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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 sys\n",
      "sys.path.insert(0,'../code') # allow us to format the book\n",
      "import book_format\n",
      "book_format.load_style()"
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      "Introduction"
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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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     "input": [
      "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."
     ]
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     "input": [
      "pos = [4,3]\n",
      "sensor = PosSensor1 (pos, (2,1), 1)\n",
      "\n",
      "for i in range (50):\n",
      "    pos = sensor.read() \n",
      "    plt.scatter(pos[0], pos[1])\n",
      "plt.show()"
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       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c6c5550>"
       ]
      }
     ],
     "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",
      "p1, = plt.plot (xs, ys, 'r--')\n",
      "p2, = plt.plot (pxs, pys)\n",
      "plt.legend([p1,p2], ['filter', 'measurement'], loc=2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+URgWERGRYvpt8xGmLd+Lq8nA9NVT8DrQGEt4uKPLKlHurk483COCh3tEOLoU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\nXosyDAAAAK9FGQYAAIDX+j+2M6ajfaTeGwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c6c55c0>"
       ]
      }
     ],
     "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=0.2)\n",
      "\n",
      "        \n",
      "p1, = plt.plot (xs, ys, 'r--', label='filter')\n",
      "p2, = plt.plot (pxs, pys, label='measurement')\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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wkSP/7nJqnTNZ9Y0rCRJx2ptN1vVUqXlV2nNtdLakGSylKNZcHN/FCRw83yMk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\ne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n6eECfZYX/X7scUjRLVgiM1wkIIIcQZSoKwOKUWWx7toINl5TjW6nv7AgdGK6+2CUOx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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c3f2048>"
       ]
      },
      {
       "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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PYGXZp0xElxdGCeJIREbJIKvxPYMmF8My0QSod/qodx10ow6mimy/IKIrc70Y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\npxMmjBI0OwGWV/vv9iNPI5fJYiqfZT8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NjY06fvx4h3mBQEDPPfecVq1apVWrVmnEiBGa\nOXNmt9WNnjFt2jTV1tZqzpw5ikQimjNnjoqLizscc65+aWxs1KpVq1RfX69gMKjRo0frwQcf7M7S\n0U0ef/xxrVixQrNnz9aQIUP0zDPPdLj/+PHjuuyyyzqMDR8+XDNmzNCiRYvaz4fKP777vmx6Zf/+\n/XrnnXcUi8VUWFioqVOnsgUjB3z33XeqrKxsv719+3bdfffdmjFjhiTWFcPl/2oBAACAc2IbBgAA\nAJAGYRkAAABIg7AMAAAApEFYBgAAANIgLAMAAABpEJYBAACANAjLAAAAQBqEZQAAACANwjIAAACQ\nxv8BXMulI/oENSIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa034824c18>"
       ]
      }
     ],
     "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": [
      "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 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 GPS 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",
      "It 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 GPS.\n",
      "\n",
      "$$ \\mathbf{Z} = \\begin{bmatrix}x_{wheel} \\\\ x_{gps}\\end{bmatrix}$$\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",
      "$$ \\begin{bmatrix}x_{wheel} \\\\ x_{gps}\\end{bmatrix} = \\begin{bmatrix}1 &0 \\\\ 1& 0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\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",
      "$$ \\begin{bmatrix}x_{wheel} \\\\ x_{gps}\\end{bmatrix} = \\begin{bmatrix}0.5 &0 \\\\ 1& 0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "Now we have to design the measurement noise matrix $\\mathbf{R}$. Suppose that the measurement variance for the GPS is twice the variance of the wheel, and the standard deviation of the wheel is 1.5m. That gives us\n",
      "\n",
      "$$\\sigma_{wheel} =  1.5\\\\\n",
      "\\sigma^2_{wheel} = 2.25 \\\\ \n",
      "\\sigma_{gps} = 1.5*2 = 3 \\\\\n",
      "\\sigma^2_{gps} = 9.\n",
      "$$\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, gps_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] = gps_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()*gps_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",
      "        plt.plot(xs[:,0], label='Kalman filter')\n",
      "        plt.plot(zs[:,0],linestyle=':', label='wheel')\n",
      "        plt.plot(zs[:,1],linestyle=':', label='GPS')\n",
      "        plt.legend(loc=4)\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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iIpcOZ9c2nDUrMd37YLr1Ac93pk24q6BFevWmsY5Xwd2+v5TXZi1nd2UMUz71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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa0347fd0b8>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see the result of the Kalman filter in blue.\n",
      "\n",
      "##### Excercise: Prove that the GPS improves the filter\n",
      "\n",
      "Devise a way to prove that fusing the GPS 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 GPS measurement by setting the measurement noise for the GPS 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": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see the error in the filter where the GPS 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",
      "plt.plot(xs[:,0], label='Kalman filter')\n",
      "plt.plot(zs[:,0],linestyle=':', label='wheel')\n",
      "plt.legend(loc=4)\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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uxNXm1nJvQ3MVaw88ycDwm4j2PbXt9YnaXWwqfo7UkBn0DprolD6IyHej0Cwi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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa0347d9cc0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On this run I got a standard deviation of 0.523 vs the value of 0.422 for the fused measurements. "
     ]
    },
    {
     "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": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So to create a trajectory starting at (0,15) with a velocity of $60 \\frac{m}{s}$ and an angle of $65^\\circ$ 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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DWwI5nU75fD6VlZVJkmpqahQTEzPmefft2xf4c1ZWlrKzs80aMoCbYBiGuruvSpISE2eP\n+oXrcDiUlMSmRIDdORwO5eTMueYD8xzCNcLSsWPHdPz4cUnS7NmzlZWVZer5Tf+NaBiGDMNQcnKy\nWltbtXLlSkmSx+PR/fffL0lKTk5WW1tb4Hs8Ho9WrFgx5vl27Ngx6uve3l6zhwyTjXx6p1b2NF79\nmpqco/bNXb3aP+Njw43x+rMvK9UuOnr4/73e0I7DTqxUP9xYenq60tPTJQ3XrqGhwdTzB9WD/fHH\nH+vFF1/U+fPnNTg4qIqKCp09e1Zf+cpXtHnzZpWXl6uvr0/19fVqbGxUXl6eJCk/P19HjhyRx+NR\nd3e3KisrVVBQYMoTAmA+Fj4BGMEWfsCNBTWDPXv2bL388st67LHH1N/fr7S0NP3617+W2+3W7t27\n1dbWpmXLlmnx4sWqrKxUYmKiJCkjI0N79+7V2rVrNTAwoO3btys/P9+UJwQAAKYHV7KAyXEYhmGE\nehDjqaurU2pqaqiHgZvEZTJ7o0XE3nj92ZfVa+f1zlVurls9PcMXv+Pjh1Rb62XXoD+xev0wvpEW\nkZycHNPOyaokAJPCrZUBAJgcU/bBBhA+uroG1dU1OOaxiW6tDCC8sec9MHnMYAMIGG4DGd4+oKJi\nkDYQAKNwJQuYHGawAUhipxAAkzPRlSx2GAGGEbABAEDQmpqcys11KzfXraYmZ6iHA4QUARuAJPor\nAUwdV8CA0ejBBhCwerVfDQ3DbwvR0fRfAwAwFcxgAxglKWmOkpL47A1g8rgCBozGb1EgAo1cuuUX\nIACzsMMI8GfMYAMRhoVIAKYLe+UDwwjYQARhIRKAUGELP0QSAjYAAJhWXDlDpCFgAxGEhUgAZhpX\nzhCJWOQIRBgWIgEAML2YwQYiEAuRAMwUrpwhEjGDDYQptuIDYBVcOUOkYQYbCEMsKAJgNVw5QyQh\nYANhhgVFAOyGLfwQbgjYAAAgZLjihnBEwAbCDAuKANgFV9wQrljkCIQhFhQBABA6zGADYYoFRQCs\njituCFfMYAM2xlZ8AOyOK24IR8xgAzbFwiAA4YIrbgg3BGzAhlgYBACAdRGwAQCAZbFHNuyIgA3Y\nEAuDAEQCWuFgVyxyBGyKhUEAwtm1rXCSVFzsUm3tAO93sAUCNmBj/KIBAMB6aBEBAACWQysc7IwZ\nbMDi2OsaQKSiFQ52xQw2YGEs8AEQ6dgjG3ZEwAYsir2uAQCwJwI2AACwJfbIhlURsAGLYoEPAIyP\nFjpYGYscAQtjgQ8AXI89smF1BGzA4viFAQCAvdAiAgAAbIUWOlgdM9iABbDXNQDcHFroYGXMYAMh\nxkIdAJga9siGVRGwgRBir2sAAMIPARsAAIQd9shGKBGwgRBioQ4AmI/WO4QaixyBEGOhDgCYhz2y\nYQUEbMACeOMHACB80CICAADCBq13sIKgAvbg4KC2bNmihIQELVq0SOvWrZPH45EkDQwMaNu2bYqN\njdXy5ctVXV096nvLy8sVHx8vt9utkpKSYIYBAAAQMNx651VtrVerV/tDPRxEoKAC9tWrV/XlL39Z\nTU1NOnfunL7+9a9r48aNkqQDBw6opaVFXV1dOnjwoLZu3aquri5J0okTJ1RaWqqjR4+qublZVVVV\n1wVwINywoh0AZg57ZCOUggrY8+bN07/+678qISFBkvTd735Xp06d0qeffqrq6mrt3LlTsbGxys7O\nVmZmpmpqaiRJhw8f1qZNm5SamqqEhAQVFRWpqqoq+GcDWBQr2gEAiBymLnJ86623lJiYqLi4OHV0\ndCglJUWFhYW67777lJaWpvb2dklSR0eHsrKyVFZWps7OTq1Zs0Yvv/zymOeMi4szc4iYAVFRUZKo\n3YiurkEVF0ePWtHe0DBHSUnWXGNM/eyN+tkXtbM36mdfI7Uzk2m/4fv6+vS9731PP/nJT+RwOOT3\n+xUTE6Pm5matWrVKLpdLnZ2dkhQ45vF4dPr0aa1fv14+n2/M8+7bty/w56ysLGVnZ5s1ZAAAEGEM\nw1B391VJUmLibDkcjhCPCKFw7NgxHT9+XJI0e/ZsZWVlmXp+UwL2lStXlJeXp2984xvKz8+XJDmd\nTvn9fp08eVKStGvXLrlcrsAxn8+nsrIySVJNTY1iYmLGPPeOHTtGfd3b22vGkDGNRj69U6th0dFS\nRcWgiouH//1XVFxQdLRfVv3PQ/3sjfrZF7WbGU1NzlHvx2YtgqR+9pKenq709HRJw7VraGgw9fxB\nb9N39epVffOb31RycrJKS0sDjycnJ6u1tTXwtcfjUUpKSuBYW1vbqGMrVqwIdiiAZbGiHQBC79qb\n0PT0zFJxsYvF55gWQQfs4uJizZo1S88888yoxzdv3qzy8nL19fWpvr5ejY2NysvLkyTl5+fryJEj\n8ng86u7uVmVlpQoKCoIdCmBprGgHACAyBNUicvr0aVVWVmrBggVauHBh4PH/+q//0u7du9XW1qZl\ny5Zp8eLFqqysVGJioiQpIyNDe/fu1dq1azUwMKDt27cHWksAAACmw8hNaK5tEWHiA9PBYRiGEepB\njKeurk6pqamhHgZuEn1o9kb97I362Re1mzkjbSFmhmvqZ18jPdg5OTmmndOa+4QBNjUdb9oAAHPx\nHo3pFnQPNoBh3EwGAABIBGzAFKxMB4Dw4PXO5f0bQSNgAwAAiCuRMA8BGzDByMr0+PghxccPsTId\nAGyGK5EwE4scAZMM30xmQBILaAAAiGTMYAMm4mYyAGBPXImEmZjBBgAAEFciYR4CNgAAwJ8QrGEG\nWkSAm8QWTgAAYCIEbOAmsIUTAAC4EQI2MEls4QQAACaDgA0AADAJtAhisgjYwCSxhRMARC5aBHEz\n2EUEuAls4QQAkefaFkFJKi52qbZ2gN8DGBcBG7hJvKECAICJ0CICAAAwAVoEcbOYwQYAALgBWgRx\nMwjYwBhGVonzJgoAGMHvBEwWLSLA57BSHAAABIOADVyDm8kAAIBg0SICAAAQpK6uQUlSdHSIBwJL\nYAYbuAYrxQEAN6upyak1a6K1Zk00rYWQxAw2cB1WigMAJoub0GAsBGxgDLwxAgCAqaJFBAAAYIpo\nLcRYmMEGAAAIwurVfjU0DEeq6Gh/iEcDKyBgAwAABCkpaThS9faGeCCwBFpEELG83rnscQ0AAExH\nwEZE4m6NAABguhCwEXG4WyMAAJhOBGwAAIBpREti5CFgI+KwpRIAYKbQkhiZ2EUEEYm7NQIApht3\neYxcBGxELN7gAADAdKBFBAAAYBrQkhi5mMEGAACYJrQkRiYCNgAAwDQiWEceWkQQ1tgaCQAAzDQC\nNsIWWyMBAIBQIGAjLHG3RgAAECoEbAAAAMBEBGyEJbZGAgDYAWuFwhO7iCBssTUSAMDKmpqcKi52\nSZIqKi5o9Wp/iEcEszCDjbDmdvcTrgEAlsNaofAWVMD+1a9+pczMTM2fP18PPvhg4PGBgQFt27ZN\nsbGxWr58uaqrq0d9X3l5ueLj4+V2u1VSUhLMEAAAAABLCapFZNGiRfr+97+v3/72t7p48WLg8QMH\nDqilpUVdXV165513tGHDBmVmZiopKUknTpxQaWmpGhoatHDhQq1Zs0Z33HGH8vPzg34yAAAAdjCy\nVujaFhGuuIaPoGaws7OzlZeXJ7fbPerx6upq7dy5U7GxscrOzlZmZqZqamokSYcPH9amTZuUmpqq\nhIQEFRUVqaqqKphhAAAA2M7wWiGvamu99F+HGVMWORqGMerrjo4OpaSkqLCwUPfdd5/S0tLU3t4e\nOJaVlaWysjJ1dnZqzZo1evnll80YBgAAgK0wax2eTAnYDodj1Nd+v18xMTFqbm7WqlWr5HK51NnZ\nOeqYx+PR6dOntX79evl8vnHPHRcXZ8YQMYOioqIkzUztDMNQd/dVSVJi4uzr/i3i5s1k/WA+6mdf\n1M7eqJ99jdTOTNMyg+10OuX3+3Xy5ElJ0q5du+RyuQLHfD6fysrKJEk1NTWKiYkZ99z79u0L/Dkr\nK0vZ2dlmDBlhwDAM1dUNqqhogSTphRcuKidnDiEbAABM6NixYzp+/Lgkafbs2crKyjL1/NMyg52c\nnKzW1latXLlSkuTxeHT//fcHjrW1tQX+rsfj0YoVK8Y9944dO0Z93dvba8aQMY1GPr1Pd6283rkq\nKnKrp2d4KUFR0QLV1nq53Bakmaofpgf1sy9qZ2/Uz17S09OVnp4uabh2DQ0Npp4/qEWOQ0NDunz5\nsgYHB3X16lVduXJFg4OD2rx5s8rLy9XX16f6+no1NjYqLy9PkpSfn68jR47I4/Gou7tblZWVKigo\nMOXJAAAAhAvu8mhfQc1gHzx4UFu3bg18/Z//+Z964oknVFJSora2Ni1btkyLFy9WZWWlEhMTJUkZ\nGRnau3ev1q5dq4GBAW3fvp0t+jAlbHEEAAhX3OXR3hzG5xuoLaSurk6pqamhHgZu0kxfJhv5dE+4\nNgeXOe2N+tkXtbM3M+vn9c5Vbu6fWyDj44dogZxGIy0iOTk5pp3TlB5sIJR4wwEAAFYSVA82AAAA\nzDXSAhkfP6T4+CFaIG2IGWwAAACLGb7L44AkrtTaEQEbAADAggjW9kWLCAAAAGAiAjZsgb1AAQCA\nXRCwYXlNTU7l5rqVm+tWU5Mz1MMBAACYEAEblub1zlVxsUs9PbPU0zNLxcUuZrIBAIClEbABAABs\nhtZJayNgw9LYCxQAgNFonbQ+tumD5bEXKAAAw65tnZSk4mKXamsH+P1oMQRs2AJvHAAAwC5oEQEA\nALAJWiftgRlsAAAAG6F10voI2AAAADZDsLY2WkQAAAAAExGwYRns6QkAAMIBARuWwJ6eAAAgXBCw\nEXLcDh0AAIQTAjY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96tQpJSYmsg+2hXzyySd65JFHNHfuXDkcjsDjJSUl+vKXv6znnnuO\nvVxtorS0VF/96le1bt06Xb16ldrZwNmzZ/XMM8/ovffeU1xcnL71rW/pzjvvpH420dTUpJ///Of6\n9NNPFRsbq40bNyonJ4f6WVB9fb2effbZUY/l5+crLy9vyrW62cwZ8oANAAAAhJOQt4gAAAAA4YSA\nDQAAAJiIgA0AAACYiIANAAAAmIiADQAAAJiIgA0AAACYiIANAAAAmIiADQAAAJiIgA0AAACY6P8B\nGTMUS0Am7EYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c050668>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sHhGGwgw2bMPt7iFcAwCiFmuS7IOADQAAAJiIgA0AAGADrEmyD3qwAQAAbII1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\nAGCi/wccrBe+dlFTlwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c050748>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "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",
      "$$\\begin{aligned}\n",
      "x_t &=  v_{x(t-1)} {\\Delta t} \\\\\n",
      "v_{xt} &= vx_{t-1}\n",
      "\\\\\n",
      "y_t &= -\\frac{g}{2} {\\Delta t}^2 + vy_{t-1} {\\Delta t} + y_{t-1} \\\\\n",
      "v_{yt} &= -g {\\Delta t} + v_{y(t-1)} \\\\\n",
      "\\end{aligned}\n",
      "$$\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": 19
    },
    {
     "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",
      "    p1 = plt.scatter(kf.x[0, 0], kf.x[2, 0], \n",
      "                     color='black', marker='+', s=75)\n",
      "    p2 = plt.scatter(x, y,                 \n",
      "                     color='green', marker='o', s=75, \n",
      "                     alpha=0.5)\n",
      "\n",
      "plt.legend([p1, p2], ['Kalman filter', 'idealized'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xa9cut21ZtGgRYmJi8Nprr+H8+fPo7Ox0Huvt7UVbW5uzWoSj3ZfXz3788cch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\nCilzy7aq2gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa0346450f0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "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": 21
    },
    {
     "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='green', marker='.', s=75, alpha=0.5)\n",
      "\n",
      "p2, = plt.plot (xs, ys,lw=2)\n",
      "plt.legend([p2, p1], ['Kalman filter', 'Measurements'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/8sYbb5CWllZRquHi4sJvv/1GTEwMI0aMYOfOnZSWlvLvf/+bkSNHEhUVhY2N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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa0346ad2e8>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "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": [
      "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')\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\")\n",
      "plt.legend([p1,p2], ['no wind', '10mph wind'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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x3TfffKNp06bp+eefl8lk0h133KGpU6cqOjpaK1eu1B133KGtW7fKbrfX+Dxv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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c32db38>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "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": 25
    },
    {
     "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='green', marker='o', s=75, alpha=0.5)\n",
      "\n",
      "p2, = plt.plot (xs, ys, lw=2)\n",
      "p3, = plt.plot (xs2, ys2, lw=4, c='#e24a33')\n",
      "plt.legend([p1,p2, p3], \n",
      "           ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)'],\n",
      "           loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9Jij1m0JgtTKnPKmqSlx6HIcuHQKgaUBTwrzDKuXNuIqHF0qnntCpJ2pGOuq+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\nh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       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c322fd0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "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='green', marker='o', s=75, alpha=0.5)\n",
      "\n",
      "    p2, = plt.plot (xs, ys,lw=2)\n",
      "    plt.legend([p1, p2], ['Measurements', 'Kalman filter'])\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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T6XTMnDmTgQMHMn36dF566SWaNm3KyZMn+f333wkKCmLjxo2sXr260LZsISEh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       "text": [
        "<matplotlib.figure.Figure at 0x7fa034705b38>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0EM8//zzx8fF06tQJgLS0NKZOncrTTz/N4MGDMRqNLFq0iNdff71Bzl09WW/p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\nubl2qhuqGZyoiVVnQo2xiIiIiB9zxjqJdcTiNX/c8S49vbEx3rzZTlR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       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c0a0860>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "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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YCyGEFahqoZTRCGvXOnDmjA1wDUc7LWPDA5k4pEuDbKxRH+xtbXgwohNjwwM5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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fa03c3a9cc0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GUSrdW1yqtPf7WNYxDl48iLOzMyEtQvDGu1K9rnp7HWPDOjE2rBOnUrKJ+PMY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\nJiZ6qj5pZ+9/tY20Z5ZR6ajl8rFWXvnDOQT6t27ixjAM0hLTCPANoKy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       "text": [
        "<matplotlib.figure.Figure at 0x7fa034680ac8>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "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": 3,
     "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": {}
  }
 ]
}