what is happening, but the same thing occurs if one sensor gives you position and a second sensor gives you velocity, or if two sensors provide measurements of position."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise: Can you Kalman Filter GPS outputs?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the section above I have you apply a Kalman filter to 'GPS-like' sensor. Can you apply a Kalman filter to the output of a commercial Kalman filter? In other words, will the output of your filter be better than, worse than, or equal to the GPS's output?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Think your answer here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Commercial GPSs have a Kalman filter built into them, and their output is the filtered estimate created by that filter. So, suppose you have a steady stream of output from the GPS consisting of a position and position error. Can you not pass those two pieces of data into your own filter?\n",
      "\n",
      "Well, what are the characteristics of that data stream, and more importantly, what are the fundamental requirements of the input to the Kalman filter?\n",
      "\n",
      "Inputs to the Kalman filter must be *Gaussian* and *time independent*. The output of the GPS is *time dependent* because the filter bases it's current estimate on the recusive estimates of all previous measurements. Hence, the signal is not white, it is not time independent, and if you pass that data into a Kalman filter you have violated the mathematical requirements of the filter. So, the answer is no, you cannot get better estimates by running a KF on the output of a commercial GPS. \n",
      "\n",
      "Another way to think of it is that Kalman filters are optimal in a least squares sense. There is no way to take an optimal solution, pass it through a filter, any filter, and get a 'more optimal' answer because it is a logical impossibility. At best the signal will be unchanged, in which case it will still be optimal, or it will be changed, and hence no longer optimal.\n",
      "\n",
      "This is a difficult problem that hobbyists face when trying to integrate GPS, IMUs and other off the shelf sensors. It is too early in the book to try to address this problem, hence the 'PS' in the this section.\n",
      "\n",
      "But let's look at the effect. A commercial GPS reports position, and an estimated error range. The estimated error just comes from the Kalman filter's $\\mathbf{P}$ matrix. So let's filter some noisy data, take the filtered output as the new noisy input to the filter, and see what the result is. In other words, $\\mathbf{x}$ will supply the  $\\mathbf{z}$ input, and  $\\mathbf{P}$ will supply the measurement covariance $\\mathbf{R}$. To exaggerate the effects somewhat to make them more obvious I will plot the effects of doing this one, and then a second time. The second iteration doesn't make any 'sense' (no one would try that), it just helps me illustrate a point. First, the code and plots."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(124)\n",
      "xs,zs = simulate_acc_system(R=R, Q=Q, count=80)\n",
      "\n",
      "# Filter measurements\n",
      "kf0 = SecondOrderKF(R, Q, dt=1)\n",
      "fxs0, ps0 = filter_data(kf0, zs)\n",
      "\n",
      "\n",
      "# filter again, using P as error\n",
      "kf1 = SecondOrderKF(R, Q, dt=1)\n",
      "fxs1 = []\n",
      "ps1 = []\n",
      "\n",
      "for z, p in zip(fxs0[:,0], ps0):\n",
      "    kf1.predict()\n",
      "    kf1.update(z, R=p[0])\n",
      "    fxs1.append(kf1.x)\n",
      "    ps1.append(kf1.P)\n",
      "    \n",
      "# one more time to exagerrate the effect\n",
      "fxs1 = np.asarray(fxs1)\n",
      "ps1  = np.asarray(ps1)\n",
      "\n",
      "kf2 = SecondOrderKF(R, Q, dt=1)\n",
      "fxs2 = []\n",
      "for z, p in zip(fxs1[:,0], ps1):\n",
      "    kf2.predict()\n",
      "    kf2.update(z, R=p[0,0])\n",
      "    fxs2.append(kf2.x)\n",
      "    \n",
      "fxs2 = np.asarray(fxs2)\n",
      "\n",
      "plot_kf_output(xs[0:30], fxs0[0:30], zs[0:30], title='KF')\n",
      "plot_kf_output(xs[0:30], fxs1[0:30], zs[0:30], title='1 iteration')\n",
      "plot_kf_output(xs[0:30], fxs2[0:30], zs[0:30], title='2 iterations')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LsAfM3r17CQoK4sSJE1hYWDB+/HhUNa6SknFDXyfAt5WxIzUPjz1W8L/VkiW6c926GT/B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\n/9dkuXK/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe158941240>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+RUIIIYzlwIEDDBw4kNDQUEA3nHnOnDm4uOTgQ39kpC55cXLK1+QlJv4BR84H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IAAAg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\nn6u+li1b8ttvv3H69Gm++OIL/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       "text": [
        "<matplotlib.figure.Figure at 0x7fe15897cc88>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8vb2xtrambNmy9O3bl2vXruW4TmJiIhMnTqRKlSpYWVlRvnx5+vfvz82bN/Ns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\nPzHK/ztFgfydXDS8PoMqr0w0GEeeffrpp2zfvp1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mTJjAb7/9BkCtWrXw9vamRYsWOo5M\nw2JjYcMGAEJ79KDivHliwfiZM2CivYkGtlZ2vOM1iDfrduXguR2cuX6Y1Nf6xgDcf3qDb/8URR+6\n9hmA4Y7hFdzdwGv8uH8xUXERKvvNTS3o23Y0jd1b6ygySZIMjUxgJEnSL998I7ajRoEW1jL816OQ\ne3j/MYeYuEiV/e4V6/NRlylYmGv3ab42JCUlsXz5cmbNmkVMTAy2trbMmTOHjz/+GHNjHAHYtg3C\nw6FxY2Lq1KHy9OmiZO/164WyjqpEMQf6th1N6/rvsP/sFi7fOZXpmOv+F7nhf4kGbq3o3PQDSttn\nLiVsrJRKJccu/8Een58yJXgO9k581GUKLm9U1lF0kiQZIpnASJKkP+7ehV27wMICxo/X/uUC/Vi3\nZz4JiXEq++tX92JAh08NciqLj48Po0aNws/PD4BevXqxbNkyXFxcdByZliiVsGqV+HzsWACi69TB\nMjhY9F4prEIQgGPJsgzu9DltG7zH3tObM1XWUqLk4q0TXLnjQ/OaHejYuDfFbUsWWnwFFhMDNjZ5\n6skUnxjHliMruXvlOO//eYNnjrYcaSdKdHu4NmBgxwnYWBnmCKckSbojF/FLkqQ/SpcWTSXHj8+x\nW7cm+D24wJrf52RKXprX7MDAjhMMLnl5/vw5Q4cOxcvLCz8/PypXrsz+/fv59ddfjTd5Sbd6NYwY\nAX36ACKBAUQCowPlHSszuscMPu45D1fnGpleT0lN5p9/9zPnx1HsPb1Z/WaYutSokSh2ERKi9ltC\nwp+wZPskfO+epmR4HE3PP6LB5ScoUNCpyftieqZMXiRJygc5AiNJkv4oWRJmzND6ZS7eOsHmwytI\nTU1R2d+uwXt0a/GhQfVBSU1N5YcffuCLL74gLCwMCwsLvvjiC7744gusrYtA/wyFApo0ER9pouvW\nFZ/4+OgoKKGaS00m9P4aP/8L7D29maAXj1ReT0xO4NCFnZz69wDtGr5HqzpdtDplMVWZSkJiPAlJ\ncZgoTDAzM8fc1BIzU7Pc/81bWorRrmvXoEzu09+u3jvD5sMrMh4QFI+MByC6hC0juk8zikawkiTp\njkxgJEkqUm4HXeL8gwMoUars79ZiIO3tPOHnn6FBg1fNLfXJZ5/B99+LRK90aSItLTl95w7Rz58T\nBrRr145Vq1ZRvbqYooNSCYmJ4uazCImrXFmsnwoIgKdPoWxZncWiUCqpNXIaNStU4OLEj9l3fjth\nkc9Ujklvhvm37x46NXmfph5tMTXN/Os5KTmRuIRY4hJjiE+IITYhhvjEWLEvIYb4xBjiEmLSjknb\nl5C2LzGW+MQ4lP9ZgwKgQCGSGTNLzE3NMTezEB+mYmtmZk5ruyQ8gEs7V3HP9H7GcWZmFlikHW+W\ndvzjZ/f5+8qfKtcoHiVKW1es2xIrmbxIklRAMoGRJKlIUCqVXHt8iiuP/lbZr0BBnzajaFGrI0yc\nCMuWwYIF+pnATJokFqtv3AgBARQH3gYaKxSU3bqVPn36qD5Jj4yEEiWgWDFwcBBT9EqXBhcXkQj9\nV2oqhIWJYwyZqSns3QtVq6o1WqBVT57AkSMoHB1p9MMP1HNrxWm/Qxw8tyNTNa70ZphHLu2idPEy\nqklIYizJKUlaCVGJkqTkRJKSE7M95o1i8XgASb6X8fHI+zU8LJwBX6wqyMX6kiQVnExgJEkqEvb4\n/JwpeTExMeXDDuNpUKOl2OGRdmd2/XrhBqcmpZMTu1u1YtG+faQ8e4ajQsH77dvTs3t3+vbtm/kN\n4eFgZgbR0eIjIEDsL18+6wuEhEC5crB7N7zzjva+kMLg5aXrCIT798W2ShUAzEzNaVWnC03c2/C3\n716OXtpNfGKsylteRITwIkL9tSaF4Wlab6SyQZG5HKnK1MSM91oNpc6dfWKHlte2SZJUNMgERpIk\n3YqMhH/+gc6d81TdKC8u3DrBkUu7VPaZm1owtMtk1bn46aMuN25oJY6CePDgAWPGjOHgwYMANG3a\nlHne3tRNX++RFVdXMYUsMhJevIDnz8VHSkrWx/v5iWlnkydDly4i+dFXfn5gawuVKuk6kpz9J4FJ\nZ2lhTcfGvfGq1ZEjl3Zx0nd/pmaY2mBhboWVhTXK1FSSUpJISk4kJTU51/cFOdsBYBmfLP6NqPF/\n1d62FEO7TKaSsxsMdBCNaVu2LPDXIEmSpMe/nSRJKhK8veGLL2D4cFi3TuOnfxEZwq/H16rss7Kw\nYWT3aVQp959pYu7uYnvzprjJNzXVeDx5lZSUxJIlS5g9ezbx8fGULFmSr7/+mmHDhmGiTpNGhUKs\nB7G3h8q5TN956y1xo33nDvz0EwwdqpGvQSsmToQjR2DnTnjvPV1Hk71sEph0ttbFecdrMG/W7caB\nc9s5e/1Ipl4p6UxMTLG2tMXawkZla2Vpm/FnK0sbbCxtsbJI22f56lgrC5ss19akpqZkJDNJyQkk\nJYvPk1MSSUybWpacksiV9uNIsLakd3ICSSmJWR+XnEhSSiKl7Bxp17AnxW1LiIv8p9CCJElSQcgE\nRpIk3YmJgSVLxOe9e2v89KmpKfx88FuVKTomClPGvTeHCk5VM7+hRAmx4PvpU/D3F2sodOj06dOM\nHDkyo6fLgAEDWLJkCY6Ojtq5oLk5zJkD/fuLctb9++tnAYA7d+DwYbC2htZ63r09PYHJJXksUcyB\n99uOoVOT93n07B6mJmb/SUBsMTez0EqFPBMTUyxNTLE0t9L4uSVJkrRBJjCSJOnO+vUQGgqNG0O7\ndho//eGLu3jw9KbKvgau7bJOXtINHgzx8aKZpo6Eh4czdepU1q4VI0d1K1Vi8apVtO3USfsXf/99\n+PprUS537Vr45BPtXzOvvL3Ftl8/UZEtJ4mJYtqcriqRzZ8v4mzQQK3D7YuVolaxxloOSpIkybAV\nOIE5ffo0ERERtGrVCltbW03EJElSURAfD4sWic+nT9f4+peA4Dv8dW6byr6yJarg5pxLCdf58zUa\nR14olUq2b9/O+PHjCQkJwdzcnClTpjAjJgbzXr1gxQr46CPtBmFiAvPmwbBhonqZvomJEVXYAMaO\nzfnYf/6BDh2gWTM4dkz7sWWlalWdj+RJkiQZG7UTmHnz5uHj48Nff/2Vsa979+7s3bsXgLJly+Lj\n40PFihU1H6UkScZn82YxVatOHejaVaOnTkiM46cDy1QaVdpaF6dFtW5626Tyv4v0vby8WLt2LR4e\nHtCwIcTGQoUKhRNMt25iCp0+PpTasgUiIkRSUq9ezse6uYlE+exZSEoSU+QkSZIkg6fGClBhy5Yt\nuKcvcAX27NnD3r17mTJlClu3biUxMZHZs2drJUhJkozQgAFiKtBXX2l89GXXyQ2ERgSp7OvXbhzW\nFvo3opCUlMTXX3+Np6cnBw8epESJEqxfv54TJ06I5CU8HC5fFlPaWrQonKAUCv1MXgDathUL+D//\nPPdj33gDatSAuDi4ckX7sRUFsbFw8SIkJKj/nitXoG9fWLlSe3FJklSkqD0CExgYiJubW8aff/vt\nN6pWrcpXX30FwO3bt9mwYYPmI5QkyThZWcGoURo/7dV7Zzlz/bDKvha13qZW5cZcDLuo8esVxJkz\nZxgxYkTGIv3+/fuzZMkSnJycXh3099+ibG2zZmBjo5tA9Unlyq8KP6jDywtu3wYfH7HWSiqYRLlI\newAAIABJREFUJk1ECesLF8TIoDpu3YIdO8S/448/1m58kiQVCWqPwCgUClJe6x1w5MgR3n777Yw/\nlytXjuDgYM1GJ0mSlAcR0WFsPbpKZZ9jyXK823KIjiLK2suXLxk9ejQtWrTAz8+PKlWqcOjQITZv\n3qyavMCrtRtt2hR+oMYgvaHlqVO6jcNYpPdKunZN/fek3xuUKaP5eCRJKpLUTmCqV6/O7t27USqV\nHDhwgKdPn9LptYo4gYGBlMytGoyUveway0mSpJZUZSqbDy8nNj4qY5+piRmD3p6IhXkeSwEfOQJT\npsD58xqNMX2Rvru7O2vWrMHU1JRp06Zx7do12rdvn/0bixXTbQKTkiKeuBsiLy8oXlw3U+ImTYLm\nzeHo0cK/trbUqiW2eUlggtKmczo7az4eSZKKJLUTmEmTJnHkyBFKlSpFt27d8PDwoN1rZU+PHj1K\nvdwWVEpZ27JF/ILVVZUcSTICJ67s5fajqyr7OjfrR3nHrBsI5mjvXvjmGzh+XEPRgb+/P507d+b9\n998nODiYFi1a4Ovry7x587C2ts7+jStXQliYmEKmC3FxYrG8lxcEBOgmhoKoUkX8/f30U+Ff++JF\nOHPGuB5Q5SeBSR+BkQmMJEkaonYC06dPHw4dOsTgwYOZPn06x48fxzytoktYWBgODg4MGzZMa4Ea\ntf79xcLIIfo1zUWSNO7QIdiwQfTm0KAnoQ/587TqDWpVl5q0rf9O/k7o4SG2N24UMDKxSP+bb77B\n09OTAwcOUKJECdatW8fJkyfxTJ+OkxtzczA1LXAs+WJtLW5aExNFk0tdSE6GS5fy916FQnd/d+lN\nLKvkI4nWVwVJYOQUMkmSNEStRfyJiYmcPXuWChUqsGzZskyvlypVit27d2s8uCKnXDldRyBJ2qNU\nimlZvr7iifTw4Ro5bWJyAj8dXEpKSnLGPmtLWz7s8CkmJvm8cU1PYK5fL1BsZ8+eZcSIEVxLu9nr\n168fS5cuzbzORd/Nng3bt8OPP8LkyaKyV2H680/o2VM0hPzll8K9dn4lJEBgoEieCqv8dWGoWFF8\n/11dRYlqK6vc3zNrlnhQV7eutqOTJKmIUGsExtTUlLZt23L48OHcD5byrnJlsU1vziZJxmj/fpG8\nlCkjSihryB6fnwl68UhlX982oylp90b+T5qewNy8CampeX77y5cvGTNmDM2bN+fatWtUrlyZgwcP\n8ssvvxhe8gKiEeNHH4m/ixkzCv/6q9IKMxhSFTF/f5G0V6hgXP1nTExEVbEDB9RLXkCsAxo0SI7A\nSJKkMWonMK6urkRFReV+sJQ3SqVosAZQvrxuY5EkbVEqYe5c8fmkSWJakgbceHiZE757VfY1dm9N\n/epeBTtxqVLiZis2Nk/rPpRKJTt27MDd3R1vb29MTU2ZOnUqfn5+dOjQoWAx6dr//geWlqIc7r//\nFt51b94U6wNtbMRNsKF48EBsjWn6mCRJkp5Quw/Mp59+ypIlSxgyZIhhPkHUVwoFPHokphtY5rFS\nkiQZiqNH4dw5cHCAkSM1csqo2Ah+ObxCZZ9DcSd6vqmZqWnMnCmaR5YoodbhAQEBjBkzhv379wPQ\nvHlz1q5dS82aNfN3/X/+EclT+/agDz9zXVxEEurk9KqUbmFYvVpsBwxQ+3uRpcBA0VPH01MUJdC2\ndu1E/5n0B1SSJEmSxqidwMTExGBra0u1atXo0aMHVapUybJyzuTJkzUaYJEhkxfJmG3dKrYTJ2qk\nnK1SqWTr0VVExb7M2KdQmPBhxwlYW2qo2aOaTTZTUlJYuXIl06dPJyYmBnt7e7755huGDRuGiYna\ndVIyW7tWrPdYuRLGjcv/eTRp0qTCvV5UFGzaJD4fO7Zg51q3TiRgn31WOAmMhQVUr67960iSJBVB\naicwU6dOzfh88+bN2R4nExhJkjJZvx66dIG2bTVyutN+h/B7oNqjpWOj3lQu66aR86vr6tWrDB8+\nnAtpPVL69OnD8uXLKVPQuf5KpWxgmW7aNDFlrXbtgp2nRQuxlQ0tJUmSDJ7aCcyD9Pm8knZER4s5\n0yVLyrUwkvExMYH33tPIqULCn7Dr5A8q+yqWqU7HJn00cn51xMXFMWfOHBYtWkRKSgouLi6sXr2a\nbt26aeYCt26J5n9OTuDurplzGiI7O1G5ThOaNRP/Di9dEmubbDQ0UldU+fnB5cvw9tvg6Jj9cbt3\ni9LpvXoZ1homSZL0mtoJjKurqxbDkPjqK1iwQJSbnDlT19FIkl5KTknipwNLSUp+1UfG0tyKgR0n\nYJrfksl5dOzYMUaOHMm9e/dQKBR8/PHHzJ8/Hzs7O01eRGzbtBHr5KSCK15cjOL4+sKFC/Dmm7qO\nyLBNnAiHD8Pvv8M7OfRb+vdf0Ri2Tp3Ci02SJKOX5wnad+7cYd26dcyfPx9/f39A9Il59OgRCQkJ\neTrXyZMn6d69Oy4uLpiYmLApfa5zmsGDB2NiYqLy0bx587yGrN8eP4bISFFbH+DhQ52GI0n6bP/Z\nbTx+dl9lX883h/NGCe13+A4LC2Po0KG0bduWe/fu4enpyenTp1mxYoVmkxcwjOlj8fGwfLkoj20o\nvNKq02l7GplSKT6MmboNLYOCxNZZ+/9HJUkqOtROYFJTUxk+fDhubm6MGjWKGTNmZCQwCQkJ1KxZ\nk5UrV+bp4jExMdSuXZvly5djbW2N4j9PGhUKBe3btyc4ODjjY78h/bJUR48eYG8Pz56JP+ehZKsk\nFSV3A/04enGXyr66VZvTxEOLN/nr16Ps2pWjM2bg7u7Oxo0bsbCwYO7cuVy+fJmmTZtq57offQSj\nR4tKVvpq82YYPx4+/1w0JjUE3bvDJ59Ay5bavc4//4jpwEOGaPc6upTXBEb2gJEkSYPUTmAWLFjA\nxo0bmTdvHmfOnEH52tMlOzs7evXqxe7du/N08U6dOjFv3jx69uyZZbUepVKJhYUFjo6OGR8lClJG\nUx89SmvAl/4LVSYwkrEYMwa+/lpUkiqg2PhoNh/8FiWvfu7YF3Ogb9vRmR58aFKkjw+Kffv4a+5c\nnj17RqtWrfj333+ZPn06FhYWWrsunTuL8sH6PHV34EAR382bolqaJj14kK8Gorlq316MGrVqpflz\nv+7+fYiIMO4SyulFFXJLYIKDxVaOwEiSpEFqJzAbN25kyJAhfPnll1TJojFXzZo1uXPnjkaDUygU\nnDp1CicnJ2rUqMGIESMIDQ3V6DV0KjYWnj8X5TYbNRL7Hj82nKeZkpSdmzdhzRqxnisyskCnUiqV\n7Di+hvDo5xn7FCj4sMOn2FppeOpWmpSUFL799ltmpJV/rmthwfr16zl+/Dg1atTQyjUNjoUFzJ4t\nPp81CxITczxcbUlJYqpXtWrw5IlmzlnY7qdNczTmJpbu7qIowp07oo9ZduQIjCRJWqD2Iv7AwECa\nNGmS7evW1tZEaeBJ6+vefvttevbsSaVKlfD392f69Om0adOGS5cuZfv08+LFixqNQZvntnz4kFpA\nvKMjfjdu4O7hQaqVFfdOniRF03PqJbVo899PUeI6cyallUqedevGo6CgVzcx+XD/2b9cvqu6ZsG9\nbBMiQxK5GJK/71dO3+c7d+4wf/58bty4Qfpz+q6VKnGvbl0uX76cr+sZrRo18KxUCWt/fwJmzCC0\nV68Cn7LkkSNUCQoirlIlrj99mu9/O7r8v1zpwgUcAH+FghdG/DPFtUsXkosXJ+j06Wx/Z9nOmoVF\naCgvg4NRhoVp9Pry57Xxk99j41atWrV8v1ftBMbJyYmHOSwwv3z5MhXTF6JrSN++fTM+9/T0pEGD\nBlSsWJF9+/bx7rvvavRaumCZNrSemPZk6uZ/ihhIkiGyDAzE4eBBlKamBA8cWKBzRcWHc/7BAZV9\nJW2dqFfxrQKdNyvx8fF8//33bN68mZSUFBwdHek7dizMnInd48diUbasCKbK1JQno0ZRdcoU7C5c\n0EgC4/jrrwA869XLYP++rQIDAUhwcdFxJNr1cMaMXI+JqV2bmEKIRZKkokXtBKZXr16sWbOGgQMH\n4uDgoPLaX3/9xaZNm5iiqXr92XB2dsbFxYV79+5le0zDhg01ft30JwAaP3dQELi6UrxuXa3ELalP\na9/jomjdOjENcvBganfvnu/TpKSmsHLndJJSXk1NMje1YNS703F2yF+vpOy+z/8tjTxu3Djmz59P\n8eLF4bvvMA0NpWGZMrJHU1YaNIBGjSj11luUKmjCkd5bpFgxKk6fTsXixfN8Cr34v5w20uDWpYtc\n+6EFevE9lrRKfo+LhoiIiHy/V+01MDNnzqRChQrUq1eP/v37A/DVV1/RpEkTunTpQt26dZk6dWq+\nA1FHaGgoT548wdlYfiF06wb+/qJLuSQZg9RUUYjCxAQK+PPg8IWdPAi6qbLvnZaD8528ZCWr0sg+\nPj6sXLlSJC8AGzfC2bM5N+vTlEWLoG1bOHhQ+9fSFIUCWrfWzGjJ6tVi++GHom+LtixeLP6eHz/W\nzvkDA0VJfLnuQ5IkSSvUTmDs7e3x8fFh2rRpBAcHY2VlxalTp4iJiWH27NmcPHkSmzx2No6JicHX\n1xdfX19SU1MJCAjA19eXx48fExMTw+eff87Zs2d5+PAhf//9N927d8fJyckopo8ZnZ9+gj//1HUU\nkq6ZmIib75s3oXr1fJ/mYfAdDpzbrrLPw7UBLWt3KmiEgCgMsG3btixLIzdr1kz14C5doEkTsLTU\nyLVztH+/6AETU0Qn3Xh5Qf36ooKdNh0/Lv6etdUPxtRU9PYy0ClwkiRJ+k7tKWQgFup/+eWXfPnl\nlxq5+IULF2iT1qhNoVAwc+ZMZs6cyeDBg1m9ejV+fn78/PPPvHz5EmdnZ9q0acPOnTuxtbXVyPUl\nDQkJgUGDxOfJyeKXt1S0FSB5iU+M46cDS0lVviqjW8zann7tPtZIyeTg4GC6du2a0VOqVatWrFu3\nTvfVxeLi4PRpcdNbVLvE9+snPrTNy0ski6dOwQcfaP96kiRJkkapPQLTunVrjh49mu3rx48fz0hG\n1PXWW2+RmppKamoqKSkpGZ9v2LABKysrDhw4QEhICAkJCTx8+JANGzZQrly5PF3DoCQlwblzhtXZ\nGuDp01ef51DoQZLUsevE9zyPCFbZ17/9xxS3LVgPqJSUFLZu3UqfPn3Yv38/9vb2rFu3Tn9KI58+\nLUoR160L/1lnaHByKqurD7y8xFZbIzBFyYEDMHly1v1gFi2CNm1gz57Cj0uSJKOmdgJz4sQJQkJC\nsn09JCSEv//+WxMxFV1xcdC0KfTqJSoeGYp69cQvKYAbN3Qbi2TQfO+e5uwN1QclXrU74VmpYAs5\nb968iZeXF0uXLiUuLo5evXpx8+ZNhg8fnmUTXZ04dkxs27bVbRwFoVSK3j/ly4t1IPqqUSPRx+ba\nNXj5UtfRGLZffxWJysmTmV+7ckVM1wsPL/y4JEkyahr7zf3kyRM5tSsvYmPhwgV49uzVvuLFoUQJ\nkcgYWsPOWrXEViYwRZMGmhi+jH7BtqOrVfY5lXShh9fgfJ8zKSmJBQsWULduXc6ePcsbb7zB4sWL\n+fXXX/WvGMj582Kbx5FsvaJQiPVPoaEwb56uo8melZWonqZUwpkzmj13eLhhPYAqqPSf/VmNwKS1\nCpCV2CRJ0rQc18D88ccf/PHHHyjTfhivW7eOI0eOZDouLCyMI0eO5NjoUvoPPz+xMLh+fbh06dV+\nV1fw9RVTsQqj6pGmtGghqk8Zc+dpKWsvX4KHB/TtK57EmuVpaR0AqcpUNh9aTmxCdMY+UxMzBr49\nEQvz/C2e9/X1ZejQoVy5cgWAjz76iP79+2OXnyaxU6fCtm2iRHT79vmKJ1cHDogn1h4e2jl/YZkz\nB377DX74AT7/HKpWzfn4yEgxGmJlVTjxpVu0CGxsXt2Aa0rduvD8uUjkKlTQ7Ln1UU4JTHoTUpnA\nSJKkYTneaVy/fp0dO3ZkLJw9d+4cl16/2UYsvre1taV169YsW7ZMe5Eam0ePxPa/v+AqVhQJTEAA\nNG5c+HHlV+/e4kMqelauFDcq167lK3lJTkliy+HvuPP4X5X9XZv3p7xj5TyfLyEhgXnz5vH111+T\nnJxMxYoVWb9+Pe3bt89/V+eXL8VDBT8/7SUwpqZgDD0P3NxEUY+NG2HWLNi8OefjFy8W5ZNXrizc\nBfUtWmj+nAkJojSzQlF0btrTExg/v8zNXtMTGFlOWpIkDctxCtmXX35JdHQ0UVFRAHz//fdERUWp\nfERGRhIUFMSePXuomtuTNumV7BIYV1exDQgo1HAkKV+iouDbb8Xn06fn+e1xCbGs/WMeF2+fUNlf\n3aUWreu/k+fznTt3jvr16zNv3jxSUlL4+OOP8fPzo31Bkw5PT7GVUyTVM3MmmJvDli1ZP5lPl5go\nRrVevABjKNDy8KG4ia9QQXz9RYGjo/iIjHz1ew3EVOiICPH3UKqU7uKTJMkoqf24NDU1NfeDJPVl\nl8A0aABvvw0uLoUfU34kJ4t1PM7OsudBUeTtLbqOt2iR59K/ETFhrPljLk9C/VX2F7cpSf8On2Ki\nUH+JXmxsLDNmzGDZsmWkpqZSvXp1fvjhB7zSq00VVPq0ruvXNXM+Y1exIowaJW7oc+qfs2uXKMNe\nsya0bFlo4WnNgwdiW9Sm0s6cKaYAvt581NwcLl8WPx/0pVCGJElGI8/zPQ4fPszx48cJDQ3ls88+\nw83NjejoaC5fvkytWrUoWbKkNuI0PtklMB9+KD4MxZ074ul0zZo5P2mVjE9sLCxZIj6fPj1PCWxI\n+BO8f59NWOQzlf1v2Dsz+t2ZlLQrrfa5Tpw4wbBhw7h37x4mJiZMnjyZWbNmYW1trfY5cpU+AnP9\neuZpMlLWli3LvSfUqlViO3ascfyd3r8vtkUtgcmq8aiZmahQKUmSpAVqJzBxcXH06NGDw4cPZ6yJ\n+eCDD3Bzc8Pc3JxevXoxduxYZs6cqbVgjYqLC7i7Q6VKuo6kYNKfOBrD9A8pb6KioHVr8PeHjh3V\nfpt/0C3W/jmf2Pgolf0Vnaoxovt07Gzs1bx8FFOmTMHb2xuAmjVrsmHDBho1aqT+16AuR0cxDSYs\nTMzrL1tWc+d++FA8oTa2Bd+5JS///iv6sNjZQf/+hRNTdsLCNDPNKSYGrK2LXgIjSZJUyNQe1502\nbRonTpxg8+bNBAQEZFQmA7C0tKR3797s3btXK0EapRUrxHx6Q1+0m/7EsXJlePJEzGfftk23MUmF\nw8lJfK9PnlT76fm1B+f5bteMTMmLh2sDxvWcq3bycvDgQWrWrIm3tzdmZmbMmjWLS5cuaSd5AfH1\n/fOPmNOvyeQFYOFCMeVqxQrNnlffpaaKxHfIEJHE6EJoqEgca9TQTOnjKVNEEjN+fMHPJUmSJGVL\n7RGYHTt2MGbMGPr168fz588zvV6jRg22bt2q0eAkA/D6nO87d2DkSGjWDN5/X7dxSYUnpzUOr/G5\ndpAdx9eiVKqup2vq0Za+bcdgapLLE3sgPDyciRMn8uOPPwLQoEEDNmzYQO3atfMcdp5pq7zx0bTG\nnYZUdVAT6tYVpaN1ub6ydGlRSOD5c/Hzq0aNgp9ToRBloSVJkiStUXsE5vnz53jk8AtcoVAQFxen\nkaAkA/L6CEz6v48bN4pWIzcpR0qlkv1ntrL9mHem5KVj4z580G6cWsnL77//joeHBz/++COWlpYs\nXLiQs2fPFk7yoi2PH8Pdu2IEwtBHY3Pj76/a8yqdLhd4KxSQXujBx0d3cUiSJEl5ovZvjvLly3Mj\nhxKiPj4+VKtWTSNBFXnXrsHPP8Pt27qOJHdmZqIZXJUqr9YJRES86sAsFWkpqSlsPbqKA+e3q+xX\nKEzo22Y0XZr1y1hTl53Q0FDef/993n33XYKDg2nRogVXr15l8uTJmOWj74xeOX5cbN98M189dAzG\n8eNidGPIEN2OuGQlPYE5dUq3cRi6X36Brl1hzx7x52HDoGlTOH9et3FJkmSU1E5gBgwYwLp16/jn\nn38y3XB4e3uzY8cOBg0apPEAiyRvbxg4EA4e1HUkufv9d4iOFs3MFArVURjJ+KSkwL17ah2akBTP\n93u+4uz1Iyr7zU0t+KjLFFrUynnhv1KpZOvWrbi7u7N9+3ZsbW1ZuXIlJ0+epIYmpvrog2PHxLZN\nG93GoW3NmolmhteuwfbtuR9fmGQCoxm3b8O+fXD6tPizry+cO6fbmCRJMlpqJzBffPEFrVq14q23\n3srorfDpp5/i7OzM2LFj6datG+PlwkX1/PuvWPj84kXWr1esKLaG0sxSoXi1iFsmMMbt11/Fk/Qp\nU3I8LCo2gu92zeD6w4sq+22s7Bj73hxqV2mS4/ufPn1Kjx496NevHy9evKBt27Zcu3aNcePGYaLr\nnhLR0WLdhCZUqyaSf2NPYKysRK8QgM8/h6Qk3cbzurp1xRQ+GxvRfDG/goPFz+yUFM3FZkhq1RLb\n9HL6QUFiW6aMbuKRJMmoqX0nYGlpyb59+/j555+pUaMGbm5uJCUlUb9+fTZt2sTvv/+OaW5lMyXh\n22/FlJFdu7J+3dASmNd16wbTpkGTnG9QJQOUmgrz54ttDmVin0cE8+2vUwkIvqOyv5TdG0zo/RWV\ny7pl+16lUsmGDRvw8PDgzz//pHjx4nz//fccPnyYSvpQcrx3b3Gze/KkZs43bZp4oFGnjmbOp88G\nDYKSJeHpU6heXX/WyZmZiWaavr6iBHJ+rVoFrq4we7bGQjMorycwqani7xREtUJJkiQNy9Oka4VC\nQb9+/ejXr5+24ikasmtimS49gXn4sFDC0aiuXcWHZHz++AP8/EQPo2ymiz5+dp81f8wlKvalyv5y\npV0Z9c4M7Itl32sjICCA4cOHc/jwYQC6du3KmjVrKKdPPYbSe4XcuAHt2uk2FkNjZgbffw89e4r+\nQfrUuFITTU9fL2hSFFWtKioSPnokqlOmpIj/L2pWKZQkScqLPCUwx48fZ8OGDfj7+xMeHq7SC0ap\nVKJQKHJc6C+lyS2BcXUVW0McgZGMU3LyqylAkydneVNyM+AKG/YtJCEpXmV/dZdafNT1C6wtbbM8\ntVKp5Pvvv2fixIlER0fj4ODAihUr+OCDD3Jd4F/oPD3F9vp13cZhqN57D27devWQxpikJzBFtYml\nmZmYQnzlChxJW/cmp49JkqQlaicwixcvZvLkyVhbW1OjRg3eeOONTMfo3c2GPlIqXyUw5ctnfYyT\nE/TqJV5PTdVtmdGcXL8OtrYiTjl90Lh5e4upIa6uorrQf5y/eZwtR74jNVV1/n+D6i3p3+ETzEzN\nszxtYGAgw4cP58CBAwD07NmT1atX4+joqPEvQSPkGq+CM5YCDP9V1BMYgGXLxHond3cxyhYfn/t7\nJEmS8iFPCUyLFi3Yu3cv9vbqdcuWshAaCgkJYmi9WLGsjzExEYul9d1HH4kqMydPQsuWuo5G0qZ+\n/cT0sW7dVKbbKJVKjlzazR6fnzK9pU39d+juNQgTReYEXKlU8vPPP/PJJ58QERFBqVKlWLVqFX37\n9tXvByHpCcz16+JhhD7HKhWeiAhRlMXaGpyddR2N7rz55qvPixfXXRySJBk9tROYuLg4BgwYIJOX\ngkpIgB49NDPnWtcePBDbovzEsahwcIC1a1V2paamsOvkBk5e3Zfp8HdbDqV1/e5Znio4OJgRI0aw\nJ61fRLdu3Vi7di3OhnDj5+wsFqLb2Ymb1hIl8nee334TI1p9+4qn1ZLuxcTA2bNgbg6tWuXtveHh\nUL++GH2QSa0kSZLWqZ3AvPXWW1y9elWbsRQN5cvD7t26jqLgoqLEaJKVVeZ5zr6+sGEDuLnBmDG6\niU/SqqTkRH4++C2+906r7Dc1NePDDuOpX90r03uUSiXbt29n7NixhIWFYW9vz/Llyxk4cKB+j7q8\nTqGAJ08K/gBi0ybR8K9SJZnA6It9+0RC2bFj3hMYV1e4dEkrYUmSJEmZqb244rvvvuPIkSN89dVX\nPHv2TJsxSYYgffSlUqXMa3SePIGVK7MvEy0ZtNj4aFb/PjtT8mJlYcPod2ZmmbyEhobSp08fPvjg\nA8LCwujYsSN+fn4MGjTIcJKXdAVNXpKT4cQJ8Xnr1gWPR9KMFi3E9vTpotvLRZIkyUConcCUL1+e\nYcOGMW3aNJydnbGyssLa2hpra2tsbGwytlIRkdOCVbnQ2Thk0acjPCqU5Tu/5P4T1Spc9ral+LTX\nAqqXr5XpPbt27cLT05OdO3dSrFgx1q1bx19//YWLi4vWQtdrly9DZKQoO5tdJUKp8JUrJx7IREW9\nasYo5Z++9PmRJMkoqT2FbNq0aXz11Ve4uLjQoEGDLNfCGNyTVH0WHi4W8qekwOjRuo4mM3NzaNgw\n6wZ8FSuKp9RBQeLrKFmy8OOTCubOHdHr5dtvM5qSPn0egPcfc4iIfqFyqFMpF0a/M5NSxVUrE4aF\nhfHxxx+zZcsWAFq3bs2GDRtwTS8TXlQdPSq2bdvqNg4psxYtwN8ffHygbl1dR2OY1q6FUaPE548e\nZV9tU5IkqQDUTmDWrVtH165d+f333zHR17K+xiQyEkaOFIuG9TGB6dZNfGTFxETM6798GW7ehObN\nCzc2qWCUShg7VixoXruWxPp1Oe13iL/ObiUuMVbl0MrO7gzv/iW2VnYq+/fu3cvw4cMJDg7GxsaG\nb775htGjR8ufHQDHjoltmza6jUPKzMsLNm+GU6fE/wEp715/kGlnl/1xkiRJBaB2ApOUlESXLl3k\nDUhBbdokFr23bSsaf2WnXDnRWyUoSFQuM7RuxukJzI0bMoExNNu3w5EjKEuW5J9+b3Jw4wii4iIy\nHVa7SlMGvj0BC7NX/zYjIiIYP348P/74IwBeXl5s3LiRqlWrFlb0hSM6WjRkdHcXvZDyYulS0ehP\nJjD65623RA+ujh3Vf09Skvh+Vq0K1appLTSDUbnyq89l1VJJkrRE7QSma9eunDhxgpF0zDdmAAAg\nAElEQVQjR2ozHuMWFweDB4vpV7k1+DIzE0nMo0fw+LH45WhIhg+HLl3EE03JcEREoJwwHgWwu0sN\n/r6edcU8r9qd6PXmMExMXjUwPXToEB999BGBgYFYWVmxYMECPvnkE0yNsclphw5w5owYTcnrQvxa\ntcSHpH9q1Mh7Dy5/f+jcWUydffhQK2EZlObNxUO6mjVlSWlJkrRG7QRm+vTpfPDBBwwfPpxhw4ZR\noUKFLG9M9LaDtj4IDBRbF5fMlbuy4uoqEpiAAMNLYF5vaCYZhNiEaJ4Nfx/X4BD8XUtyon7m/8vm\nZhZ0btqPNvXfyVjzFhUVxaRJk1ib1iemSZMm/Pjjj7i5uRVq/IXKw0MkMDduyEpiRZ3sh6XKxkYk\ndebmuo5EkiQjpnYC45FWWerq1av88MMPWR6jUChIkeUns/fokdiqW3moYkWxlU/1JC2KiYvkb989\nnPDdR22zEErZWbK9dx2UJq+enlqYW9Gydifa1H8HO5tXzRuPHz/O0KFDefjwIRYWFsyePZvPP/8c\ns5ymRxqD9Ep716/nfJxk/HKqyFhUWVnpOgJJkoyc2ncZM2bMyPUYWYUsF3lNYLp3F9PIatfWXkz5\n8fixKDPq6fkqyZIMTlRsBMcv/8E//+4nIUlMaTzfpAKX65cj2VyMrlpaWPNmna68Va8bxayLZ7w3\nJiaGqVOnsnLlSgDq16/Ppk2bqFmzZuF/Ibrg6Sm2slS4JBMYSZKkQqd2AjNr1iwthlFE5DWB6dVL\nfOibAwdgxAixnmfjRl1HI+VRZEw4xy7/zql/D5CYnJDp9WRzU6wtbXmrbjferNsVG6tiKq/7+Pgw\nePBg7t27h5mZGf/73/+YOnUq5kVpykh+eh0lJoppNfJBj3GRCYwkSVKhM/J5HnrG0xM++AAaN9Z1\nJAWT/gv79Wozkt57Gf2Co5d2c/raIZJSErM8xtbKjtb1utOyTmesLVWra8XFxfG///2PpUuXolQq\nqVWrFps2baJevXqFEb5+cXER/58rVBAFOdSZMjNtGuzYAUuW6OeDCemVP/8Ui/mHDct9PZ+nJ4SG\nigIAkiRJUqGQCUxh0tcRlbxSd9HqX3+Jm7V27eCLL7Qfl5SlsMhnHLm4izM3jpCSkpzlMXbW9rRp\n0AOvWm9jaWGd6fXz588zaNAgbt26hampKV988QUzZszAwsJC2+HrJ4UC/Pzy9p5jx8QobIkSuR8r\n6ZaPj+gHU7587gnMggWFE5MkSZKUQSYwUt6pOwITHS26jltnviGWtO95RDCHL/zGuZvHSE3NurhG\n7ScJtDKpgOusZVhY2WR6PSEhgdmzZ7Nw4UJSU1Nxd3dn06ZNNGrUSNvhG5ewMLhyBSwsZF8kQ+Dl\nBd98IxIZSZIkSe/IBEbKO3VHYPKzTkAqsGfhTzh0YScXb50gVZma5TElijnQvk53vAZ+geLmAXCt\nB6NGqRxz5coVBg0axLVr11AoFEyaNIk5c+ZgJSsM5d2JE6BUQrNmosyspN/Sk8zz5w2zkbAkSZKR\nkwmMvvv1V9Fv4qOPXlU+0qXEROjWDZ48gdKlcz62WjUwNRU9AWJj5Y2blgW9eMyhC79y+c4plNkk\nLqXs3qB9o140dm+D+aLFcPOW+D4NGZJxTFJSEgsWLGDevHkkJydTtWpVNm3aRHM5cpB/x46JbZs2\nuo1DUo+Dg3gAc+MGXL4sEk9JkiRJb8gERt/99hts3w716ulHAmNhAT/9pP6x1arBrVtw+7b4GiSN\nSU1NISDkLjceXuK6/yUCQx9ke2xp+zJ0aNSbRm5vYmpqJpLKuXPFi6tXZzxhvnbtGoMGDeLKlSsA\nfPLJJ3z11VfYyOSzYJ49E+tm2rbVdSSSury8RALj4yMTGEmSJD0jE5jCcu0aHD8uKpA1bar++9L7\nrAQEaCcubfPwEAnMzZsygdGAmPgobgVc4br/JW4GXCYmPirH4x1LlqNj497Ur94SUxPR2wWlEj75\nBOLi4P33oV07kpOTWbRoETNnziQpKYlKlSqxceNG3sxtAXNRd+UKXL0K774L9vbZH7d9O3h7Q/Hi\n2R8j6ZeRI0UvrhYtsj9m/35ISoKWLaFUqcKLTZIkqYiTCUxhOXYMxo+HsWPzlsC4uoqtoSYws2bB\nzJlQvbquIzFISqWSp88DuP7wIjf8L+EffDvb6WGvc3aoQMfGfahbtRkm6YlLuuhoeP5c3EwvXcrN\nmzcZPHgw58+fB2DUqFEsWrSIYsWKZXFmScXIkXDhgiho0apVzsfKG1zDUr9+7sfMmQPnzok1Trl9\n/yVJkiSNkQlMYclrE8t06SMwDx9qNJxCU6uWriMwOAlJ8dx5/C/X/S9y4+ElXka/UOt9ChS4Oteg\nTf13qFWlCSYKk6wPtLMDHx9Srl/n2y1bmDZtGgkJCZQvX54ffviB9u3ba/CrMXKeniKBuX5d3sAW\nRbKJpSRJkk7IBKawFDSBMdQRGEktoS+D0tayXOTuE79s+7X8l7WlLe4V6+Hh2gD3ivWws1Gvx8jd\n+/cZMno0PmllYocOHcrSpUuxz2kalJRZ+ro0WWmv6ImMFCOZVlbg7KzraCRJkooUmcAUlvwmMK6u\nMHs2VK2q8ZDyZe1acHKCzp3FIn0pX5JTkrj/5AbXH17ihv9Fnr18qvZ7nR0q4OnaEM9KDXB1dnu1\ntkUNqamprFq1iilTphAXF4ezszPr16+nS5cu+fkypPRS4dev6zYOqfC93g/LJJvRTkmSJEkrZAJT\nWPKbwNjawowZmo8nPxITYfRoUU0pLk7X0RiciOgwkbA8vMTtR74kJMWr9T5zMwuql6+Np2tDPFwb\nUKr4G/m6vr+/P0OHDuXvv/8GYMCAASxfvpxScm1G/uU2AnPxIkREiL4isqGr4YqPFyMtr1O3oa8k\nSZKkcTKBKQxKpbjxDwgw7KkGDx+Kr6VixfyNvqSkiL4wRUh4VChX7p7G9+5pHgbfVvt9DvZOGQlL\nNZeamJvlf7RLqVSyZ9Ikxnt74x8bi6OjI2vWrOHdd9/N9zmlNOXLQ48eYoQ0ORnM/vMjddky2LIF\nVqyAjz/WTYxSwbRrBydPiodQZcq82l+uHAwdqt5if0mSJEmjZAJTGBQK/RlFKYj8PnFct05UIhs5\nUlQlM3LhUc/xvXeaK3d9eBikXtJiYmJK1bIeeFRqiKdrAxxLlkOhUBQ4lsePHzP+ww9Zc+IEl4AZ\nnTox86efKJ1bE1JJPSYmsHt31q8pla8aWMr+L4ZLoRClkn18oGfPV/ubNZP9YSRJknREJjCS+h6k\nNUrMa8UdKysIDha9YIzUy+gX+KaNtDwIUu/rLG5TEg/X+nhWakj18nWwttRcs0ilUsmPP/7I+PHj\nWRQZyRtAiKcnK/ftEzdkkvbduiX+3ZcpA+7uuo5Gyi8vLzhyBE6dUk1gJEmSJJ2RCYykvvyOwKQv\ndDaySk0R0WEZIy0PnqqXtFQsUx1P1wZ4VmpIuTcqZV/quACCgoIYMWIEe/fupSkwAlCam+O0c6dM\nXgpT+uhLmzby792QpTeyPHVKt3FIkiRJGXSawJw8eZLFixdz+fJlnj59ysaNGxk0aJDKMbNmzWL9\n+vWEh4fTpEkTVq1ahUf6DXFRce8eLF0Kjo66nYLVogVEReV92oSbm9jevp31OgEDEhkTju+9MyJp\neXIDJcpc3+PqXIN61VpQt2ozStrlbwG+OpRKJVu3bmXcuHGEh4fjYG/PPnt7ePQIxaRJr74PUuF4\nPYGRDFeTJmLt3pUrEBMjCqtIkiRJOqXTO8mYmBhq167NoEGDGDhwYKY5/wsXLmTp0qVs2rSJ6tWr\nM2fOHNq3b8/t27eLVpfw6Gjw9hYVj3SZwPTsmb8pFMWKieprjx6JaWjVq2s+Ni2KjHnJ1bSRlvtq\nJi0Vy1RPS1qa57tqWF6EhIQwevRodqetx+jUqRObhgyh1Pvvi1Lc06ZpPQbpP7p1E1u5/sWw2dlB\n3bqvfn7J5rySJEk6p9MEplOnTnTq1AmAwYMHq7ymVCr59ttvmTp1aka1pE2bNuHo6MiWLVsYMWJE\nYYebfytXQmwsDByYvypk6c0s06uAGeJ0FA8PCAwEf3+DSGCiYl9y9d5Zrtz14d6T6yiVqbm+p4JT\nNZG0VGuGQ3GnQohS/D/ZsmULn3zyCWFhYdjZ2bFs2TKGDh0qHghUqSISYBvNra+RsrBtG1y6JBLF\nEmnNRAcPFh+S4Tt0CEqWfPWz188P9u4Vo9Fvvqnb2CRJkoogvZ3L4+/vT0hICB06dMjYZ2VlRatW\nrTh9+rRhJTCrVonpU1275i+BKVFCPAWMioKwMHBw0HyM2vbjj2Bvn7mXgh6JT4rB59pBrtz14W6g\nn3pJi2NV6lUXIy0O9oWTtKQLCgpi1KhR/PnnnwB06NCB9evXU+H1XkOyxGvhWLxYJDDvvCMWfUvG\n5b+9kk6ehKlTYdgwmcBIkiTpgN4mMMHBwQA4OaneFDo6OvL0afZdyy9evKi1mPJ1bqWSeg8fYgpc\nDg0lNZ/xeTg5YRMVxY2//iLWUNcyPH6s6wiyFBYdjO/jkzwJu6vW9LBStmVwLe1BxdLu2FmVBCX4\n332MP4Xz9SmVSvbt28fSpUuJiorC1taWiRMn0q1bN549e8azZ88KJQ5DpumfE65lylAaeLh/P8/1\nOEkvSrT5u8Dl/+3deVxU9f7H8dcAsoq4IKKogF73JfcFNZfcu9d2S9OyMrUyLTPLrKuV19LC3Mu6\nWt5W9XevWWqJlWVuuZS75oa7oChiIMgy5/fHEXQEkWWGYfD9fDzmcYbvWb4f53h0Pny3desIBk54\neRHjwHokd468x1I86B6XbLVq1SrwucU2gcmNPdbHKCoeCQm4X75Mur8/1kKM20kNDsb34EE8T592\n3QSmmEm4dI5tx37h6Lmbz45W3i+Y0MB6hFWoh7+P81auj42N5a233mLdunUAtGvXjrFjx2ZL9KVo\npYSHA+ATHe3kSKQoeJ08CcDlqlWdHImIyK2p2CYwwVdWPI6NjaXqNf9JxMbGZu3LSYsWLeweS+Zv\nAAp07d9/B8AjPLxwsY0fD+fP87f27aFKlYJfp6C+/RZ27jS7wTVuXPT129H5i2f47reFbNq7Otdu\nYiGBYVfGtLQjqJwTPvNrGIbB/PnzGTVqFBcvXqRs2bJMnz6dgQMH2ib0J06AvlTdUKGe5dycPg2z\nZlEpLo5KDvg3SPLOYff4WufOAVCzWzdo3txx9UiOiuQei1PpHt8aEhISCnxusU1gwsPDCQ4OJioq\niuZX/oNISUlh7dq1vPvuu06OLh+OHTO3145LKIiuXQsfS2EsXgyffmpO5eyiCczFpHiiNi9m3c4o\nMqzpOR5TuUJ1mtVuT5Na7ahULqSII8zZsWPHePLJJ4mKigKgT58+vP/++1S5PpHdv9+8N/36wb//\nbU79KkWjQQNzu2cPzJoFGzbAM89ARIRz4xL7MQxzcdKTJwu+qK+IiNiF06dRPnDgAABWq5WjR4+y\nbds2KlSoQLVq1XjuueeYNGkSdevWpVatWkycOBF/f3/69+/vzLDzp149mDz56kxirspe/2GfP2/O\n5FOuXOFjyqOklL/4cevX/LLtW9LSU3M8ppxfJZpW78xd3R4sNl0UDcPgww8/ZPTo0SQmJlK+fHlm\nzpxJv379ssd47pw5oPjyZfPzVfJStMLCYMwY83n/+GNzkLdWbS9Z9u0zZ1MMCoLXXzcTmcwZ50RE\npEg5NYHZvHkzXa4s8maxWBg/fjzjx49n0KBBzJ8/nzFjxpCcnMwzzzxDfHw8bdq0ISoqCj9XWkis\nTh3zi42rO3TI3NaoUfBrjB0Lb78NU6bAiy/aJ65cpKQm88u2b/lx69ekpF7K8ZigciHc2bY/6Rc8\nsVgsxSZ5iY6OZvDgwfx0ZTHEe++9l9mzZ2fvPpmWBh98YHYxjI83Z6ibMsUJEd/i3NzMX1RcugRD\nh5pJZKdOzo5K7KluXfP5OnMG7r/fTFpFRMQpnJrAdOrUCas196lqM5MacaJLlyAmBkqVKtz4isxW\nqD03HzRfGGnpqazd8T1RW/6PpOSLOR5T3r8ivdo8RIu6nXB3cy82M51YrVbef/99XnrpJZKSkggM\nDGT27Nk88MADOSdXH38MI0aY77t0MdccCgws2qDlqvXrITXVnL76+ql3xbVZLGaXwG+/hbVrlcCI\niDhRsR0DI8VIZvexsLDCdU2qX9/cOiiBychIZ+OeH1m5aREXEs/leIy/b1l6tHqAtg26U8qjlEPi\nKKhDhw7xxBNP8MsvvwDQt29fZs2aRcWKFW980qBBsGQJDBsGffq45iKnJcmVFjOutCxLCdO+/dUE\nZsAAZ0cjInLLUgLjSl591fwN7wcfFO1q9hUqQGQkeHoW7jrXJjCGYbcv21bDyu9//sqKjV8SlxCT\n4zG+XqW5o8W93H5bb7xKFa91OqxWKzNnzmTs2LEkJycTFBTEnDlzuC8vYyg8PeG77xwfpOTNzz+b\nWyUwJVPmIqVr1zo3DhGRW5wSGFeyeTOsXg0HDhRtAlO5MowaVfjrBAZCxYpw9qw53W+1aoW6nGEY\n7Dy8ieUbPuf0uWM5HuNVyptOTfvQuVkffL0Kvg6Po+zfv5/HH388a12X/v37M2PGDCpUqHD1oPR0\n+PBDqFRJA8OLu+++g19/hdtvd3Yk4gjNm5v3tm1bsFrNsU8iIlLklMA40smT8NprcNttMHJk4a+X\nOYbkyJHCX8tZGjc2k5e4uAInMIZhsP/4Dpat/4yjsQdyPMbDvRQdGveia4v78PcNKEzEDpGRkcG0\nadN49dVXSUlJITg4mLlz59KnTx/bA3/4AZ5/HnbtgpAQ6NULfH2dE7TcXECAuVaSlExeXnCli6eI\niDiPEhhHOnDAHGTdvr19E5ijRwt/LWeJiirUby0Pn9rHsg2fcfDErhz3u7m506b+HfRo1Zdy/sVz\nMPvevXt5/PHH2bhxIwCPPPII7733HuWvHfR98CC88AJ88435c1gYvPsu+PgUfcAiIiIixYgSGEey\n1yKWmUpCAlPA5OXk2WiWbfic3dE5zxZmwULzOrfTq81DVCxbueDxGQa0aWOO1+nRw1xA1E6zeqWn\np/Puu+8yYcIELl++TEhICHPnzuXOO+/MHsODD8Lvv4OfH4wbZ7bCeBevsTsiIiIizqAExpHsncBk\nTtvpyl3I8skwDFZt/j+Wb/gCAyPHYxrXbE3vNv2pEmiHxUL37oVNm8zXJ5+YEw00b2523Xr99QJP\nPLBr1y4ee+yxrOmaH3/8cSIjIymb00J4Fou5Xs4XX8CkSeYYJBEREREBlMA4lr0TmEaNYOlS+Nvf\n7HO9vIiJMRedbNrUPgP58yE1/TJfrprF1v2/5ri/TvXb+HvbhwkNtuOEBvXqwbZtZle3qChzQPaW\nLeb00W+8ke/Lpaam8vbbbzNx4kTS0tKoVq0aH330ET169Mj9xG7dzJeIiIiI2FAC40j2TmACAsy1\nPorSn3/CZ5/BoUNFmsAkJJ7no2VvcSyHQfrhlevy94iHqVW1kf0rtljMSRduu81M3C5dgjVrzG5d\nOVm3Dj79FLp3hzvuMO/RFVu3buXxxx9nx44dAAwdOpQpU6ZQpkwZ84DoaJg4EaZOtTlPRERERG5M\nCYwjjRkDd94JTZo4O5KCO3TI3NaoYb9rnj8Pu3dDeDhUrZpt97HYg3y07C0SrluM0tfbn/5dh9Oo\nRqucV6UvqKVLKeXhQVqlStn3+fpCz543PnfJEpg713y5u0Pr1qR16cKs2FhenD+fjIwMatSowb//\n/W86d+5snvPXX2bXsKlTzVXbK1Y0u4yJiIiIyE0pgXGkLl1cf0G7w4fNbc2a9rvmSy/Bv/8NM2fC\n8OE2u/44sI7PoqaTlp5qU16pfFWG/GNc4Qbo5yQ+Hu67j0bAth9/zP/5jz4KZcua3c02bID16ym1\nfj37AKvFwnPPPcfEiRPx8/Mz14345BN45RWIjTXPHzAg22cgIiIiIjemBEZy54gWmPr1ze2ePVlF\nVsPK978t5PvfFmY/PLQZj/Z6AR8vP/vFkGnVKsjIIKlZM6x+Bbh+o0bQqBGXRo3izRdfZO+cOXQD\nDtSowdpPPyUiIuLqsVu2wBNPmO9bt4Zp08wZz0REREQkz5TASO4c0QKTmcDs3QtAatplPls1nW0H\n1mc7tHPTPtzV/lHc3NztV/+1li8H4EL79gW+xOrVqxk8eDCHDx/G3d2dei++yIrx4/G+ftrjVq1g\nxAho2RL699cq3iIiIiIFoATG1fzyC7z8svllePp0x9f31ltmopGZdNjDNS0w8X/F8dGySZw4c9jm\nEHc3D/p2Hkrbhg6cictqhe++AyChXbt8n37x4kVeeuklPvjgAwAaN27M/Pnzad68+Y1PKop7JiIi\nIlKCKYFxNRkZsHEjeBTRrXPEOJ6qVaF0aThzhvc/epYY92Sb3X4+ZRh850vUDGlg33qvt3kznD0L\nYWGkhIfn69Tvv/+eIUOGcPz4cUqVKsWrr77Kyy+/jKenp4OCFRERERFQAuM4779vTr87ZAhkzj5l\nD5mLWR49ar9rFjWLhfMdWnLi5J9cTjgH5X2zdlWuUJ0h/xhHhYAcZgSzt/LlYeRIcxawPM5qFh8f\nz6hRo/jkk08AaNGiBfPnz6dRIwdM6SwiIiIi2SiBcZSff4ZFi+Af/7DvdatWNb9snzwJaWlQqpR9\nr+9gVsPKig1fENWjDNDSZl/D8JY80nMU3p4+RRNMrVrmQHowB9jfxNKlSxk2bBgxMTF4eXnxxhtv\nMGrUKDyKqjVMRERERJTAOIy9F7HM5OkJVaqYCczJk1dbZFzA5dRkPo2azo5DG7Pt69r8Xv4e8bDj\nBusXwtmzZ3n22WdZuNCcIa1du3bMmzePOnXqODkyERERkVuPpkFyFEclMAChoeb2yBH7X9tBzl88\nw7TFY7MlL+7uHgzoPpI+7R8pdsmLYRh89dVX1K9fn4ULF+Lr68uMGTNYs2aNkhcRERERJ1ELjCOk\npsLp0+Y0uVWq2P/6H3wAXl6Ob30ZPhzOnIE334RCfGE/fGof85a9xV/JCTbl/j4BDP7HWMIr1y1s\npHZ36tQpnn76aZYuXQpAly5d+Oijj6hhz/VwRERERCTflMA4wsmTYBjmeBVHjI8oqgHj331nrgPz\n+usFvsSmvav58sfZZGSk25SHBIbx5D/GUb5MxcJGaVeGYbBgwQKef/55Lly4gL+/P5GRkQwePBhL\nHgf6i4iIiIjjKIFxhKAgWLkSUlKcHUnBpaVdneksn1MMA1itGXy7/jN+3Lok277GNdswsPtIvHbt\nhU3/he7doShbNn7+GV55BQYPhscfzyqOiYmhV69erFy5EoDevXszd+5cqlatWnSxiYiIiEiulMA4\ngp+f+aXclR0/bq45ExIC168ofxMpqcks+D6S3dHZZ/bq0eoBerXph5vFDaZOhc8/h3nzijaB+fZb\n2LABOnQAwGq1smjRImbPns2lS5coV64cM2bM4OGHH1ari4iIiEgxowRGcnbokLmtWTNfp51LiOXD\nb//F6XPHbMo93EvxcLdnaV7n9quF9eub2z17ChNp/q1YYW5792bPnj08+eSTrF+/HoB7772X2bNn\nExwcXLQxiYiIiEieKIGRnB0+bG7z0TJy8ORu5i2fTFLyRZvyMn7lePLvYwkNrm17Qr165rYoE5jD\nh2HfPoyAAN784QcmTp5MWloaFSpUYMyYMYwZM6boYhERERGRfFMC46q6dYOtW2HnTrObl73dd5+5\n0GO5cnk6fMOuVSxaPZcMq+1g/WpBNXnyH69QtnSF7Cc5owVm+XIAvrdaGT9xIgBDhgzhoYcewt/f\nv+jiEBEREZEC0TowrurCBYiPvzrQ3t4CA6FLF2ja9KaHrty0yJxp7LrkpUmtCEbePynn5AXM7mml\nSpl/hsREe0Sdq4sXL7J55kwAvvrrL2rXrs3PP//M3LlzlbyIiIiIuAglMPZmGNC+Pdx9N1y+7Lh6\nMhezdFQCk0eHTu5hxYYvs5X3atOPx3q9iGcprxuf7OEBTz8Nr71mznrmQN988w3169en1YEDtHB3\np9YLL7B9+3Y6duzo0HpFRERExL7UhczeLlyAdevA3x88PR1XT+YilkeOOK6Om0hNv8yXP8zCwMgq\nK+XhyYDuI2laq13eLjJtmoOiM8XExDBixAgWL14MQKtWrfjoo49o3LixQ+sVEREREcdQC4y9Hbsy\n+1b16uDIKXiLQQvMdxu/4syFUzZlT/79lbwnLw5kGAbz5s2jXr16LF68GD8/P6ZNm8b69euVvIiI\niIi4MLXA2Nu1CYwjZSYwx47lfpyDHI3Zz0+/L7Upa9ewB3VDmzglnmsdOHCAoUOHsnr1agB69erF\n+++/T2jmZyYiIiIiLkstMPZWVAlMly5m68s339j/2v/7HzRqBJMn57g7LT2NL36YhWFYs8rKlQ6k\nT/tH7R9LPqSlpfH222/TuHFjVq9eTWBgIJ9//jnLly9X8iIiIiJSQqgFxt6KKoEpXdp8OcLevbBr\nF8TF5bg7avPibAtVPnjH0/h4+TomnjzYsmULgwcPZvv27QA88sgjREZGEhgYaB6weTMEBEDt2rlc\nRURERESKO7XA2NuoUbBmDfTr5+xICi5zEcuaNbPtOnH2MKu2/NemrHW9LtQPa1bw+hYuhGefhQMH\n8n1qUlISL7zwAq1bt2b79u2Eh4ezcuVKFixYcDV5AfO+1KkDy5YVPE4RERERcTq1wNhbpUrmy5Ud\nOmRua9SwKc7ISOeLVbOwWjOyysr4luOe2x8vXH0LF8KSJRARYS6emUcrV65k2LBhHDlyBDc3N154\n4QVef/11/Pz8bA88fx7Wrzenbb799sLFKiIiIiJOpRYYye4GLTA/bF3CibOHbcr6dhmGr3chu7LV\nr29u9+zJ0+FxcXE88sgj9OzZkyNHjtCkSRN+++033n333ezJC0BUFFit0KEDlKwLkoQAACAASURB\nVClTuFhFRERExKmUwLg6w7DvgpmXL8OJE+DubjOO5/S5Y3y/aaHNoc1qd6BxzdaFr7NePXN7kwTG\nMAw+//xz6tWrx6effoq3tzdvv/02mzZtokWLFjc+cflyc3vnnYWPVUREREScSgmMK5s/H/z84MUX\n7XdNT084eRI2bIBSpQCwWjP4YtVMMjLSsw4r7RPA/Z2etE+deWiBOXLkCL169WLAgAHExcXRuXNn\ndu7cyUsvvUSpK3HmKCMDvvvOfK8ERkRERMTlaQyMKwsIgORk+y5mabFA5crm64qft33L0VjbAfb3\nd3qS0j526o5Vp45Z78GDkJpqJlFXpKWlMX36dMaPH8+lS5coW7YskZGRPPbYY1jyslBocjIMHQo7\ndpj1iIiIiIhLUwJjT4sXwz//CQMHwiuvOL6+zLVNjhxxWBVn4k+xfP0XNmWNa7ahaa129qvE1xfe\neQdCQswucVf89ttvDB06NGtq5L59+zJ9+nSCg4Pzfu3SpeFf/7JfrCIiIiLiVEpg7OngQdi3Dy5c\nKJr6MhMYe7bAXMNqWPnyh1mkZaRmlfl6leaBzkPy1vqRHy+8kPU2ISGBcePGMWfOHAzDICwsjDlz\n5tCrVy/71ikiIiIiLkdjYOwpM5EoqlXfAwPN1ouEBPNlZ2t3fMehU7bjUu7t+AQBfuXtXheYg/T/\n+9//Ur9+fWbPno2bmxsvvfQSu3fvVvIiIiIiIoBaYOzr2JXV6a+ZvcuhLBYzWTpyBE6fNsfEFJbV\nCm5unEuI5Zt1n9rsqh/WnJZ1OxW+jhwcPXqU4cOHs+zKQpNt2rRh7ty5NG7c2CH1iYiIiIhrUguM\nPRV1AgOwcSMkJUHduoW/lmFAhQoYtWuzeMU0UtNSsnZ5e/ryYJen7N51LD09ncjISOrXr8+yZcso\nU6YMc+bMYd26dUpeRERERCQbtcDYi2Fc7UJWlAmMPRdmjImBCxdINzLYc2avza67OwyinH+g/eoC\nNm3axNChQ9m2bRtgDtKfNm0ala+ZAa3AUlOhUyfz9eab5ro2IiIiIuLy1AJjT4cOwebNULassyMp\nmMOHAYgJsF1XpXa1xrRt0M1u1Vy8eJERI0bQpk0btm3bRmhoKMuXL2dhvXpUfvhh83MsrF9/Ndey\n+fZbJS8iIiIiJUixTmAmTJiAm5ubzatKlSrODitnFgsEBUGLFuZ7F2QcPAjAmQo+WWWeHl70u+MZ\nu3QdMwyD//3vf9SrV4+ZM2fi5ubGiy++yO7du+ndu7fZHW71ati5s9B1sXy5udXilSIiIiIlSrFO\nYADq1q1LTExM1munPb7cSo5ObfoJgHMVfLPK/tFuIBUCKhX62seOHeOuu+7ivvvu49SpU7Ru3Zqt\nW7cyZcoU/Pz8zIPq1ze3e/fe+EJ5pQRGREREpEQq9mNg3N3dCQoKcnYYxVt6ujkLWbVqBb7ExaR4\nTm5fRwgQF2gmFDWq1KPDbb0LGVo6M2fO5LXXXiMpKYkyZcrw1ltvMXToUNyv79qVmcDs2ZP9Qvlx\n8CDs32925WvbtnDXEhEREZFipdgnMIcPHyYkJAQvLy9at27NpEmTCA8Pd3ZYxYfVak6ffOkSJCZC\nZmtGPhiGwaLVc9lxfwP+17s2Ge4WSrl70r/rcNwsBW+k27JlC0OGDOGPP/4A4IEHHmDatGk37gZo\nrwTml1/MbY8e4FHs/4qLiIiISD5YDMMwnB3EjXz//fckJiZSt25dYmNjmThxIvv27WP37t2UL391\nMcWEaxZxPHDggDNCNWchc9LYl4b33IP3iRPsWrSIlAIkd0fi9rDmz//ZlDUPu4MGIQVrvUhKSuL9\n999n8eLFWK1WgoODGTNmDB06dMj1PPeLF2l6xx1keHnxx5o14Fbw5Mnr2DEsGRkF+jxERERExLFq\n1aqV9T4gn2sZFutfT/fs2TPrfcOGDWnbti3h4eEsWLCA559/3omRZVf7qafwOnWKg++8Q3KdOkVa\nd2pwMN4nTuB5+nS+v7CnpF1i0+HvbcoCS1ehXpXWBYrl559/5p133uHMmTO4u7szYMAAhgwZgo+P\nz03PzShThoOTJ3PZDtNQ2+MaIiIiIlL8FOsE5nq+vr40aNCAg1dmy8pJixYt7F7vli1bbn7tM2fg\n9GkaRERAUf/Wv3Fj2LKF2p6e5ixo+bDgu0hS0i5l/ezu7sGTd79M5Qr5SwCOHz/Os88+y9KlSwFo\n1aoVc+fOpUmTJvm6Tn7jt5c83WNxebrPJZ/uccmne1zy6R7fGq7tQZVfxX4WsmulpKSwd+9e+yx0\naE/p6XDypNmFLCSk6OsPDTW3mQtp5tGOQ7+xdf+vNmU9Wz2Yr+QlNTWVd955h3r16rF06VL8/f2Z\nNWsW69evz3/yIiIiIiJyE8W6BWb06NH06dOHatWqcebMGd58802Sk5N59NFHnR2arVOnzMH0VaqA\np2fR1x8WBuXK5euUSymJLFr9QdbP3slpVKxSk67N78nzNVavXs0zzzzD3ivTHt93331Mnz6dEGck\ncSIiIiJySyjWCczJkyfp168fcXFxVKxYkbZt27Jx40aqFWK6YIc4dszcOmvcxcCB8Mgj+Tplya8f\nczEpPuvnf6zYR/t132NJaQhDhuR67qlTpxg9ejRffvklYA7CmjlzJj169Mh/7PZ06hTExkKTJi67\nmKiIiIiI5K5YJzCZX5CLvZMnza2zEph8flnfe/QPftvzo01ZnXR/LFYrVLrxopVpaWnMnDmT8ePH\nk5iYiI+PD+PGjWP06NF4eXkVKHS7+uQTGDcORo6EadOcHY2IiIiIOECxTmBcxoMPQq9ekJLi7Ehu\nKvnyJb76YbZNWeUK1al47sraKzVq5HjemjVreOaZZ9i1axcAd999N++99x5hYWH2D/K++2DtWtiy\nJX+Lc65YYW5vv93+MYmIiIhIseBSg/iLtTJlICjI2VHc1Dfr/kN8YlzWzxaLG/07P4XlyJUJAK5L\nYGJiYhg4cCAdO3Zk165d1KhRg2XLlrFkyRLHJC8AcXHmrG5XxtbkyblzsGEDlCoF3bo5Ji4RERER\ncTolMLeQ/cd3sm6n7ZovXZr1ITTDD1JTze5jfn4ApKenM2PGDOrUqcNnn32Gl5cXEyZMYPfu3dx5\n552ODbRePXO7Z0/ez1m50pxI4fbbwd/fMXGJiIiIiNOpC1lJkZJiTqPs72/Ohnady2kpfPnjLJuy\nimWr0KtNP9ix22w9qlkTgHXr1vH000+zY8cOAO68805mzJhBjRt0L7O7+vXNbX5aYDK7j/Xubf94\nRERERKTYUAtMSTFxItStC3Pn5rh7+frPOZcQm/WzBQv9uw7H08MLmjWD2FjOLFrEoEGDaN++PTt2\n7CA0NJSlS5eybNmyokte4GoCk58WmDZtICICHN06JCIiIiJOpQSmsDIyisfg/VwWszx8ah+/bFtm\nU9bhtt7UDDEThYyMDGbPnk2dhg1ZsGABnp6evPbaa+zZs4c+ffo4PPRsMhOY/fvzfs7w4bBuHdSp\n45iYRERERKRYUAJTWHv3go8PtG/v3DgyB9Rfl8CciT/FZ1HTMDCyyiqUqcQ/2g0EYOPGjbRs2ZLh\nw4dz4cIFevTowa5du3jjjTfw9fUtquhtVa4MO3fC8ePOqV9EREREii2NgSmszEUsrwx+d5ocWmC2\nHVjP5z/M5HJqss2hD93xNBcv/MXYscOZN28eANWqVWPatGncc889WJy9CKTFAg0bOjcGERERESmW\nlMAUVmYC46xFLDNl1n/8OOmpKSzd8Fm2bmMAbep15efvNjJ27Fji4+MpVaoUo0ePZty4cfg5OwkT\nEREREbkJJTCFldni4ewExtsbmjQhzdODDz99iT8Ts4+FKWtUZ+orn7B161YAunbtyuypU6nt7BYX\nEREREZE80hiYwspsgcnswuVEe5b8m9cer5steUlNzuDo2stMHDWLrVu3EhISwqJFi4iKiqJ2Who0\nagStWzsp6kIaMQJGjtR4GREREZFbhFpgCispydw6sQXGas1gxcaviNq8+Lpyg8Nb41i/fDcJFxLw\n8PDg+eef55///CelS5c2Dzp82NwW5TTJ+XHuHFSokPO+y5dh/nzzHoweXbRxiYiIiIhTKIEprK+/\nNr9IuzmnMeti0gX+830k+0/stCk/eegcm749yIkjMQB06dKFmTNnUj9ziuJMmQnMlUUsiw3DMGOK\njoa4uJyTmDVrzOSlcWOoVq3oYxQRERGRIqcExh68vJxS7cGTu/nku3e5mBSfVZZ4IZl13+xh/+8n\nAKhevTpTp07l3nvvzXl2sUOHzG1xa4GxWMykJTranKo6p2mqly83t1q8UkREROSWoQTGBVkNKz9u\n/Zrl6z/DalgByEjP4I+fD7Fl1QHSLqfj7e3NSy+9xJgxY3Jfz6W4tsCAuaDlli2wZ48SGBEREREB\nlMC4nKSUv/gsajq7o7dklR3ZE8uvS3by19kkGgD3tGvHoM8+IyxzccvcBAWZ3a+KawIDZgJzvSNH\n4OBBKFfOdScgEBEREZF8UwLjQo7GHODjFVM4/9dZAC6cTeTXJbs4sicWgGa1arH1wAHYujXvs6J9\n/rmjwi28zARm797s+8LCzJnH/vwTPPTXWERERORWoW9+hREXB6VKQUCAQ6sxDIO1O77jf7/OJyMj\nndTL6WxZtZ8/Vh/CmmHFr7Qfb7z+Bs8++ywEB8P58xAba753ZfXrg7s7pKXlvL9qVfMlIiIiIrcM\nJTCFMX48zJkDs2bBM884pIqU1GS++nEOv+//FcMwOPD7SdZ+s5ukhBQA+j38EFPffY/gzGQlNNRM\nYI4edf0EJjwcLl0CT09nRyIiIiIixYQSmMLIXMQyJMQhlz8Vd5T5K6ZwJv4kZ08msOZ/Ozl16BwA\nNeuE8sm8z2jf7rrB7aGh8McfZgLj6mND3NyUvIiIiIiIDSUwhZGZwDhgEctNe1ez8Kf3+SshkY3f\n7WPXumgMA3xKezH65eeYMHYSbjmtPZM5cP/oUbvHJCIiIiLibEpgCsMBCUxq+mX++/O/Wbczij0b\njrJhxV5SklKxuFmI6NaYjz/4nNrhDW58gSZNoEsXqFz55pWtX2+uYVO/Pvj42O3P4FCGARs3QsuW\nGrwvIiIicgvSN8CCungRLlwwv/jntEp8AZy9cJr5K6awZdNWfvnvDs6eSAAg5G+BDH9xMKMem4Bn\nqZssmvnoo+YrL555BrZtg99+g1atChl9Edm2DSIioFEj2LHD2dGIiIiISBFTAlNQ58+bq9f7+Zmr\nxhfS9oMbmPt/U/jpv1v4c8sJAEqX9aHTvbcx9vk3iGjYrdB12DAMOHTIfF+jhn2vbW9nz5prvrRt\nCytWmGWuPr5HRERERApECUxBhYWZCYBhFOoyVsPKf1fPY/r0aWxa+SdplzNw93CjWZe/0eO+2xl2\nzyuEVAy3T8zXOncO/voLypSxWwuSQ6Snm5MkpKeb8S5fbpbfeadz4xIRERERp1ACU1iFaH0xDIM3\n3h3LtCmzSYhLAiC8YTAd7m5Ixzbd6Nd1OD5evvaK1Na1rS92aEFyGA8PqF0bdu+GdevM8S+entC1\nq7MjExEREREnUALjJH/88QfPPPs0G9ZtBKBcUGk63NOQGg1CuLvDIG6/7U4sjkwsDh82t8W9+xhA\nvXpmAvPee2aLV8eOULq0s6MSERERESdQAlPETp8+zbhx4/jkk08wDANv31K06lWXhhFhlPELYEif\nVwmvXKdwlezbB9u3Q9OmZutFTsqWhe7doU2bwtVVFOrXN7exsWbLy913OzceEREREXEaJTBF5NKl\nS0RGRjJ58mSSkpLw8HCnYfswWnavjbevuVjjg12eKnzyAjBzJsyZA9Om3TiB6dXLfLmCzASmenX4\n+mvnxiIiIiIiTqUEpqD++MNca6VSpVzHkFitVr788ktefvllTpwwZxfr3qsrwc0sBFS8Or6lRd2O\nNKkVYZ/YQkPNbUlZzLJhQ7MbWeafS0RERERuWUpgCiIjw1xIMSMDkpPB2zvHw9atW8eoUaPYtGkT\nAE2bNuXtyW+x8eQS4hJiso4LKF2B+zs9ab/4Mr/oHzliv2s6U4MGsGePs6MQERERkWLAzdkBuKTT\np83kpVKlHJOX6OhoHnzwQdq3b8+mTZuoXLkyH3/8MZs3b+aCe7RN8gLwcNdn8fWy46D0ktYCIyIi\nIiJyhVpgCuLYMXNbvbpN8cWLF5k0aRLTpk3j8uXL+Pj4MHr0aMaMGUPp0qXZe/QP1u783uacDo17\nUze0iX3jCwszt0pgRERERKSEUQJTENclMOnp6cybN4/XXnuNs2fPAjBgwAAmTZpEtWrVALiUksgX\nq2baXKZiQGX6tH/E/vEFBUGfPuYCkBkZ4O5uu3//fti0yZylrEED+9cvIiIiIuIgSmAK4poEZtWq\nVYwaNYpdu3YB0K5dO6ZOnUqrVq1sTln884ckJJ3P+tlicWNAj5F4lcp5/EyhuLnB0qU33r9yJYwY\nAUOGwNy59q9fRERERMRBlMAUROnSpPztb/w7Kopn33sPgLCwMKZMmcL999+fbQHK3/evZeufa2zK\nurW4l/DKdYssZBuZi1jWrOmc+kVERERECkgJTD6dO3eOCXv38n50NBkZGfj7+zNu3DhGjhyJdw4D\n+hOSzrNotW0rR0hgGD1bP1hUIWd36JC5rVHDeTGIiIiIiBSAEpg8SktL47333uONN97gwoULuLm5\nMXToUN544w2CgoJyPMcwDL76YQ6XUv7KKnN392BA9+fwcC9VVKFnpxYYEREREXFRSmDy4OzZswwd\nOpTjx48D0K1bNyIjI2nUqFGu523Y/QO7j2yxKevdpj8hFcMcFerNGcbVBEYtMCIiIiLiYpTA5EFg\nYCDlypXDz8+PyMhIevXqlW2cy/XOJcSyZM08m7LwynW5o9ldjgz1qoQE+PprSEuDwYOvll++bA7e\nj42FgICiiUVERERExE6UwOSBxWJh8uTJ3HHHHZQqdfOuX1ZrBp9FTedyWkpWmWcpbwZ0H4mbm3su\nZ9rRxYswaBAEB9smMN7eMG1a0cQgIiIiImJnbs4OwFUEBgaaycvJk/DLL3Dq1A2P/Xnbtxw6tcem\n7O72g6hYtrKjw7yqShXw8ICYGEhJufnxIiIiIiIuQAlMfi1bBp06wWuv5bj79LljLFv/uU1Z3dCm\ntGvUowiCu4a7O1Star6/MnZHRERERMTVKYHJr2sWsbxeekYan66cRnpGWlaZj5cf/bsOv+mYGYcI\nDTW3R44Ufd0iIiIiIg6gBCa/cklgVm5azImzh23K+nYeStnSFYoisuzCwszt0aPOqV9ERERExM40\niD+/bpDAHI3Zz6rN/2dT1rRWO5rV7lBUkWXXuzdUqAANGlwt+9e/zIH9AweCp6fzYhMRERERKQAl\nMPmVQwKTmn6ZT6OmYzWsWWVlfMvRt/NQ53Qdy9S3r/nKlJgIr75qJi6DBjktLBERERGRgnKJLmRz\n5swhPDwcHx8fWrRowdq1a50XTOvW0Lz51QHywLfrPuVM/Embw/p1fQY/nzJFHV3uoqPNbViYOchf\nRERERMTFFPsEZuHChTz33HO8+uqrbNu2jYiICHr16sVxZ82s9dVXsGUL+PgAsP/4Dn7ZtszmkIiG\n3WgQ3sIZ0eXu0CFzW7Omc+MQERERESmgYp/ATJ06lccee4wnnniCOnXqMGPGDCpXrsz777/v7NBI\nvpzE51EzbMoqlKnE3R0ed1JEN3H4ygQDNWo4Nw4RERERkQIq1glMamoqv//+O927d7cp7969O+vX\nr3dSVFf975d5xCfGZf1swcLD3Ufg7enjxKhyoRYYEREREXFxxXoQf1xcHBkZGVSqVMmmPCgoiJiY\nmBzP2bJli8Piufbax879yW/7frLZX69Kay6cTmbLacfFkF9lf/kFv507Ode7N561a+P/yCNcKF+e\nJAd+Tq7MkX9/pPjQfS75dI9LPt3jkk/3uGSrVatWgc8t1glMcZWcmsTGQ8ttygJ8Amka2sk5AeWi\nXFQUFaKiSAkP59ydd3KxXTtnhyQiIiIiUmDFOoEJDAzE3d2d2NhYm/LY2FgqV66c4zktWth/8Hzm\nbwBanDuHYbXyn4u/kZJ2KWu/m5s7Q+4eS7WgYtg1q1kziIoi3M2NcAd8NiVF1j3WZ1Si6T6XfLrH\nJZ/uccmne3xrSEhIKPC5xXoMjKenJ82bNycqKsqmfNWqVURERBR9QC+/jKV3b85uWm1T3LNV3+KZ\nvACEhprbI0ecGoaIiIiIiD0U6xYYgFGjRjFw4EBatWpFREQEH3zwATExMQwbNqzIY7EePYobEF/u\n6iD90Eq16Nby/iKPJc8yE5ijR50bh4iIiIiIHRT7BKZv376cO3eOiRMncvr0aRo1asSKFSuoVq1a\nkcZhSUrCLT6eNA83Ev28ACjl7smAHs/h7laMF4VUAiMiIiIiJUix7kKW6amnniI6OpqUlBQ2b95M\n+/btizyGE7t+BCC+rA+GmwWAPu0foVK5kCKPJV/CwuCVV8zt6NHmIpwiIiIiIi7KJRIYZ0u4dI7T\nu80pkzO7j9Wu2ogOt/V2Zlh54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       "text": [
        "<matplotlib.figure.Figure at 0x7fe15890ec50>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that the filtered output of the reprocessed signal is smoother, but it also diverges from the track. What is happening? Recall that the Kalman filter requires that the signal not be time correlated. However the output of the Kalman filter *is* time correlated because it incorporates all previous measurements into its estimate for this time period. So look at the last graph, for 2 iterations. The measurements start with several peaks that are larger than the track. This is 'remembered' (that is vague terminology, but I am trying to avoid the math) by the filter, and it has started to compute that the object is above the track. Later, at around 13 seconds we have a period where the measurements all happen to be below the track. This also gets incorporated into the memory of the filter, and the iterated output diverges far below the track. \n",
      "\n",
      "Now let's look at this in a different way. The iterated output is *not* using $\\mathbf{z}$ as the measurement, but the output of the previous Kalman filter estimate. So I will plot the output of the filter against the previous filter's output."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_kf_output(xs[0:30], fxs0[0:30], zs[0:30], title='KF')\n",
      "plot_kf_output(xs[0:30], fxs1[0:30], fxs0[0:30:,0], title='1 iteration')\n",
      "plot_kf_output(xs[0:30], fxs2[0:30], fxs1[0:30:,0], title='2 iterations')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lkPwclw93j6AqKpMOGg0ODmb16tVs27bNYB5FQeLj47l8+TKVC7lLrxBCCCHu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\n/9dkuXK/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15886cd30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VigkTJpCcnEz//v2Jjo5m1KhRmJiYGDu8bA4OMHQoDBtWoMtv3LpKdOxhvbJ2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YG5npvNibNHCldazhzkWvbVUp1Xz92btkGdCQ/pRuvm7akT/jE8+iimsWOh/q3XvhQUFPDmm2+y\nYMECrly5gouLC3PmzOG5557Dw8OjTDGLiIiIiFQmJTCV7dQpOH8efHwgPLzE6hn/Sed48kGOnz7A\nyfNHKSjIL1U3fg0DCA/pRnhwV4L8WmI2O/1ycMwYuO8+8PW95byvv/6ap556isOHDwMwcOBAVqxY\nQcuWLUv3v09EREREpAopgalsN7aPRUWB2XzbKhczU9n/3S6OJx/gfPrpUjVrNplp4d+W8JCuhAd3\nxad+k+JPaNbM6mN6ejpz585l3bp1AAQEBPD6668zYsSIcj3cUkRERESkKiiBqWx9+sBLL0HHjrc9\nfO7CaZZunEN+QV6JTbm7eBAW1JnwkK60CeyEh1u9ModTUFDAX/7yF+bOnUtGRgZ16tRh1qxZzJ8/\nn7p165a5PRERERGRqqQEprK1aQMLFtzx8Nav3i82ebnLuzHtgrsRHtKNFk3b4ORU/iE7cOAATz31\nFAcPHgTg/vvvZ+XKlYSGhpa7TRERERGRqqQExo5SL58j4cxBqzITJoKahBZdz+LXsFmFt3RdunSJ\n+fPns3btWgzDwN/fn6VLlzJq1ChtFxMRERERh6IExo6+OPxPq88Bvi2YPPx5PD1uvVNYeRQUFLBm\nzRoWLFhARkYGzs7OzJgxgxdeeIF69cq+/UxERERExN6UwNjJ1WtX2J/4hVVZv84jbJa87N69m6lT\npxIfHw9AVFQUK1asICwszCbti4iIiIjYw+1viyWVbs/RT62ufWno6UP7u3tWuN2UlBQeeeQRevfu\nTXx8PM2bN+fvf/87//rXv5S8iIiIiIjDUwJTWXbvLryAf8mSWw7l5l9n97FPrcoiO/4Gp18/u6WM\nrl+/ziuvvEJoaCgffPABbm5uLFy4kMTEREaOHKlrXURERESkRtAWssryr3/BiRPw44+3HDqQ+AXX\nsq8WfXZ38aBn2/7l7mrr1q0888wznDp1CoARI0bw2muvERQUVO42RURERESqIyUwleXGAyz79bMq\nthgWdh3aZFUW0W4Abi7uZe4iKSmJZ555hi1btgDQunVrli9fTv/+5U+GRERERESqM20hqwxZWfDN\nN2A2Q2Sk1aGE5INcuPLLqozZ7ETv9g+Usfks5s2bR9u2bdmyZQuenp7ExMRw9OhRJS8iIiIiUqNp\nBaYyxMVBfj507w7e3laHbl596dSqFw08G5WqWcMwWL9+PbNnzyYlJQWAcePGsXjxYvz8/GwTu4iI\niIhINaYEpjIcOVL496btY2fTkkhKSbAqi+o0vFRNxsfHM23aNOLi4gDo0qULK1asoEePHhWPV0RE\nRETEQSiBqQzz5sHjjxduIfuVm1dfWjVrRzOfkGKbunz5Mi+88AJvvPEGFouFRo0asXjxYv7whz9g\nNmsHoIiIiIjULkpgKou/v9XHy1fTOXxqr1VZ32JWXwoKCvjLX/7C/PnzuXTpEk5OTkybNo3o6Gga\nNGhQKSGLiIiIiFR3SmCqSFz8ZiyGpehz44bNaBPU6bZ19+3bx9SpUzl06BAAffr0Yfny5bRr165K\nYhURERERqa60B6kKZF+/xt7j26zK+nYcjtlk/fX/9NNPPPbYY9x7770cOnSIgIAANm7cyM6dO5W8\niIiIiIigFZgq8VXCdq7nZhd99nT3pmvrX26vnJuby7Jly/jjH/9IVlYWrq6uzJ49m+eee466deva\nI2QRERERkWpJCYwtXboEJ09C167gXPjVFhTk8+XhzVbVerUfQh1nFwzDYNOmTcyePZukpCQAhg8f\nzmuvvUZISPEX94uIiIiI1EbaQmZL//wnRETAo48WFR1J2kdG1sWiz3WcXOjVbhCHDx8mKiqKESNG\nkJSUROvWrfn000/5+OOPlbyIiIiIiNyBVmBsaceOwr+9egGFD57cedOtk1v6dmL6lBm88847GIZB\nw4YNefHFF5k0aRJ16tSp6ohFRERERByKEhhbMYxfEpioKACSUhI4d+F7APJy8zm863vWxW3n52s/\nU6dOHaZOncqCBQt0W2QRERERkVJSAmMriYmQmgp+fhAWBhQ+uNKwGJw8dJ59m78j60oOACNGjGDJ\nkiW0bNnSnhGLiIiIiDgcJTC28uvVF5OJtIwUtu34jD0fHyft7BUAwsLbsGrFavr06WO/OEVERERE\nHJgSGFsJCICBA2HIEJKTk3lk/Ci+/rLwQZR1vVwZOqYPf1u5GWdnfeUiIiIiIuWlX9O28uCDXI2K\nYtGiRbw+YQLXr1/HuY4THfu2oFO/lvzP8DlKXkREREREKki/qG0gPz+fdevW8fzzz5Oeng5AaJdm\n9BwahmcDdxp4+tChZYSdoxQRERERcXxKYCpo+/btzJw5k+PHjwMQEdGTlr0b4OX3yy2RIzs8gJPZ\nyV4hioiIiIjUGHqQZTklJiYydOhQBgwYwPHjxwkKCmLjxo28+uZCq+TFzcWDnm372zFSEREREZGa\nQwlMGV26dImpU6fSrl07tm7diqenJ6+88gqJiYmMHDWSLw5/YlU/Irw/7q4edopWRERERKRmUQJT\nSnl5eSxdupS7776blStXYhgGkyZN4sz69cz5/nvcdu8m8cwh0jLOF51jNpnp3f4BO0YtIiIiIlKz\n6BqYUkhPT2fSpEmcO3cOgP79+xMTE0O7du1g/nx46y3w9GRnhPVKS8eW99LQy8ceIYuIiIiI1EhK\nYEqhUaNGNGjQgLp16xITE8PgwYMxmUyFB//7AMv0TmGcOm+9faxvp+FVHaqIiIiISI2mBKYUTCYT\nS5YsoV+/ftSp88sF+mRmwoED4OzMdvcLVufc7d+W5o3vruJIRURERERqNl0DU0qNGjWyTl4AvvwS\nLBbyO3dkf8pBq0NRnR6swuhERERERGoHJTAV8d/tY9+3boLFUlBU7NvAn7DgzvaKSkRERESkxlIC\nUxELFpD7biyfNM+3Ku7bcRhmk75aERERERFb06/sivDxYW9Yfc7e9cvWsnru3nRt08d+MYmIiIiI\n1GBKYCqgwFLAl0es7zzW655BuDi72ikiEREREZGaTQlMBcQnfcXl/6QXfXZ2qsN99wy2Y0QiIiIi\nIjWbQyQwq1evJjg4GHd3d7p06cKePXvsHRKGYbDz0Carsm5t+uDpUd9OEYmIiIiI1HzVPoHZsGED\nzzzzDAsWLODIkSNEREQwePBgzp07Z7+gsrM5nXyEs2mnrIr7dtSDK0VEREREKlO1T2Bee+01xo8f\nz4QJEwgNDWX58uU0adKEN954w35BvfcegW26M/DzfxcVtQ3qQuOGzewXk4iIiIhILVCtE5jc3FwO\nHTrEgAEDrMoHDBjAvn377BQV5Hy6GefcPK7VdSkq69tJqy8iIiIiIpXN2d4BFOfixYsUFBTQuHFj\nq3JfX19SU1Nve87BgwcrLZ6DBw+CxULYfx9gebJlIwAa1vUjMzWHg2mV17dUjcr870eqD41zzacx\nrvk0xjWfxrhma9myZbnPrdYrMNWR+d8JeFy9xhVvNy741gMgzL8HJpPJzpGJiIiIiNR81XoFplGj\nRjg5OZGWlmZVnpaWRpMmTW57TpcuXWwex41/AejSpQsn/rYCgH+38gGTifr17mLkgLE4OVXrr1JK\n8OsxlppL41zzaYxrPo1xzacxrh0yMzPLfW61XoFxcXGhc+fObNu2zap8+/btREREVHk8efm5nD99\nlBxX56LtY5EdfqPkRURERESkilT7X94zZ87kscceo1u3bkRERPDmm2+SmprK5MmTqzyWgye+5J9R\ngWyODMBsGLi6uBMR3r/K4xARERERqa2qfQIzevRoLl26xMsvv8xPP/1Eu3bt2Lp1KwEBAVUah2EY\n7Dr8TwAsTmYsQK+2/XF3rVulcYiIiIiI1GbVPoEBePLJJ3nyySftGsOPV74n9fIvD880m8z06fCA\nHSMSEREREal9qvU1MNVJQsrXVp87tIygoZevnaIREREREamdlMCUwuWsVFIzz1iV9e2oB1eKiIiI\niFQ1JTCl8N2P39Dkx6t0PXAOr8wcWjQNI9Cv/A/fERERERGR8lECU4IrWZdIvphAl2/P8djfDtHn\ny+/p20mrLyIiIiIi9qAEpgRHv/8aw7DQ6uRFANI6hhIe0tXOUYmIiIiI1E4mwzAMewdRURV5kqeI\niIiIiNiPt7d3meprBUZERERERByGEhgREREREXEYNWILmYiIiIiI1A5agREREREREYehBEZERERE\nRByGEhgREREREXEYSmBKYfXq1QQHB+Pu7k6XLl3Ys2ePvUMSG4mOjsZsNlu9mjZtau+wpALi4uIY\nNmwYzZo1w2w2Exsbe0ud6Oho/P398fDwoG/fvnz33Xd2iFTKq6QxHjdu3C3zOiIiwk7RSnksXryY\nrl274u3tja+vL8OGDSMhIeGWeprLjq0046z57NhWrVpF+/bt8fb2xtvbm4iICLZu3WpVpzzzWAlM\nCTZs2MAzzzzDggULOHLkCBEREQwePJhz587ZOzSxkdatW5Oamlr0OnbsmL1Dkgq4du0a99xzD8uW\nLcPd3R2TyWR1fMmSJbz22musXLmSAwcO4OvrS//+/cnKyrJTxFJWJY2xyWSif//+VvP65v/DlOrt\nyy+/ZMqUKXz11Vfs3LkTZ2dn7r//fjIyMorqaC47vtKMs+azYwsICODVV1/l8OHDfPvtt0RFRfHg\ngw8SHx8PVGAeG1Ksbt26GRMnTrQqa9mypTF37lw7RSS2tHDhQiM8PNzeYUglqVevnhEbG1v02WKx\nGH5+fsaiRYuKyrKzsw1PT09jzZo19ghRKujmMTYMw3j88ceNBx54wE4RSWXIysoynJycjM2bNxuG\noblcU908zoah+VwTNWzY0Fi7dm2F5rFWYIqRm5vLoUOHGDBggFX5gAED2Ldvn52iEls7ffo0/v7+\nhISEMGbMGJKTk+0dklSS5ORk0tLSrOa0m5sbvXv31pyuQUwmE3v27KFx48aEhoYyceJE0tPT7R2W\nVMDVq1exWCw0aNAA0FyuqW4eZ9B8rkkKCgpYv349OTk59O7du0LzWAlMMS5evEhBQQGNGze2Kvf1\n9SU1NdVOUYkt9ejRg9jYWD7//HPeeustUlNTiYiI4PLly/YOTSrBjXmrOV2zDRo0iHfffZedO3cS\nExPD/v37iYqKIjc3196hSTlNnz6djh070rNnT0Bzuaa6eZxB87kmOHbsGPXq1cPNzY2JEyeyceNG\nQkNDKzSPnSstWhEHMGjQoKL34eHh9OzZk+DgYGJjY5kxY4YdI5OqdvN1FOK4HnrooaL3bdu2pXPn\nzgQGBrJlyxZGjBhhx8ikPGbOnMm+ffvYs2dPqeap5rJjutM4az47vtatW3P06FEyMzP58MMPefjh\nh9m1a1ex55Q0j7UCU4xGjRrh5OREWlqaVXlaWhpNmjSxU1RSmTw8PGjbti1JSUn2DkUqgZ+fH8Bt\n5/SNY1LzNGnShGbNmmleO6AZM2awYcMGdu7cSVBQUFG55nLNcqdxvh3NZ8dTp04dQkJC6NixI4sW\nLaJHjx6sWrWq6Ld0eeaxEphiuLi40LlzZ7Zt22ZVvn37dt3Cr4bKyckhMTFRCWoNFRwcjJ+fn9Wc\nzsnJYc+ePZrTNVh6ejopKSma1w5m+vTpRT9qW7VqZXVMc7nmKG6cb0fz2fEVFBRgsVgqNI+doqOj\noys5Tofm5eXFwoULadq0Ke7u7rz88svs2bOHt99+G29vb3uHJxU0a9Ys3NzcsFgsnDx5kilTpnD6\n9GnWrFmj8XVQ165d47vvviM1NZV169bRrl07vL29ycvLw9vbm4KCAl555RVCQ0MpKChg5syZpKWl\nsXbtWlxcXOwdvpRCcWPs7OzMvHnz8PLyIj8/nyNHjvDEE09gsVhYuXKlxthBPP300/z1r3/lww8/\npFmzZmRlZZGVlYXJZMLFxQWTyaS5XAOUNM7Xrl3TfHZwzz33XNHvrHPnzvH666/z/vvv8+qrr9Ki\nRYvyz+PKvlVaTbB69WojKCjIcHV1Nbp06WLs3r3b3iGJjTz88MNG06ZNDRcXF77AePAAAAefSURB\nVMPf398YNWqUkZiYaO+wpAJ27dplmEwmw2QyGWazuej9+PHji+pER0cbTZo0Mdzc3Iw+ffoYCQkJ\ndoxYyqq4Mc7OzjYGDhxo+Pr6Gi4uLkZgYKAxfvx44/z58/YOW8rg5rG98XrxxRet6mkuO7aSxlnz\n2fGNGzfOCAwMNFxdXQ1fX1+jf//+xrZt26zqlGcemwzDMKouDxMRERERESk/XQMjIiIiIiIOQwmM\niIiIiIg4DCUwIiIiIiLiMJTAiIiIiIiIw1ACIyIiIiIiDkMJjIiIiIiIOAwlMCIiIiIi4jCUwIiI\nyG316dOHvn372juMW6SkpODu7s6uXbvsFsOqVasIDAwkNzfXbjGIiNRWSmBERGqxffv28eKLL5KZ\nmXnLMZPJhMlkskNUxXvxxRfp0KGDXZOrCRMmcP36ddasWWO3GEREaislMCIitVhxCcz27dvZtm2b\nHaK6s/T0dGJjY5k8ebJd43Bzc+Pxxx8nJiYGwzDsGouISG2jBEZERG77I9zZ2RlnZ2c7RHNn7733\nHgAjRoywcyTw0EMPcfbsWXbu3GnvUEREahUlMCIitVR0dDTPPvssAMHBwZjNZsxmM3FxccCt18Cc\nOXMGs9nMkiVLWL16NSEhIdStW5f777+fs2fPYrFYeOmll2jWrBkeHh4MHz6cS5cu3dLvtm3biIyM\nxNPTE09PTwYPHkx8fHypYv7444/p2rUrXl5eVuVpaWk88cQTBAQE4Obmhp+fH0OGDOG7774rV98n\nT55kzJgx+Pr64u7uTqtWrZgxY4ZVnU6dOtGwYUP+8Y9/lCp2ERGxjer1T2siIlJlRo4cyalTp/jg\ngw94/fXXadSoEQBt2rQpqnO7a2DWr1/P9evXmTZtGpcvX+bVV1/ld7/7HX369GH37t3MnTuXpKQk\nli9fzsyZM4mNjS069/333+exxx5jwIABvPLKK+Tk5LB27Vruu+8+Dhw4QGho6B3jzcvL48CBA0yc\nOPGWY6NGjeL48eNMnTqV4OBgLly4QFxcHKdOnSIsLKxMfSckJHDvvffi7OzMxIkTCQkJITk5mY0b\nN7J06VKrfjt16sTevXvL8K2LiEiFGSIiUmv9+c9/Nkwmk/HDDz/cciwyMtLo27dv0efk5GTDZDIZ\nPj4+RmZmZlH5vHnzDJPJZLRr187Iz88vKn/kkUcMFxcXIycnxzAMw8jKyjIaNGhgTJgwwaqfjIwM\nw9fX13jkkUeKjTUpKckwmUzGsmXLbjnfZDIZMTExdzy3LH1HRkYanp6expkzZ4qNxzAMY+LEiYar\nq2uJ9URExHa0hUxERMpk5MiRVlu4unXrBsDYsWNxcnKyKs/Ly+PcuXNA4U0Brly5wpgxY7h48WLR\nKz8/n169epV4W+Qb29EaNGhgVe7u7o6Liwu7du0iIyPjtueWtu/09HTi4uIYN24cgYGBJX4XDRo0\nIDc3l6ysrBLrioiIbWgLmYiIlEnz5s2tPnt7ewMQEBBw2/IbScXJkycB6N+//23b/XXyUxzjphsO\nuLq6smTJEmbNmkXjxo3p3r07Q4YM4bHHHqNZs2Zl6vv06dMAhIeHlymW6ni7aRGRmkoJjIiIlMmd\nEo07ld/4kW+xWACIjY3F39+/zP3euEbndqss06dPZ/jw4WzatInt27fz0ksvsWjRIjZv3kxkZGSF\n+76TjIwMXF1dqVu3rs3aFBGR4imBERGpxapy5aBFixZAYSISFRVV5vObN2+Oh4cHycnJtz0eFBTE\n9OnTmT59OikpKXTo0IE//elPREZGlrrvG/WOHTtWqpiSk5OtbnogIiKVT9fAiIjUYjdWDi5fvlzp\nfQ0aNIj69euzaNEi8vLybjl+8eLFYs93dname/fuHDhwwKo8Ozub7OxsqzJ/f398fHyKHtA5cODA\nYvtOT08HChOcyMhI3nnnHc6cOWNV5+atawCHDh0iIiKi2LhFRMS2tAIjIlKLde3aFYC5c+cyZswY\nXFxc6NevHz4+PsDtf7SXl6enJ2+++SaPPvooHTt2LHrOytmzZ/nss88IDw/n7bffLraN4cOHM3v2\nbDIzM4uusfn3v/9NVFQUo0ePJiwsDFdXV7Zu3cqJEyeIiYkBwMvLq9R9r1ixgl69etG5c2cmTZpE\ncHAwZ8+eZcOGDUXX0gB8++23ZGRk8OCDD9rsOxIRkZIpgRERqcU6d+7M4sWLWb16NX/4wx8wDINd\nu3bh4+ODyWQq9RazO9W7uXz06NE0bdqURYsWERMTQ05ODv7+/tx7771Mnjy5xH4effRRnn32Wf7x\nj38wbtw4oHBr2dixY9mxYwfvv/8+JpOJ0NBQ/vd//7eoTln6Dg8P5+uvv+b5559nzZo1ZGdn07x5\nc4YNG2YVy8aNG2nevDn3339/qb4jERGxDZNhy39eExERqWSTJ08mPj6er776ym4x5OTkEBQUxLx5\n85g2bZrd4hARqY10DYyIiDiUF154gfj4+BKfG1OZ1q1bh5ubG08++aTdYhARqa20AiMiIiIiIg5D\nKzAiIiIiIuIwlMCIiIiIiIjDUAIjIiIiIiIOQwmMiIiIiIg4DCUwIiIiIiLiMJTAiIiIiIiIw1AC\nIyIiIiIiDuP/AxRw/1JxA/VRAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15886ce10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V1TVdeWxsLO+++y6Ojo4UL16cMmXK4OTkxP3794mLi9PXu3jxIrVr187Svd57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z7zJSc3m4++Xcyuw5swDIMju06T+O8DZGXkADDksUeZ+/d5+Pr6lndqERERERHTqYCpaIYB3t5F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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1589ba320>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I hope the problem with this approach is now apparent. In the bottom graph we can see that the KF is tracking the imperfect estimates of the previous filter, and incorporating delay into the signal as well due to the memory of the previous measurements being incorporated into the signal."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Excercise: Prove that the PS improves the filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Devise a way to prove that fusing the PS and wheel measurements yields a better result than using the wheel alone.\n",
      "\n",
      "##### Solution 1\n",
      "\n",
      "Force the Kalman filter to disregard the PS measurement by setting the measurement noise for the PS to a near infinite value. Re-run the filter and observe the standard deviation of the residual. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fusion_test(1.5, 3.0, do_plot=False)\n",
      "fusion_test(1.5, 1e80, do_plot=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fusion std: 0.391\n",
        "fusion std: 0.438\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see the error in the filter where the PS measurement is almost entirely ignored is greater than that where it is used.\n",
      "\n",
      "\n",
      "##### Solution 2\n",
      "\n",
      "This is more work, but we can write a Kalman filter that only takes one measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "from numpy.random import randn\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from filterpy.kalman import KalmanFilter\n",
      "from numpy import array, asarray\n",
      "\n",
      "dt = 0.1\n",
      "wheel_sigma = 1.5\n",
      "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
      "\n",
      "kf.F = array ([[1., dt], [0., 1.]])\n",
      "kf.H = array ([[1., 0.]])\n",
      "kf.x = array ([[0.], [1.]])\n",
      "kf.Q *= 0.01\n",
      "kf.P *= 100\n",
      "kf.R[0,0] = wheel_sigma**2\n",
      "\n",
      "random.seed(1123)\n",
      "xs = []\n",
      "zs = []\n",
      "nom = []\n",
      "for i in range(1, 100):\n",
      "    m0 = i + randn()*wheel_sigma\n",
      "    z = array([[m0]])\n",
      "\n",
      "    kf.predict()\n",
      "    kf.update(z)\n",
      "\n",
      "    xs.append(kf.x.T[0])\n",
      "    zs.append(z.T[0])\n",
      "    nom.append(i)\n",
      "\n",
      "xs = asarray(xs)\n",
      "zs = asarray(zs)\n",
      "nom = asarray(nom)\n",
      "\n",
      "\n",
      "res = nom-xs[:,0]\n",
      "print('std: {:.3f}'.format (np.std(res)))\n",
      "\n",
      "bp.plot_filter(xs[:,0], label='Kalman filter')\n",
      "bp.plot_measurements(zs[:,0],label='Wheel')\n",
      "plt.legend(loc=4)\n",
      "plt.xlim((-1,100))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "std: 0.523\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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INHLHTh1kWeJ8ktLWYTNs1db4+7ak6LN/UlbSDNebbsZ963aIjIRly6B7d3uR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\nESlzCh4iIiIiIlLmFDxERERERKTM/X9vfiZEk46KUQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c2ef98>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On this run I got a standard deviation of 0.523 vs the value of 0.391 for the fused measurements. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise: Different Data Rates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is rare that two different sensor classes output data at the same rate. Assume that the PS produces an update at 1 Hz, and the wheel updates at 4 Hz. Design a filter that incorporates all of these measurements.\n",
      "\n",
      "**hint**: This is a difficult problem in that I have not explained how to do this. Think about which matrices incororate time, and which incorporate knowledge about the number and kind of measurements. All of these will have to be designed to work with this problem. If you can correctly enumerate those matrices you are most of the way to a solution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your solution here!"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can do this by setting the data rate to 0.25 seconds, which is 4 Hz. As we loop, on every iteration we call `update()` with only the wheel measurement. Then, every fourth time we will call `update()` with both the wheel and PS measurements. \n",
      "\n",
      "This means that we vary the amount of data in the z parameter. The matrices associated with the measurement are $\\mathbf{H}$ and $\\mathbf{R}$. In the code above we designed H to be \n",
      "\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1 &0 \\\\ 1& 0\\end{bmatrix}$$\n",
      "\n",
      "to account for the two measurements of position. When only the wheel reading is available, we must set\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1 &0\\end{bmatrix}.$$\n",
      "\n",
      "The matrix $\\mathbf{R}$ specifies the noise in each measurement. In the code above we set\n",
      "\n",
      "$$\\mathbf{R} = \\begin{bmatrix}\\sigma_{wheel}^2 &0 \\\\ 0 & \\sigma_{PS}^2\\end{bmatrix}$$\n",
      "\n",
      "When only the wheel measurement is available, we must set\n",
      "\n",
      "$$\\mathbf{R} = \\begin{bmatrix}\\sigma_{wheel}^2\\end{bmatrix}$$\n",
      "\n",
      "The two matrices that incorporate time are $\\mathbf{F}$ and $\\mathbf{Q}$. For example,\n",
      "\n",
      "$$\\mathbf{F} = \\begin{bmatrix}1 & \\Delta t \\\\ 0& 1\\end{bmatrix}.$$\n",
      "\n",
      "Since the wheel and PS reading coincide once every 4 readings we can just set $\\delta t =0.25$ and not modify it while filtering. If the readings did not coincide in each iteration you would have to calculate how much time has passed since the last predict, compute a new $\\mathbf{F}$ and $\\mathbf{Q}$, and then call `predict()` so the filter could make a correct prediction based on the time step required.\n",
      "\n",
      "So here is the code. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "from numpy.random import randn\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from filterpy.kalman import KalmanFilter\n",
      "from numpy import array, asarray\n",
      "\n",
      "def fusion_test(wheel_sigma, ps_sigma, do_plot=True):\n",
      "    dt = 0.25\n",
      "    kf = KalmanFilter(dim_x=2, dim_z=2)\n",
      "\n",
      "    kf.F = array([[1., dt], [0., 1.]])\n",
      "    kf.H = array([[1., 0.], [1., 0.]])\n",
      "    kf.x = array([[0.], [1.]])\n",
      "    kf.Q *= array([[(dt**3)/3, (dt**2)/2],\n",
      "                   [(dt**2)/2,  dt      ]]) * 0.02\n",
      "    kf.P *= 100\n",
      "    kf.R[0,0] = wheel_sigma**2\n",
      "    kf.R[1,1] = ps_sigma**2 \n",
      "\n",
      "    random.seed(1123)\n",
      "    xs = []\n",
      "    zs_wheel = []\n",
      "    zs_ps = []\n",
      "    nom = []\n",
      "    for i in range(1, 101):\n",
      "        \n",
      "        if i % 4 == 0:\n",
      "            m0 = i + randn()*wheel_sigma\n",
      "            m1 = i + randn()*ps_sigma\n",
      "            z = array([[m0], [m1]])\n",
      "            kf.H = array([[1., 0.], [1., 0.]])\n",
      "            R = np.eye(2)\n",
      "            R[0,0] = wheel_sigma**2\n",
      "            R[1,1] = ps_sigma**2      \n",
      "            \n",
      "            zs_wheel.append(m0)\n",
      "            zs_ps.append((i,m1))\n",
      "        else:  \n",
      "            m0 = i + randn()*wheel_sigma\n",
      "            z = array([m0])\n",
      "            kf.H = array([[1., 0.]])\n",
      "            R = np.eye(1) * wheel_sigma**2\n",
      "            zs_wheel.append(m0)\n",
      "\n",
      "        kf.predict()\n",
      "        kf.update(z, R)\n",
      "\n",
      "        xs.append(kf.x.T[0])\n",
      "        nom.append(i)\n",
      "\n",
      "    xs = asarray(xs)\n",
      "    nom = asarray(nom)\n",
      "\n",
      "    res = nom-xs[:,0]\n",
      "    print('fusion std: {:.3f}'.format (np.std(res)))\n",
      "    if do_plot:\n",
      "        bp.plot_measurements(zs_wheel,  label='Wheel')\n",
      "        plt.plot(*zip(*zs_ps), linestyle='--', label='Pos Sensor')\n",
      "        bp.plot_filter(xs[:,0], label='Kalman filter')\n",
      "        plt.legend(loc=4)\n",
      "        plt.ylim(0,100)\n",
      "        plt.show()\n",
      "\n",
      "fusion_test(1.5, 3.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fusion std: 0.452\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fzT7BxYzpDOm6wummiHcE16Vbs0EKJCL/o2AiIiIikk+Szp/h9+W/sP3gYsJC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\niIiISHH/A4xSCxc3xJxCAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1589accf8>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see from the standard deviation that the performance is a bit worse than when the PS and wheel were measured in every update, but better than the wheel alone.\n",
      "\n",
      "The code is fairly straighforward. The `update()` function optionally takes R as an argument, and I chose to do that rather than alter `KalmanFilter.R`, mostly to show that it is possible. Either way is fine. I modified `KalmanFilter.H` on each update depending on whether there are 1 or 2 measurements available. The only other difficulty was storing the wheel and PS measurements in two different arrays because there are a different number of measurements for each. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking a Ball"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's turn our attention to a situation where the physics of the object that we are tracking is constrained. A ball thrown in a vacuum must obey Newtonian laws. In a constant gravitational field it will travel in a parabola. I will assume you are familiar with the derivation of the formula:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "y &= \\frac{g}{2}t^2 + v_{y0} t + y_0 \\\\\n",
      "x &= v_{x0} t + x_0\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "where $g$ is the gravitional constant, $t$ is time, $v_{x0}$ and $v_{y0}$ are the initial velocities in the x and y plane. If the ball is thrown with an initial velocity of $v$ at angle $\\theta$ above the horizon, we can compute $v_{x0}$ and $v_{y0}$ as\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "v_{x0} = v \\cos{\\theta} \\\\\n",
      "v_{y0} = v \\sin{\\theta}\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because we don't have real data we will start by writing a simulator for a ball. As always, we add a noise term independent of time so we can simulate noise sensors."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import radians, sin, cos\n",
      "import math\n",
      "\n",
      "def rk4(y, x, dx, f):\n",
      "    \"\"\"computes 4th order Runge-Kutta for dy/dx.\n",
      "    y is the initial value for y\n",
      "    x is the initial value for x\n",
      "    dx is the difference in x (e.g. the time step)\n",
      "    f is a callable function (y, x) that you supply to \n",
      "      compute dy/dx for the specified values.\n",
      "    \"\"\"\n",
      "    \n",
      "    k1 = dx * f(y, x)\n",
      "    k2 = dx * f(y + 0.5*k1, x + 0.5*dx)\n",
      "    k3 = dx * f(y + 0.5*k2, x + 0.5*dx)\n",
      "    k4 = dx * f(y + k3, x + dx)\n",
      "    \n",
      "    return y + (k1 + 2*k2 + 2*k3 + k4) / 6.\n",
      "\n",
      "def fx(x,t):\n",
      "    return fx.vel\n",
      "    \n",
      "def fy(y,t):\n",
      "    return fy.vel - 9.8*t\n",
      "\n",
      "\n",
      "class BallTrajectory2D(object):\n",
      "    def __init__(self, x0, y0, velocity, \n",
      "                 theta_deg=0., \n",
      "                 g=9.8, \n",
      "                 noise=[0.0,0.0]):\n",
      "        self.x = x0\n",
      "        self.y = y0\n",
      "        self.t = 0\n",
      "        \n",
      "        theta = math.radians(theta_deg)\n",
      "\n",
      "        fx.vel = math.cos(theta) * velocity\n",
      "        fy.vel = math.sin(theta) * velocity\n",
      "        \n",
      "        self.g = g\n",
      "        self.noise = noise\n",
      "        \n",
      "        \n",
      "    def step(self, dt):\n",
      "        self.x = rk4(self.x, self.t, dt, fx)\n",
      "        self.y = rk4(self.y, self.t, dt, fy)\n",
      "        self.t += dt \n",
      "        return (self.x + random.randn()*self.noise[0], \n",
      "                self.y + random.randn()*self.noise[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So to create a trajectory starting at (0,15) with a velocity of $100 \\frac{m}{s}$ and an angle of $60^\\circ$ we would write:\n",
      "\n",
      "    traj = BallTrajectory2D (x0=0, y0=15, velocity=100, theta_deg=60)\n",
      "    \n",
      "and then call `traj.position(t)` for each time step. Let's test this "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def test_ball_vacuum(noise):\n",
      "    y = 15\n",
      "    x = 0\n",
      "    ball = BallTrajectory2D(x0=x, y0=y, \n",
      "                            theta_deg=60., velocity=100., \n",
      "                            noise=noise)\n",
      "    t = 0\n",
      "    dt = 0.25\n",
      "    while y >= 0:\n",
      "        x,y = ball.step(dt)\n",
      "        t += dt\n",
      "        if y >= 0:\n",
      "            plt.scatter(x,y)\n",
      "         \n",
      "    plt.axis('equal')\n",
      "    plt.show()\n",
      "    \n",
      "test_ball_vacuum([0,0]) # plot ideal ball position\n",
      "test_ball_vacuum([1,1]) # plot with noise "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KwgoAAJBKysAoWtlsNnbu7KlPrVKfCgBQYlzdUZR6NoBqaKiKhoaqaGmxYy0A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\nFsPsxgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15898beb8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V1dXJhg0bcm30eWn5q7/6q6S+vj750Y9+lLz00kvJ5s2bk2nTpiV/\n8zd/k2ujz4vboUOHkl27diW7du1KJk6cmPzd3/1dsmvXrtz12HD1b3/X9n0peFj5yU9+klRUVCSZ\nTCapqKjI/ctkMsmTTz6Za3fgwIHkuuuuS84888zkzDPPTK6//vqks7Mz77lefvnlZOnSpcnEiROT\nKVOmJLfcckte4CH9NmzYkMycOTMZN25csnDhwuTpp58e7VNiEE72nq6oqEi++tWv5rVbu3Ztcu65\n5ybjx49PLr300uSFF17IO97V1ZWsXLkymTJlSjJx4sRk2bJlecuTk369ly7uod9Ly49+9KNk3rx5\nyfjx45N3v/vdyT/+4z+e0Eafl45Dhw4lf/3Xf53MnDkzmTBhQnLBBRckt912W9LV1ZXXTp8Xr55r\n8+P/ljc3N+faDEf/DuTa/mQqksQsdQAAIH1Ssc8KAADA8YQVAAAglYQVAAAglYQVAAAglYQVAAAg\nlYQVAAAglYQVAAAglYQVAAAglf4/zEy3aGQDoPEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe15898b2b0>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This looks reasonable, so let's continue (excercise for the reader: validate this simulation more robustly)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Step 1: Choose the State Variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We might think to use the same state variables as used for tracking the dog. However, this will not work. Recall that the Kalman filter state transition must be written as $\\mathbf{x}' = \\mathbf{F x}$, which means we must calculate the current state from the previous state. Our assumption is that the ball is traveling in a vacuum, so the velocity in x is a constant, and the acceleration in y is solely due to the gravitational constant $g$. We can discretize the Newtonian equations using the well known Euler method in terms of $\\Delta t$ are:\n",
      "\n",
      "$$\\begin{aligned}\n",
      "x_t &=  x_{t-1} + v_{x(t-1)} {\\Delta t} \\\\\n",
      "v_{xt} &= vx_{t-1}\n",
      "\\\\\n",
      "y_t &= -\\frac{g}{2} {\\Delta t}^2 + vy_{t-1} {\\Delta t} + y_{t-1} \\\\\n",
      "v_{yt} &= -g {\\Delta t} + v_{y(t-1)} \\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "> **sidebar**: *Euler's method integrates a differential equation stepwise by assuming the slope (derivative) is constant at time $t$. In this case the derivative of the position is velocity. At each time step $\\Delta t$ we assume a constant velocity, compute the new position, and then update the velocity for the next time step. There are more accurate methods, such as Runge-Kutta available to us, but because we are updating the state with a measurement in each step Euler's method is very accurate.*\n",
      "\n",
      "This implies that we need to incorporate acceleration for $y$ into the Kalman filter, but not for $x$. This suggests the following state variables.\n",
      "\n",
      "$$\n",
      "\\mathbf{x} = \n",
      "\\begin{bmatrix}\n",
      "x \\\\\n",
      "\\dot{x} \\\\\n",
      "y \\\\\n",
      "\\dot{y} \\\\\n",
      "\\ddot{y}\n",
      "\\end{bmatrix}\n",
      "$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "**Step 2:**  Design State Transition Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our next step is to design the state transistion function. Recall that the state transistion function is implemented as a matrix $\\mathbf{F}$ that we multipy with the previous state of our system to get the next state$\\mathbf{x}' = \\mathbf{Fx}$.\n",
      "\n",
      "I will not belabor this as it is very similar to the 1-D case we did in the previous chapter. Our state equations for position and velocity would be:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) + (0 * a_y) \\\\\n",
      "v_x &= (0*x) +  (1*v_x) + (0*y) + (0 * v_y) + (0 * a_y) \\\\\n",
      "y' &= (0*x) + (0* v_x)         + (1*y) + (\\Delta t * v_y) + (\\frac{1}{2}{\\Delta t}^2*a_y)  \\\\\n",
      "v_y &= (0*x) +  (0*v_x) + (0*y) + (1*v_y) + (\\Delta t * a_y) \\\\\n",
      "a_y &= (0*x) +  (0*v_x) + (0*y) + (0*v_y) + (1 * a_y) \n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Note that none of the terms include $g$, the gravitational constant. This is because the state variable $\\ddot{y}$ will be initialized with $g$, or -9.81. Thus the function $\\mathbf{F}$ will propagate $g$ through the equations correctly. \n",
      "\n",
      "In matrix form we write this as:\n",
      "\n",
      "$$\n",
      "\\mathbf{F} = \\begin{bmatrix}\n",
      "1 & \\Delta t & 0 & 0 & 0 \\\\\n",
      "0 & 1 & 0 & 0 & 0 \\\\\n",
      "0 & 0 & 1 & \\Delta t & \\frac{1}{2}{\\Delta t}^2 \\\\\n",
      "0 & 0 & 0 & 1 & \\Delta t \\\\\n",
      "0 & 0 & 0 & 0 & 1\n",
      "\\end{bmatrix}\n",
      "$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Interlude: Test State Transition"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Kalman filter class provides us with useful defaults for all of the class variables, so let's take advantage of that and test the state transistion function before continuing. Here we construct a filter as specified in Step 2 above. We compute the initial velocity in x and y using trigonometry, and then set the initial condition for $x$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin,cos,radians\n",
      "\n",
      "def ball_kf(x, y, omega, v0, dt):\n",
      "\n",
      "    g = 9.8 # gravitational constant\n",
      "\n",
      "    kf = KalmanFilter(dim_x=5, dim_z=2)\n",
      "\n",
      "\n",
      "    ay = .5*dt**2\n",
      "\n",
      "    kf.F = np.array([[1, dt,  0,  0,  0],   # x   = x0+dx*dt\n",
      "                     [0,  1,  0,  0,  0],   # dx  = dx\n",
      "                     [0,  0,  1, dt, ay],   # y   = y0 +dy*dt+1/2*g*dt^2\n",
      "                     [0,  0,  0,  1, dt],   # dy  = dy0 + ddy*dt \n",
      "                     [0,  0,  0,  0, 1]])   # ddy = -g.\n",
      "    \n",
      "    # compute velocity in x and y\n",
      "    omega = radians(omega)\n",
      "    vx = cos(omega) * v0\n",
      "    vy = sin(omega) * v0\n",
      "    \n",
      "    kf.Q *= 0.\n",
      "    kf.x = np.array([[x, vx, y, vy, -g]]).T\n",
      "    \n",
      "    return kf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can test the filter by calling predict until $y=0$, which corresponds to the ball hitting the ground. We will graph the output against the idealized computation of the ball's position. If the model is correct, the Kalman filter prediction should match the ideal model very closely. We will draw the ideal position with a green circle, and the Kalman filter's output with '+' marks."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = 15.\n",
      "x = 0.\n",
      "theta = 20. # launch angle\n",
      "v0 = 100.\n",
      "dt = 0.1   # time step\n",
      "\n",
      "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, \n",
      "                        velocity=v0, noise=[0,0])\n",
      "kf = ball_kf(x, y, theta, v0, dt)\n",
      "t = 0\n",
      "while kf.x[2, 0] > 0:\n",
      "    t += dt\n",
      "    kf.predict() \n",
      "    x, y = ball.step(dt)\n",
      "    p2 = plt.scatter(x, y,                 \n",
      "                     color='g', marker='o', s=75, \n",
      "                     alpha=0.5)\n",
      "    p1 = plt.scatter(kf.x[0, 0], kf.x[2, 0], \n",
      "                     color='k', marker='+', s=200)\n",
      "\n",
      "plt.legend([p1, p2], ['Kalman filter', 'idealized'], scatterpoints=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Hjx9HcnIyAOCRRx5BQkIC1qxZg+eeew7JycnYt28fDh8+jJdffhnPPvusODbb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\nkwIAAAAgrvw/HoftmojTDboAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe158926f60>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we can see, the Kalman filter agrees with the physics model very closely. If you are interested in pursuing this further, try altering the initial velocity, the size of dt, and $\\theta$, and plot the error at each step. However, the important point is to test your design as soon as possible; if the design of the state transistion is wrong all subsequent effort may be wasted. More importantly, it can be extremely difficult to tease out an error in the state transition function when the filter incorporates measurment updates."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "**Step 3**: Design the Motion Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have no control inputs to the ball flight, so this step is trivial - set the motion transition function $\\small\\mathbf{B}=0$. This is done for us by the class when it is created so we can skip this step."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "**Step 4**: Design the Measurement Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The measurement function defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. We will assume that we have a sensor that provides us with the position of the ball in (x,y), but cannot measure velocities or accelerations. Therefore our function must be:\n",
      "\n",
      "$$\n",
      "\\begin{bmatrix}z_x \\\\ z_y \\end{bmatrix}= \n",
      "\\begin{bmatrix}\n",
      "1 & 0 & 0 & 0 & 0 \\\\\n",
      "0 & 0 & 1 & 0 & 0\n",
      "\\end{bmatrix} * \n",
      "\\begin{bmatrix}\n",
      "x \\\\\n",
      "\\dot{x} \\\\\n",
      "y \\\\\n",
      "\\dot{y} \\\\\n",
      "\\ddot{y}\\end{bmatrix}$$\n",
      "\n",
      "where\n",
      "\n",
      "$$\\mathbf{H} = \\begin{bmatrix}\n",
      "1 & 0 & 0 & 0 & 0 \\\\\n",
      "0 & 0 & 1 & 0 & 0\n",
      "\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "**Step 5**: Design the Measurement Noise Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As with the robot, we will assume that the error is independent in $x$ and $y$. In this case we will start by assuming that the measurement error in x and y are 0.5 meters. Hence,\n",
      "\n",
      "$$\\mathbf{R} = \\begin{bmatrix}0.5&0\\\\0&0.5\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Step 6: Design the Process Noise Matrix\n",
      "Finally, we design the process noise. As with the robot tracking example, we don't yet have a good way to model process noise. However, we are assuming a ball moving in a vacuum, so there should be no process noise. For now we will assume the process noise is 0 for each state variable. This is a bit silly - if we were in a perfect vacuum then our predictions would be perfect, and we would have no need for a Kalman filter. We will soon alter this example to be more realistic by incorporating air drag and ball spin. \n",
      "\n",
      "We have 5 state variables, so we need a $5{\\times}5$ covariance matrix:\n",
      "\n",
      "$$\\mathbf{Q} = \\begin{bmatrix}0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Step 7: Design the Initial Conditions\n",
      "\n",
      "We already performed this step when we tested the state transistion function. Recall that we computed the initial velocity for $x$ and $y$ using trigonometry, and set the value of $\\mathbf{x}$ with:\n",
      "\n",
      "    omega = radians(omega)\n",
      "    vx = cos(omega) * v0\n",
      "    vy = sin(omega) * v0\n",
      "\n",
      "    f1.x = np.array([[x, vx, y, vy, -g]]).T\n",
      "    \n",
      "    \n",
      "With all the steps done we are ready to implement our filter and test it. First, the implementation:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin,cos,radians\n",
      "\n",
      "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.):\n",
      "\n",
      "    g = 9.8 # gravitational constant\n",
      "    kf = KalmanFilter(dim_x=5, dim_z=2)\n",
      "\n",
      "    ay = .5*dt**2\n",
      "    kf.F = np.array ([[1, dt,  0,  0,  0],   # x   = x0+dx*dt\n",
      "                      [0,  1,  0,  0,  0],   # dx  = dx\n",
      "                      [0,  0,  1, dt, ay],   # y   = y0 +dy*dt+1/2*g*dt^2\n",
      "                      [0,  0,  0,  1, dt],   # dy  = dy0 + ddy*dt \n",
      "                      [0,  0,  0,  0, 1]])   # ddy = -g.\n",
      "\n",
      "    kf.H = np.array([[1, 0, 0, 0, 0],\n",
      "                     [0, 0, 1, 0, 0]])\n",
      "    \n",
      "    kf.R *= r\n",
      "    kf.Q *= q\n",
      "\n",
      "    omega = radians(omega)\n",
      "    vx = cos(omega) * v0\n",
      "    vy = sin(omega) * v0\n",
      "\n",
      "    kf.x = np.array([[x, vx, y, vy, -9.8]]).T\n",
      "    \n",
      "    return kf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we will test the filter by generating measurements for the ball using the ball simulation class."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = 1.\n",
      "x = 0.\n",
      "theta = 35. # launch angle\n",
      "v0 = 80.\n",
      "dt = 1/10.   # time step\n",
      "\n",
      "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, \n",
      "                        noise=[.2,.2])\n",
      "kf = ball_kf(x,y,theta,v0,dt)\n",
      "\n",
      "t = 0\n",
      "xs = []\n",
      "ys = []\n",
      "while kf.x[2,0] > 0:\n",
      "    t += dt\n",
      "    x,y = ball.step(dt)\n",
      "    z = np.array([[x, y]]).T\n",
      "\n",
      "    kf.update(z)\n",
      "    xs.append(kf.x[0,0])\n",
      "    ys.append(kf.x[2,0])\n",
      "    \n",
      "    kf.predict() \n",
      "    \n",
      "    p1 = plt.scatter(x, y, color='r', marker='.', s=75, alpha=0.5)\n",
      "\n",
      "p2, = plt.plot (xs, ys,lw=2)\n",
      "plt.legend([p2, p1], ['Kalman filter', 'Measurements'], scatterpoints=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7joz0JNK/nEP6+TRSnPJJcLNyyh0ys89y2ASHPS7cRQrMegQvZ3dCjVbCAj0IL7BQJf0U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\nAQAAABBUKCkAAAAAggolBQAAAEBQoaQAAAAACCqUFAAAAABBhZICAAA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       "text": [
        "<matplotlib.figure.Figure at 0x7fe1658a5780>"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that the Kalman filter reasonably tracks the ball. However, as already explained, this is a silly example; we can predict trajectories in a vacuum with arbitrary precision; using a Kalman filter in this example is a needless complication."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking a Ball in Air"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**author's note** - I originally had ball tracking code in 2 different places in the book. ONe has been copied here, so now we have 2 sections on ball tracking. I need to edit this into one section, obviously. Sorry for the duplication.\n",
      "\n",
      "We are now ready to design a practical Kalman filter application. For this problem we assume that we are tracking a ball traveling through the Earth's atmosphere. The path of the ball is influenced by wind, drag, and the rotation of the ball. We will assume that our sensor is a camera; code that we will not implement will perform some type of image processing to detect the position of the ball. This is typically called *blob detection* in computer vision. However, image processing code is not perfect; in any given frame it is possible to either detect no blob or to detect spurious blobs that do not correspond to the ball. Finally, we will not assume that we know the starting position, angle, or rotation of the ball; the tracking code will have to initiate tracking based on the measurements that are provided. The main simplification that we are making here is a 2D world; we assume that the ball is always traveling orthogonal to the plane of the camera's sensor. We have to make that simplification at this point because we have not yet discussed how we might extract 3D information from a camera, which necessarily provides only 2D data. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Implementing Air Drag"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our first step is to implement the math for a ball moving through air. There are several treatments available. A robust solution takes into account issues such as ball roughness (which affects drag non-linearly depending on velocity), the Magnus effect (spin causes one side of the ball to have higher velocity relative to the air vs the opposite side, so the coefficient of drag differs on opposite sides), the effect of lift, humidity, air density, and so on. I assume the reader is not interested in the details of ball physics, and so will restrict this treatment to the effect of air drag on a non-spinning baseball. I will use the math developed by Nicholas Giordano and Hisao Nakanishi in *Computational Physics*  [1997]. \n",
      "\n",
      "**Important**: Before I continue, let me point out that you will not have to understand this next piece of physics to proceed with the Kalman filter. My goal is to create a reasonably accurate behavior of a baseball in the real world, so that we can test how our Kalman filter performs with real-world behavior. In real world applications it is usually impossible to completely model the physics of a real world system, and we make do with a process model that incorporates the large scale behaviors. We then tune the measurement noise and process noise until the filter works well with our data. There is a real risk to this; it is easy to finely tune a Kalman filter so it works perfectly with your test data, but performs badly when presented with slightly different data. This is perhaps the hardest part of designing a Kalman filter, and why it gets referred to with terms such as 'black art'. \n",
      "\n",
      "I dislike books that implement things without explanation, so I will now develop the physics for a ball moving through air. Move on past the implementation of the simulation if you are not interested. \n",
      "\n",
      "A ball moving through air encounters wind resistance. This imparts a force on the wall, called *drag*, which alters the flight of the ball. In Giordano this is denoted as\n",
      "\n",
      "$$F_{drag} = -B_2v^2$$\n",
      "\n",
      "where $B_2$ is a coefficient derived experimentally, and $v$ is the velocity of the object. $F_{drag}$ can be factored into $x$ and $y$ components with\n",
      "\n",
      "$$F_{drag,x} = -B_2v v_x\\\\\n",
      "F_{drag,y} = -B_2v v_y\n",
      "$$\n",
      "\n",
      "If $m$ is the mass of the ball, we can use $F=ma$ to compute the acceleration as\n",
      "\n",
      "$$ a_x = -\\frac{B_2}{m}v v_x\\\\\n",
      "a_y = -\\frac{B_2}{m}v v_y$$\n",
      "\n",
      "Giordano provides the following function for $\\frac{B_2}{m}$, which takes air density, the cross section of a baseball, and its roughness into account. Understand that this is an approximation based on wind tunnel tests and several simplifying assumptions. It is in SI units: velocity is in meters/sec and time is in seconds.\n",
      "\n",
      "$$\\frac{B_2}{m} = 0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}}$$\n",
      "\n",
      "Starting with this Euler discretation of the ball path in a vacuum:\n",
      "$$\\begin{aligned}\n",
      "x &= v_x \\Delta t \\\\\n",
      "y &= v_y \\Delta t \\\\\n",
      "v_x &= v_x \\\\\n",
      "v_y &= v_y - 9.8 \\Delta t\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "We can incorporate this force (acceleration) into our equations by incorporating $accel * \\Delta t$ into the velocity update equations. We should subtract this component because drag will reduce the velocity. The code to do this is quite straightforward, we just need to break out the Force into $x$ and $y$ components. \n",
      "\n",
      "I will not belabor this issue further because the computational physics is beyond the scope of this book. Recognize that a higher fidelity simulation would require incorporating things like altitude, temperature, ball spin, and several other factors. My intent here is to impart some real-world behavior into our simulation to test how  our simpler prediction model used by the Kalman filter reacts to this behavior. Your process model will never exactly model what happens in the world, and a large factor in designing a good Kalman filter is carefully testing how it performs against real world data. \n",
      "\n",
      "The code below computes the behavior of a baseball in air, at sea level, in the presence of wind. I plot the same initial hit with no wind, and then with a tail wind at 10 mph. Baseball statistics are universally done in US units, and we will follow suit here (http://en.wikipedia.org/wiki/United_States_customary_units). Note that the velocity of 110 mph is a typical exit speed for a baseball for a home run hit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, exp, cos, sin, radians\n",
      "\n",
      "def mph_to_mps(x):\n",
      "    return x * .447\n",
      "\n",
      "def drag_force(velocity):\n",
      "    \"\"\" Returns the force on a baseball due to air drag at\n",
      "    the specified velocity. Units are SI\"\"\"\n",
      "\n",
      "    return (0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))) * velocity\n",
      "\n",
      "v = mph_to_mps(110.)\n",
      "y = 1\n",
      "x = 0\n",
      "dt = .1\n",
      "theta = radians(35)\n",
      "\n",
      "def solve(x, y, vel, v_wind, launch_angle):\n",
      "    xs = []\n",
      "    ys = []\n",
      "    v_x = vel*cos(launch_angle)\n",
      "    v_y = vel*sin(launch_angle)\n",
      "    while y >= 0:\n",
      "        # Euler equations for x and y\n",
      "        x += v_x*dt\n",
      "        y += v_y*dt\n",
      "\n",
      "        # force due to air drag    \n",
      "        velocity = sqrt ((v_x-v_wind)**2 + v_y**2)    \n",
      "        F = drag_force(velocity)\n",
      "\n",
      "        # euler's equations for vx and vy\n",
      "        v_x = v_x - F*(v_x-v_wind)*dt\n",
      "        v_y = v_y - 9.8*dt - F*v_y*dt\n",
      "        \n",
      "        xs.append(x)\n",
      "        ys.append(y)\n",
      "    \n",
      "    return xs, ys\n",
      "        \n",
      "x,y = solve(x=0, y=1, vel=v, v_wind=0, launch_angle=theta)\n",
      "p1 = plt.scatter(x, y, color='blue', label='no wind')\n",
      "\n",
      "x,y = solve(x=0, y=1,vel=v, v_wind=mph_to_mps(10), launch_angle=theta)\n",
      "p2 = plt.scatter(x, y, color='green', marker=\"v\", label='10mph wind')\n",
      "plt.legend(scatterpoints=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wh97/7t3r/fL5efrPJfGzDEZr9+jAgd7y/3xqHVK1Uz37ntLJfSdVvq/l7/vi6Bf6axA/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\nP2lLpz9p2UclsjT0NLsqAAAQ4woLpYq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A8O3bN6xZswZEhJKSEvHajwFLly6F0WiUXO+h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\njDHGGGPMYXgBwhhjjDHGGHOY/wFx3wsQkOsgFAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c0a6d8>"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can easily see the difference between the trajectory in a vacuum and in the air. I used the same initial velocity and launch angle in the ball in a vacuum section above. We computed that the ball in a vacuum would travel over 240 meters (nearly 800 ft). In the air, the distance is just over 120 meters, or roughly 400 ft. 400ft is a realistic distance for a well hit home run ball, so we can be confident that our simulation is reasonably accurate.\n",
      "\n",
      "Without further ado we will create a ball simulation that uses the math above to create a more realistic ball trajectory. I will note that the nonlinear behavior of drag means that there is no analytic solution to the ball position at any point in time, so we need to compute the position step-wise. I use Euler's method to propagate the solution; use of a more accurate technique such as Runge-Kutta is left as an exercise for the reader. That modest complication is unnecessary for what we are doing because the accuracy difference between the techniques will be small for the time steps we will be using. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import radians, sin, cos, sqrt, exp\n",
      "\n",
      "class BaseballPath(object):\n",
      "    def __init__(self, x0, y0, launch_angle_deg, velocity_ms, \n",
      "                 noise=(1.0,1.0)): \n",
      "        \"\"\" Create 2D baseball path object  \n",
      "           (x = distance from start point in ground plane, \n",
      "            y=height above ground)\n",
      "        \n",
      "        x0,y0            initial position\n",
      "        launch_angle_deg angle ball is travelling respective to \n",
      "                         ground plane\n",
      "        velocity_ms      speeed of ball in meters/second\n",
      "        noise            amount of noise to add to each position\n",
      "                         in (x,y)\n",
      "        \"\"\"\n",
      "        \n",
      "        omega = radians(launch_angle_deg)\n",
      "        self.v_x = velocity_ms * cos(omega)\n",
      "        self.v_y = velocity_ms * sin(omega)\n",
      "\n",
      "        self.x = x0\n",
      "        self.y = y0\n",
      "\n",
      "        self.noise = noise\n",
      "\n",
      "\n",
      "    def drag_force(self, velocity):\n",
      "        \"\"\" Returns the force on a baseball due to air drag at\n",
      "        the specified velocity. Units are SI\n",
      "        \"\"\"\n",
      "        B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))\n",
      "        return B_m * velocity\n",
      "\n",
      "\n",
      "    def update(self, dt, vel_wind=0.):\n",
      "        \"\"\" compute the ball position based on the specified time \n",
      "        step and wind velocity. Returns (x,y) position tuple.\n",
      "        \"\"\"\n",
      "\n",
      "        # Euler equations for x and y\n",
      "        self.x += self.v_x*dt\n",
      "        self.y += self.v_y*dt\n",
      "\n",
      "        # force due to air drag\n",
      "        v_x_wind = self.v_x - vel_wind\n",
      "        v = sqrt(v_x_wind**2 + self.v_y**2)\n",
      "        F = self.drag_force(v)\n",
      "\n",
      "        # Euler's equations for velocity\n",
      "        self.v_x = self.v_x - F*v_x_wind*dt\n",
      "        self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt\n",
      "\n",
      "        return (self.x + random.randn()*self.noise[0], \n",
      "                self.y + random.randn()*self.noise[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can test the Kalman filter against measurements created by this model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = 1.\n",
      "x = 0.\n",
      "theta = 35. # launch angle\n",
      "v0 = 50.\n",
      "dt = 1/10.   # time step\n",
      "\n",
      "ball = BaseballPath(x0=x, y0=y, launch_angle_deg=theta,\n",
      "                    velocity_ms=v0, noise=[.3,.3])\n",
      "f1 = ball_kf(x,y,theta,v0,dt,r=1.)\n",
      "f2 = ball_kf(x,y,theta,v0,dt,r=10.)\n",
      "t = 0\n",
      "xs = []\n",
      "ys = []\n",
      "xs2 = []\n",
      "ys2 = []\n",
      "\n",
      "while f1.x[2,0] > 0:\n",
      "    t += dt\n",
      "    x,y = ball.update(dt)\n",
      "    z = np.array([[x, y]]).T\n",
      "\n",
      "    f1.update(z)\n",
      "    f2.update(z)\n",
      "    xs.append(f1.x[0,0])\n",
      "    ys.append(f1.x[2,0])\n",
      "    xs2.append(f2.x[0,0])\n",
      "    ys2.append(f2.x[2,0])    \n",
      "    f1.predict() \n",
      "    f2.predict()\n",
      "    \n",
      "    p1 = plt.scatter(x, y, color='r', marker='o', s=75, alpha=0.5)\n",
      "\n",
      "p2, = plt.plot (xs, ys, lw=2)\n",
      "p3, = plt.plot (xs2, ys2, lw=4)\n",
      "plt.legend([p1,p2, p3], \n",
      "           ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)'],\n",
      "           loc='best', scatterpoints=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tlps3b9KvX78cbTqY1SpSWaWnb2i/88477N+/n08++YRatWoZhlH16NHD5Llz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\nmAiTJlm3xETrcf/x8/WnZ7v+9Ov8BOUCglm7ZTk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paURNn47P4cPHL7U0MjNxhoWxr2dP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ioZJjWDoKAg47/dFXjQtKIFyO1u3LiBbt264bXXXsP8+fMBsACxBaU37DDp3d/gcnF7Y5udSmDl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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe16595c0f0>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin blue line, and a Kalman filter with R=10 as a thick red line. These R values are chosen merely to show the effect of measurement noise on the output, they are not intended to imply a correct design.\n",
      "\n",
      "We can see that neither filter does very well. At first both track the measurements well, but as time continues they both diverge. This happens because the state model for air drag is nonlinear and the Kalman filter assumes that it is linear. If you recall our discussion about nonlinearity in the g-h filter chapter we showed why a g-h filter will always lag behind the acceleration of the system. We see the same thing here - the acceleration is negative, so the Kalman filter consistently overshoots the ball position. There is no way for the filter to catch up so long as the acceleration continues, so the filter will continue to diverge.\n",
      "\n",
      "What can we do to improve this? The best approach is to perform the filtering with a nonlinear Kalman filter, and we will do this in subsequent chapters. However, there is also what I will call an 'engineering' solution to this problem as well. Our Kalman filter assumes that the ball is in a vacuum, and thus that there is no process noise. However, since the ball is in air the atmosphere imparts a force on the ball. We can think of this force as process noise. This is not a particularly rigorous thought; for one thing, this force is anything but Gaussian. Secondly, we can compute this force, so throwing our hands up and saying 'it's random' will not lead to an optimal solution. But let's see what happens if we follow this line of thought.\n",
      "\n",
      "The following code implements the same Kalman filter as before, but with a non-zero process noise. I plot two examples, one with `Q=.1`, and one with `Q=0.01`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_ball_with_q(q, r=1., noise=0.3):\n",
      "    y = 1.\n",
      "    x = 0.\n",
      "    theta = 35. # launch angle\n",
      "    v0 = 50.\n",
      "    dt = 1/10.   # time step\n",
      "\n",
      "    ball = BaseballPath(x0=x, \n",
      "                        y0=y, \n",
      "                        launch_angle_deg=theta, \n",
      "                        velocity_ms=v0, \n",
      "                        noise=[noise,noise])\n",
      "    f1 = ball_kf(x,y,theta,v0,dt,r=r, q=q)\n",
      "    t = 0\n",
      "    xs = []\n",
      "    ys = []\n",
      "\n",
      "    while f1.x[2,0] > 0:\n",
      "        t += dt\n",
      "        x,y = ball.update(dt)\n",
      "        z = np.array([[x,y]]).T\n",
      "\n",
      "        f1.update(z)\n",
      "        xs.append(f1.x[0,0])\n",
      "        ys.append(f1.x[2,0]) \n",
      "        f1.predict() \n",
      "\n",
      "\n",
      "        p1 = plt.scatter(x, y, color='r', marker='o', s=75, alpha=0.5)\n",
      "\n",
      "    p2, = plt.plot (xs, ys,lw=2)\n",
      "    plt.legend([p1, p2], ['Measurements', 'Kalman filter'], scatterpoints=1)\n",
      "    plt.show()\n",
      "    \n",
      "plot_ball_with_q(0.01)\n",
      "plot_ball_with_q(0.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cOMC9997Lww8/zPDhw3n11Vfp168f77zzDhMnTmTcuHEYhsGUKVMYPHgwe/fu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\niIhsikUHERERERHZFIsOIiIiIiKyqf8HcjfhqRBMJ40AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c830f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6VvoZUnIMSE245oK8wsJCLBYLQUFB+Pr6smHDBtt9ZrOZbdu20bNnzxoJUggh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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165be2438>"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second filter tracks the measurements fairly well. There appears to be a bit of lag, but very little.\n",
      "\n",
      "Is this a good technique? Usually not, but it depends. Here the nonlinearity of the force on the ball is fairly constant and regular. Assume we are trying to track an automobile - the accelerations will vary as the car changes speeds and turns. When we make the process noise higher than the actual noise in the system the filter will opt to weigh the measurements higher. If you don't have a lot of noise in your measurements this might work for you. However, consider this next plot where I have increased the noise in the measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_ball_with_q(0.01, r=3, noise=3.)\n",
      "plot_ball_with_q(0.1, r=3, noise=3.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6TBGRq6KeFBERkXIiNTOZ/8yeyAHv4wDEeWXxgzWelnmVuCEvlLpn/DGSk+3D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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe165c220b8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1YV8Tff0UK7d9yp7IXxneYzKNajctU/t6Vc+BEzv4ae8yMrJSATh24SBPhbz8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\niIhMhgkIERERERGZDBMQIiIiIiIymf8Pfsz8qnu5MXIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe1587be940>"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This output is terrible. The filter has no choise but to give more weight to the measurements than the process (prediction step), but when the measurements are noisy the filter output will just track the noise. This inherent limitation of the linear Kalman filter is what lead to the development of nonlinear versions of the filter.\n",
      "\n",
      "With that said, it is certainly possible to use the process noise to deal with small nonlinearities in your system. This is part of the 'black art' of Kalman filters. Our model of the sensors and of the system are never perfect. Sensors are non-Gaussian and our process model is never perfect. You can mask some of this by setting the measurement errors and process errors higher than their theoretically correct values, but the trade off is a non-optimal solution. Certainly it is better to be non-optimal than to have your Kalman filter diverge. However, as we can see in the graphs above, it is easy for the output of the filter to be very bad. It is also very common to run many simulations and tests and to end up with a filter that performs very well under those conditions. Then, when you use the filter on real data the conditions are slightly different and the filter ends up performing terribly. \n",
      "\n",
      "For now we will set this problem aside, as we are clearly misapplying the Kalman filter in this example. We will revisit this problem in subsequent chapters to see the effect of using various nonlinear techniques. In some domains you will be able to get away with using a linear Kalman filter for a nonlinear problem, but usually you will have to use one or more of the techniques you will learn in the rest of this book."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking Noisy Data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we are applying a Kalman filter to a thermometer in an oven in a factory then our task is done once the Kalman filter is designed. The data from the thermometer may be noisy, but there is never doubt that the thermometer is reading the temperature of *some other* oven. Contrast this to our current situation, where we are using computer vision to detect ball blobs from a video camera. For any frame we may detect or may not detect the ball, and we may have one or more spurious blobs - blobs not associated with the ball at all. This can occur because of limitations of the computer vision code, or due to foreign objects in the scene, such as a bird flying through the frame. Also, in the general case we may have no idea where the ball starts from. A ball may be picked up, carried, and thrown from any position, for example. A ball may be launched within view of the camera, or the initial launch might be off screen and the ball merely travels through the scene. There is the possibility of bounces and deflections - the ball can hit the ground and bounce, it can bounce off a wall, a person, or any other object in the scene.\n",
      "\n",
      "Consider some of the problems that can occur. We could be waiting for a ball to appear, and a blob is detected. We initialize our Kalman filter with that blob, and look at the next frame to detect where the ball is going. Maybe there is no blob in the next frame. Can we conclude that the blob in the previous frame was noise? Or perhaps the blob was valid, but we did not detect the blob in this frame.\n",
      "\n",
      "**author's note: not sure if I want to cover this. If I do, not sure I want to cover this here.**"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}