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     "source": [
      "[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": [
      "Unscented Kalman Filters"
     ]
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      "#format the book\n",
      "%matplotlib inline\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import book_format\n",
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     "source": [
      "In the last chapter we discussed the difficulties that nonlinear systems pose. This nonlinearity can appear in two places. It can be in our measurements, such as a radar that is measuring the slant range to an object. Slant range requires you to take a square root to compute the x,y coordinates:\n",
      "\n",
      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
      "\n",
      "The nonlinearity can also occur in the process model - we may be tracking a ball travelling through the air, where the effects of gravity and air drag lead to highly nonlinear behavior. The standard Kalman filter performs poorly or not at all with these sorts of problems.\n",
      "\n",
      "In the last chapter I showed you a plot like this. I have altered the equation somewhat to emphasize the effects of nonlinearity."
     ]
    },
    {
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     "input": [
      "from nonlinear_plots import plot_transfer_func\n",
      "from numpy.random import normal\n",
      "import numpy as np\n",
      "\n",
      "data = normal(loc=0.0, scale=1, size=500000)\n",
      "\n",
      "def g(x):\n",
      "    return (np.cos(4*(x/2+0.7)))-1.3*x\n",
      "\n",
      "plot_transfer_func (data, g, lims=(-3.5,3.5), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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KNXzGkoiI2jdLljNkfRwdNHhyykvo7ttTFk9KOYZfz2+EJEmNLElEbcms41Bs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\n7P31/iAH+FN8TAf96M7nNeW6uz3WbTuw1v+B2igKBQAAqFd1TaVe+uc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iohQREWFxuoZ5\n8sknNXXqVCUlJam0tFRvv/221q1bpxUrVvg/jAEAALxy4sQJY/LkyUZCQoIRHBxsdO7c2ZgzZ46R\nlZVldbQGW7NmjWGz2Qy73W7YbDb3H7vdbqxbt87qeA3yzDPPmHJ/+b8LFy60OtplLViwwOjWrZsR\nEhJipKWlGf/+97+tjtRgX/69+frfnfvuu8/qaA1S3995m81mPPvss1ZHa7C5c+caXbt2NUJCQoyE\nhARj4sSJxqpVqyzJwjkUAAAAALzGVZ4AAAAAeI1CAQAAAMBrFAoAAAAAXqNQAAAAAPAahQIAAACA\n1ygUAAAAALxGoQAAAADgNQoFAAAAAK/9f81xEuat3+HiAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff686693c18>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I generated this by taking 500,000 samples from the input, passing it through the nonlinear transform, and building a histogram of the result. From the output histogram we can compute a mean and standard deviation which would give us an updated, albeit approximated Gaussian.\n",
      "\n",
      "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a 'monte carlo' approach, and it used by some Kalman filter designs, such as the *Ensemble filter*. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the function is, as long as we sample with enough points we will build an accurate output distribution.\n",
      "\n",
      "\"Enough points\" is the rub. The graph above was created with 500,000 points, and the output is still not smooth. You wouldn't need to use that many points to get a reasonable estimate of the mean and variance, but it will require many points. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you only needed $50$ points for 1 dimension, you'd need $50^2=2,500$ for two dimensions, $50^3=125,000$ for three dimensions, and so on. So while this approach does work, it is very computationally expensive. The Unscented Kalman filter uses a similar technique but reduces the amount of computation needed by a drastic amount by using a deterministic method of choosing the points."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Choosing Sigma Points"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at the problem in terms of a 2D covariance ellipse. I choose 2D merely because it is easy to plot. Naturally this will extend to any number of dimensions. Assuming some arbitrary nonlinear function, we will take random points from the first covariance ellipse, pass them through the nonlinear function, and plot their new position."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ukf_internal\n",
      "ukf_internal.show_2d_transform()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Z79fv5qa19Xv2vIH/+7/DZGb280Zk6VAq/nKxgCv+Tz/9LA7HN4HAW09ZgoUJ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\nAAcdd3XP5gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff6a3571e80>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here on the left we show an ellipse depicting the $1\\sigma$ distribution of two state variables. The arrows show how three randomly sampled points might be transformed by some arbitrary nonlinear function to a new distribution. The ellipse on the right is drawn semi-transparently to indicate that it is an *estimate* of the mean and variance of this collection of points - if we were to sample, say, a million points the shape of the points might be very far from an ellipse. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at that by running a bunch of points through a nonlinear function. We will write a function to pass randomly generated points with a Gaussian distribution through the system\n",
      "\n",
      "$$\\begin{aligned}x&=x+y\\\\\n",
      "y &= 0.1x^2 + y^2\\end{aligned}$$ \n",
      "\n",
      "for the mean and covariance $$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}, \n",
      "\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "import numpy as np\n",
      "from numpy import sin, cos, tan,log\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "from numpy.random import multivariate_normal\n",
      "\n",
      "\n",
      "def f(x,y):\n",
      "    return x+y, .1*x**2 +y*y\n",
      "\n",
      "mean = (0, 0)\n",
      "p = np.array([[32, 15],[15., 40.]])\n",
      "\n",
      "xs ,ys = multivariate_normal(mean=mean, cov=p, size=50000).T\n",
      "fxs, fys = [], []\n",
      "for x,y in zip(xs,ys):\n",
      "    fx, fy = f(x,y)\n",
      "    \n",
      "    fxs.append(fx)\n",
      "    fys.append(fy)\n",
      "\n",
      "# Compute mean\n",
      "mean_fx = f(*mean)\n",
      "\n",
      "computed_mean_x = np.average(fxs)\n",
      "computed_mean_y = np.average(fys)\n",
      "\n",
      "plt.subplot(121)\n",
      "plt.scatter (xs,ys, marker='.', alpha=0.1)\n",
      "plt.axis('equal')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.scatter(fxs, fys, marker='.', alpha=0.1)\n",
      "plt.scatter(mean_fx[0], mean_fx[1], \n",
      "            marker='v', s=300,c='k', label='Linearized Mean')\n",
      "plt.scatter(computed_mean_x, computed_mean_y, \n",
      "            marker='*',s=120,c='r', label='Computed Mean')\n",
      "plt.ylim([-10,290])\n",
      "plt.xlim([-150,150])\n",
      "plt.legend(loc='best', scatterpoints=1)\n",
      "plt.show()\n",
      "print ('Difference in mean x={:.3f}, y={:.3f}'.format(\n",
      "       computed_mean_x-mean_fx[0], computed_mean_y-mean_fx[1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4oUtjSSbkk0IQhwA9dfoXItK8qqcCQk/6Q8LJ4OX666/H6tWrsW7dOlgsFhw4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t25dbuy4/n/++iSxqK4giiii+iWG6E4zojPEio5BJgLU1gSBwUS4vUalwrG42CQzyec5zRgq/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\n6NHl3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       "text": [
        "<matplotlib.figure.Figure at 0x7ff67e970c18>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Difference in mean x=0.020, y=43.466\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This plot shows the strong nonlinearity that occurs with this function, and the large error that would result if we linearized the function at (0,0)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We used 5,000 points to generate this solution. While the computed mean is quite accurate, computing 5,000 points for every update would cause our filter to be very slow. So, what would be fewest number of sampled points that we can use, and what kinds of constraints does this problem formulation put on the points? We will assume that we have no special knowledge about the nonlinear function as we want to find a generalized algorithm that works for any function. For reasons that come clear in the next section, we will call these points *sigma points*.\n",
      "\n",
      "Let's consider the simplest possible case and see if it offers any insight. The simplest possible system is *identity* - the transformation does not alter the input. In mathematical notation this is just $f(x) = x$. It should be clear that if our algorithm does not work for the identity function then the filter will never converge. In other words, if the input is  1 (for a one dimensional system), the output must also be 1. If the output was different, such as 1.1, then when we fed 1.1 into the transform at the next time step, we'd get out yet another number, maybe 1.23. The filter would run away (diverge). \n",
      "\n",
      "The fewest number of points that we can use is one per dimension. This is the number that the linear Kalman filter uses. The input to a Kalman filter for the distribution $\\mathcal{N}(\\mu,\\sigma^2)$ is just $\\mu$ itself. So while this works for the linear case, it is not a good answer for the nonlinear case.\n",
      "\n",
      "Perhaps we can use one point per dimension, but altered somehow. However, if we were to pass some value $\\mu+\\Delta$ into the identity function $f(x)=x$ it would not converge, so this is not a possible algorithm. We must conclude that a one point sample will not work.\n",
      "\n",
      "So, what is the next lowest number we can choose? Consider the fact that Gaussians are symmetric, and that we probably want to always have one of our sample points be the mean of the input for the identity function to work. Two points would require us to select the mean, and then one other point. That one other point would introduce an asymmetry in our input that we probably don't want. It would be very difficult to make this work for the identity function $f(x)=x$.\n",
      "\n",
      "The next lowest number is 3 points. 3 points allows us to select the mean, and then one point on each side of the mean, as depicted on the chart below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ukf_internal.show_3_sigma_points()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hKwfw66dv1+6fxuiBUwU3s1w8t6g28Lx6esXFxTWuN9mv6JRKJQIDA7Fnzx5J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\nda5VragrvaM1L7fTomhGi6IZ5bXFd9ReKBDCSmytOSRiG0w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       "text": [
        "<matplotlib.figure.Figure at 0x7ff67ea25eb8>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For this to work for identity we will want the sums of the weights to equal one. We can always come up with counterexamples, but in general if the sum is greater or less than one the sampling will not yield the correct output. Given that, we then have to select *sigma points* $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the input Gaussian. So we can write\n",
      "\n",
      "$$\\begin{aligned}\n",
      "1 &= \\sum_i{w_i}\\;\\;\\;&(1) \\\\\n",
      "\\mu &= \\sum_i w_i\\mathcal{X}_i\\;\\;\\;&(2) \\\\\n",
      "\\Sigma &= \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\\;\\;\\;&(3)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "If we look at this is should be clear that there is no one unique answer - the problem is unconstrained. For example, if you choose a smaller weight for the point at the mean for the input, you could compensate by choosing larger weights for the rest of the $\\mathcal{X}$, and vice versa if you chose a larger weight for it. Indeed, these equations do not require that any of the points be the mean of the input at all, though it seems 'nice' to do so, so to speak.\n",
      "\n",
      "But before we go on I want to make sure the idea is clear. We are choosing 3 points for each dimension in our covariances. That choice is *entirely deterministic*. Below are three different examples for the same covariance ellipse."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ukf_internal.show_sigma_selections()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Dw160tLSIjpJzTpzgLKTRcTpTt75S+rD4p0kymcTx480oLubJboSqqgiFQmhq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\nO/4AAFAA4Q8AAAUQ/gAAUADhDwAABfg72j7u+BqWhAYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff6862759e8>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that while I chose the points to lie along the major and minor axis of the ellipse, nothing in the constraints above require me to do that; however, it is fairly typical to do this. Furthermore, in each case I show the points evenly spaced; again, the constraints above do not require that. However, the technique that we develop in the next section *does* do this. It is a reasonable choice, after all; if we want to accurately sample our input it makes sense to sample in a symmetric manner.\n",
      "\n",
      "There are several published ways for selecting the sigma points. For now I will stick with the original implementation by Julier and Uhlmann [2]. This method defines a constant kappa ($\\kappa$) which controls how spread out the sigma points are. Before we work through the derivation, let's just look at some examples. I will use the class UnscentedKalmanFilter from FilterPy to generate the sigma points for us. It is convention to write\n",
      "\n",
      "    import UnscentedKalmanFilter as UKF\n",
      "    \n",
      "because UKF is the standarized shorthand used in the literature for this filter.\n",
      "\n",
      "I will plot the sigma points on top of a covariance ellipse showing the first and second deviations, and size them based on the weights assigned to them. I am using the covariance ellipse\n",
      "\n",
      "$$\\mathbf{P} = \\begin{bmatrix} 4&2\\\\2&4\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import array\n",
      "import matplotlib.pyplot as plt\n",
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "from filterpy.common import plot_covariance_ellipse\n",
      "\n",
      "x = array([0, 0])\n",
      "P = array([[4, 2],\n",
      "           [2, 4]])\n",
      "\n",
      "sigmas_kp5 = UKF.sigma_points(x=x, P=P, kappa=0)\n",
      "sigmas_k2 = UKF.sigma_points(x=x, P=P, kappa=2)\n",
      "W0 = UKF.weights(2, kappa=0)\n",
      "W1 = UKF.weights(2, kappa=2)\n",
      "\n",
      "for i in range(len(W0)):\n",
      "    p1 = plt.scatter(sigmas_kp5[i,0], sigmas_kp5[i,1], s=W1[i]*500, c='g')\n",
      "    p2 = plt.scatter(sigmas_k2[i,0], sigmas_k2[i,1], s=W0[i]*500, c='b')\n",
      "\n",
      "plt.legend([p1, p2], ['Kappa = 0.5', 'Kappa = 2'])\n",
      "plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, std=[1,2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nlbwfymX8Xn3c1ELA5+S4OT76hvuwbQvLtjl+XptChYhUlc7wIiIyfUZlLES4\nU+CPgDcGlhOKAeBAd6hyLWs46/m8Thb0+Nk32A+AaRgsnddW41qJSDNRoBARkaPWM9fC4U9QMTPg\ni46FCct8W5AYm/Gpu6t29ZQxXreD43oC7BsYwDBMHKbBIo2pEJEqUaAQEZEpsyyb4XgG2x/nnIsj\n/NtPE2MPlHxgHzz16/r1ZZYerylh64HX7WDBHB/7hvpwGCZOh8l8zf4kIlWgQCEiIkdk2zajiSwD\nkTSRTJzhzDDrL8nzys4Qo8OuSX+nq9vif7y/gsetdRDqhc/rZH63j97hXlymi5aAh5B/ksH1IiJH\nQYFCREQOK57O0zuSJJKOM5IdwXCUmdvt5fiFPnq+VuB7D8P/+39OKpWxgb5Op8369WX+x/srnHSi\nLlbrTcDnpK3FSX9qAP+gh+WLunBoRW0ReQcUKEREZFLFUoW9wwmGE0kG04NUyNPV7iUU+F2Lw8kn\nebnxM2WuuKLIm2/mAFi0yMfS4x1qmahjnW1e3silGUyNEhhya5C2iLwjChQiIjKBbdsMxTL0jSYY\nTo8SL0TpavPQ1hKatLzH7eRd73Ji8xoA73rX8mNZXZmm+d1+3ugbwR/zEw546Aj7a10lEWlQChQi\nIjIulS2wdyjBaDrOYGYIvw+WLgjiVJeYpuNymnS1e+iP9+Mf9hL0ufG4dVkgIkdPZw4REaFcsegd\nSTIYSzCUHqJgZ5nb5SPg08dEM2sNuUnnMgykhvAPujhpYWetqyQiDUifFCIis9xIPEPfaJLhdIRo\nbpS2sIv54aBWU54l5nb6eb0vzmAyQGvUy5z2YK2rJCINRoFCRGSWyuZL7B1OMJJKMJgexOWqsHh+\nAJdT3ZtmE4dp0NPhZWh0iNZoiK7WAKapMCkiU6dAISIyy9i2Td9oiv5IguHMMJlyijlvm71JZpeg\n38Wos0A0m2AkHlQrhYgcFQUKEZFZJJsv8cZgnKFklKHMIC1BB0vnBHVHWuhs9TAcGWUo1kp3W0Bd\n3kRkyhQoRERmicFomn3DcQbSgxSsNMf1+PF6HLWultSJoN/FSCxPLJtgNBGkqzVQ6yqJSINQoBAR\naXLFUmV/q0Sc/mQfwaDJknYNupaDdbZ6GY2OMhgN0xn26xgRkSlRoBARaWLRZI43h+IMpoZJlmL0\ndHkJ+l21rpbUqVDAxUgsRTSbJJIM0anF7kRkChQoRESaUKVi8eZQgsF4gv5UHy5PhcXzAlqgTo6o\ns80zoZV7fbIPAAAgAElEQVRCRORIFChERJpMKlvgjcE4g6lRItkRuto9tIY0g5NMTUvAzUgsRSyb\nIp5uoTWoY0dEDk+BQkSkSRyYDrZvNE5/agDLzGtdCZmW1pCbZDZBPN2hQCEiR6RAISLSBPLFMnv6\nY+PTwbaFnXS2ai0BmZ6Q38neeJpEOo9t2xqcLSKHpUAhItLg4uk8rw/E6Ev2k62kNB2svGNulwPT\nYZEuZEnnioT8nlpXSUTqmAKFiEgD6xtJsm80Rl9ybOD1Ei1SJ1US9DtJFVPE03kFChE5LHWsFRFp\nQJWKxe7eCK8NDfNG/A1aWmB+t19hQqom5HeRKqaJp/O1roqI1Dm1UIiINJhcocRr/TH6E8NE8yPM\n6/YT8Ol0LtXl8zqp2FnS+Ty5QgmfR+uXiMjk9AkkItJAoskcrw9G6UsOUCLD4nlBzeIkM2aslWKs\n25MChYgcij6FREQagG3b9I4k+U3vMHtib2C6ciyaWz9Twtq2jcvpwuV0Ydt2rasjVRL0O0kVUur2\nJCKHpRYKEZE6V65Y7OmPMZCIMpDqp7PNRVtL/axgPJwaZufQTn7y5k8AeJ/xPpbPWU53qLu2FZN3\nLOBz0melyOSLWJatMToiMikFChGROpbNl3itP0p/Yoh4McqCOT583vo5dQ+nhrn9Z7fzzOvPjG/7\n4es/ZP2S9Vz/nusVKhqcYRi4HAaFcpF8sYzfq25PInKw+mgrFxGRg0STOf5r7zB7Im+SrsRYPDdQ\nV2HCtm12Du2cECYOeOb1Z9g5vFPdn5qAx+2gUCmQL5ZrXRURqVMKFCIidWgommZ33wh7Ym/g9BZZ\nNDeAs07GSxxg2RZb92095ONb927Fsq1jWCOZCR6XSbFSIFco1boqIlKn6udWl4iIALBvOMHekSi9\nqX20h520h721rpLMYh63g0RWLRQicmj1dbtLRGQWs22bPf0xXh8eYV/yTbo7XLSH63eFYtMwOfu4\nsw/5+NkLz8Y09DHT6Nwuk0KlSE6BQkQOQWd6EZE6MLbydZQ3R4fpT/Uyf46PloC71tU6LMMwWD5n\nOeuXrD/osfVL1rO8ezmGoVmBGp3bZVKyihSKZSxLY2JE5GDq8iQiUmOlcoXdvVH69q98fdxcP163\no9bVmpLuUDfXv+d6zl1yLj95/ScAvG/J+1jerWljm4VhGLidJvlygUKprAXuROQgChQiIjWUK5T4\nbV+UffEBMuU4i+tw8PWRdIe66Qp2Md+aD8AJS09Qy0STcbtNipUiuYIChYgcTIFCRKRG0rkiu3sj\n7Ev0UTYyLJoXxNGgC4cZhkGpXBr/XpqLx+WgWBxroRAReTsFChGRGoilcrzWH2VvYh8Od5GFXQFd\niEvdMk2Dim1rDIWITEqBQkTkGBuOZXhjKMrexF58fpuejkCtqyRyWKYBJdvC0kKFIjIJBQoRkWNo\nIJLi9aEI+xJ7aWt10qE1JqSO2bZNsVRh9+4i/fsMBv4rz6nv8rBihROPx6FWNREBqhwoNm/ezBNP\nPMGuXbvweDycccYZbN68mRUrVlRzNyIiDal/NMUbwxH2JffS2e6iNVTf08LK7GbbNr/ZVeDhhxz8\nv3/1YJVcEHPjLHv4wAdKbNxYYtUqr0KFiFR3HYqtW7fy8Y9/nO3bt/Pv//7vOJ1Ozj33XGKxWDV3\nIyLScPpGkrw+NMrexNiCdQoTUs8OhIkbbnDz1FMurIoBhgXYlMsG3/mOm4su8vDKK/laV1VE6kBV\nWyieeeaZCT9/97vfJRwO8/zzz3PBBRdUc1ciIg2jdyTJm/tbJuZ0uut+wTqRYqnCww85GBnef9/R\nNsCwx7726+sz+fu/d3D33WW8XvWgFpnNZnSy82QyiWVZtLW1zeRuRETq1liYGGVfci89nR6FiSqx\nbJtSuUK+WCZbKJErlMiXyhRLZcqVigYPv0N7XqvwzDNvDwljLRRv9dBDLl59VVPJisx2hm3P3Fn3\n8ssv57XXXuOll14a72OZSCTGH9+9e/dM7VpEpOYG4zkGE0mG8kN0tjrwextrwbpaq1QsimWbUqVC\nsWxRLFuUK2NTl1q2hYWNZVewgQO9+A1MTMPAwMTlNHE5TNzOse89LgfuBls0sFb2vjmPz32u9Xcb\njAqYJYieCNmuCWUffHCUE09849hWUESOqWXLlo1/Hw6HD3p8xtooP/GJT/D888/z3HPPacCWiMw6\nQ/EcQ4kUQ/khutoc+Dy6kD2SYtkiXyyTL1rkSxXKlQolu0ypUqJMiWKlRMWuYGMBYJpjXwb775vb\nYNtg7f/XxIHLdOI0nTgNF27Tjdflwu9x4nc78bpNfT4dDcPm7S0UIiIwQ4Hihhtu4NFHH2XLli0s\nXrz4kOVWr149E7tvSi+99BKg90yqR8fUzOkbSVLwjZIK7GNt13KCfletq3RM7PyvnQAsf9fyKZW3\nbZtMvkg6VyKdL1IpFDDL+f1fOZw2+FwuPM4gLpeB2+XA5TAwHQYGRw4CpXKFUtmmtL91I5ev4DCc\nmE4/Drcfl8tLe4uPtpAPh6nA91YGBRwOm0pl//s8PoZiYjmXy+akk4KcdtrMnUd0rpJq0zF19N7a\nw2gyVQ8UGzdu5LHHHmPLli2ceOKJ1X56EZG69rupYffR0+mZNWHiaOQKJRKZAslMnkwpT6aYIV/O\nUbHLeD0OfH4HrW43LqfjHe3H5XTgetunXKFUIZvPMppLYmecxPNhwskQ7SEfbS0+nAoWACw93sH6\n9WWeemr/8WvYYJljweItrryyxIoVGpAtMttV9SzwsY99jAceeIAnn3yScDjM4OAgAKFQiEBAK8GK\nSHMbiPxunYmeTg+hgMLEAcVSmUSmQCJbIFPIkymmSRczmGaFgM9JZ4sTj8sz4/XwuBx4XA7aQh7y\nxQrxVJR4PE4830I4FWZue5BwQIsNul0O3n9lgRdePDDTkw22E+zfBa758y02bqzg9WqiAZHZrqq3\nYu666y7S6TR//Md/zLx588a/vvrVr1ZzNyIidWcomh5bAXv/1LAKE2OyhRK9Iwl290V4bWSQN6J7\nGUr3YzuzdHe6mN8doDXkweN6Z60R0+F1O+jp8NPd7iJbidOb6OWN4Sh9o0kqlnXM61NPDMPgpBM9\nfO1rRS68sITptMbChG3ictls2FDkBz8osGqVwpeIVLmFwprlJ2ARmZ2iyRxvDEXZl9hLV4dr1k8N\na9s2yWyBaDJHMp8jlU+SLqfxex20t7rweWa+JeJoePYHi1S2xGCyn1y5jVyhxIKuMF737O3OYxgG\nJ5/k5cbPlDnvwjwDvQaLW0qseleBFSucapkQkXGz90wpIlIFqWyB1/oj7E3uo73VSTg4ey+ybNsm\nlSvxWn+UZD5LspCgaOUJ+Z0saK//gc8hvwuv22QkHiefyFG2bI7raiEwyy+cPW4nxx/vYulxPlYe\n52Nep1olRGQiBQoRkWnKFUr8ti/KvmQvAb9Ne3j2XmjF03l6I1nSxSxpD2CUaQm66fb7pzQjU71w\nOR3M7fQxGi/QnxzAti0WdrfO+lBRsWxcphOH2Th/SxE5dhQoRESmoViqsLs3yt5EL053iTkd/lpX\nqSZSuQLDsQzJfJaBzDA4SiwOt+P31le3pqNhYNDV6iUSLzCQGsIwTBbPaZ3V3Z8qlo0HE6ejvluZ\nRKQ2Zu/ZUURkmioVi929EfbF+6kYWRZ2zb5Z7LKFEsOxDPFsmlguTsnOEwxY+Lwu/N7m+GjpaPUw\nEs8zmB7C6TBZOrcNc5YuhFep2DhdDgUKEZlUc5z1RUSOEdu2+W1flL7EMNlKgkXzgrNqteWyZTES\nyxBJZojkoxQqWcJBF6GAn9dzzXex2dnqoX8kSzSTIBB1MbcjVOsq1UTFsnGYDhwKFCIyCQUKEZGj\nsKc/Rl98lFhhlMVzA7OqT3k8nWc4liaaT5DIxwgFnHQG/U19197AoKvNy+BoBG/SS9DvJuRr3O5c\n01WxbExDLRQiMjkFChGRKdo7lKAvFmU4O8DCngBO5+y4uMqXygxG0sSzaUazozicFeZ2et/xStaN\nwu10EA66GMmM4Iu4Ccx3H5MQZds2lj02HbtpmDVrCbNtm1LZwu1w4Z4lf3MROToKFCIiUzAYTbNv\nNEp/qpf5c/x43LPjwmo0kWEoliaWi5GtpGkPuwk08IDr6QoH3WTyWRK5FPG0n/aQb0b3N5waZufQ\nTrbu2wrA2cedzfI5y+kOdc/ofidTLFm4TDdetwtzFrXIicjUKVCIiBxBJJHljaEIval99HR6m2bQ\n8eEUS2X6I2kimSSj2RECPgfzOvw4mrh705G0Bt3EEnEiiRBtQe+MtRgMp4a5/We388zrz4xv+8Fv\nf8D6Jeu5/j3XH/NQUShV8Dg9+GbxLFcicnizo71eRGSa0rkiewai7E3so6PVSSjgqnWVZlw8nWfP\nYJze2CCR3DBdbR46wp5ZHSaAsSBplknm08TT+RnZh23b7BzaOSFMHPDM68+wc3gntm3PyL4PpVC0\n8Do8+DzNf+yLyPQoUIiIHEKpXGFPf4zeZB/BALS1NHdXn7Jl0TuS4I3hCL2JXiqOHPO6/fg8s6N7\n11S0hjzE8wmiqdyMPL9lW+PdnCazde/W8XEVx0qhuL+FwqMWChGZnAKFiMgkbNvmtf4YfYlBcOaZ\n0zGzfeZrLVco8Xp/jN7YCEOZAcItJt1t3lnfKvF2Aa+Tkl0kWyhQKJVrXZ1jIl+s4FYLhYgchgKF\niMgk9g0nGUxESBajzOtq7lWwY6kcewai9CUHyFYSzOvyEfTp4vFQAl4H2XKWVK5Y9ec2DZOzjzv7\nkI+fvfBsTOPYfXRblk2lAl6nB49LLVUiMjkFChGRtxlNZOmNxBhMD7BgTqBp5963bZuBSIo3R6L0\npfpxusvM7fQ37eutFp/XSbaYI52tfqAwDIPlc5azfsn6gx5bv2Q9y7uXH9PpY4slC7fDjdftnFUL\nOIrI0VGHSBGRt8jkirw5FKM32UtXuwdvk44fKJUr9I2mGE3FGc2P0hF2q1ViinweB6NWlnS+QNmy\ncJrVDWDdoW6uf8/1nLvkXLbu3T9t7MKzWd597KeNzRcreJxejZ8QkcPSGUJEZL9yxWLPQIzeRB+B\nALSG3LWu0ozIFkr0DicYzkTIllP0dHrxaMGyKTMNA7fToFgpki+UCfqqf5x0h7rpCnZx5pIz9++z\nNgvbFYoVPBo/ISJHoEAhIsJY9589/TH6E0OUjRzz2wO1rtKMSGbz9I0mGUwNYziKzOue3WtLTJfb\n6aBkFSmWKzO2D8MwcBi1DXqFUoWAW2tQiMjh6QwhIgL0jaYYSESJF6Msnhdoyv7i0VSO/kiCwfQg\nXi90hJt75qqZ5HIZlHIliqWZCxS1Zts2+YKFz+/D71ULhYgcmgKFiMx60WSOfSMxBlL9LJjja8pB\nycOxNAPxJEPpQVqCDsLB5uzOday4nA4yVol8sXmnjs0XKrhMNwGPG5e6xInIYShQiMisliuUeH0w\nSm+ql652Nz5vc50WbdumP5JiJJlkKDNEe9ilwddV4HYalKwCpRns8lRrmXwZvytAyN/cCzqKyDvX\nXJ+cIiJHwbL2L16XHMDntWgNeWtdpaqybJvekQTDyTiR3ChdbV6tel0lhmmMrdFg27WuyozJ5su0\nu/yE/GrNEpHDa752fRGRKdo3nGAoGaFop+npbK7xBJZts284wWAiRjQ/ypwOhYlqMg0DsLGt5gwU\ntm2TK1j4XH61UIjIESlQiMisFE/n6Y8mGMkOMa/L31SDsC3bZu9QgqFklHghQk+HV6sczwQDbGzs\nJmylyBUquE03Qa+nKccUiUh16SwhIrNOqVzhzcE4/al+OlrdeNzNc7F9IEwMp6LEC1F6OrwaUDtD\nDMPAsm2sJgwUmVyZoDtIS0CtEyJyZAoUIjLrvDmUYDA1jOkq0h5ungumA92cDoSJuZ0+hYkZNNam\n1ZwtFOlsiYA7SIu6O4nIFChQiMisMhLPMBSPEytEmNfpr3V1qsbePwB7KBkbb5lQV5WZZdk2pmHi\nMJvrfS5XLIolCLo1IFtEpqa5zoIiIoeRL5bZOxynL9VPT4cPp7N5ToH9kRTDyfj4mAm1TMwsy7bB\nNjBNs6nG38BYd6eAe2y62GZ7bSIyM5rn01RE5DBs2+b1gRiDqSH8PptQoHnWYhiKpRlOJonkRulW\nmDgmbMvGYZo4zea74E5nywRd6u4kIlOnQCEis8JAJM1wMka6nGBOR/NMERtJZhmMJxnODNHV5sWj\nMHFMlPd3dzKbrLuTbdv7B2QHCGtAtohMUXOdCUVEJpHOFekdjTOYGWRelx+zSe4qJzJ5BiJJhtKD\ndLS6tM7EMWRVwGE4cTTJsXRAOlvG6/DT4vfhcWvtWxGZGgUKEWlqlmXzxmCcgdQA4ZADv7c5LpIy\n+SK9IwkGM4O0BB0EvM3ThasRlMoVXKYTd5O1CCXSRVo8LXS0NM+EBSIy8xQoRKSpja2GPUrZyNHZ\n2hxdOIqlMvtGkgxlhvF6IRzUTDzHWqlk43K6muoufsWyyeQqhL0ttIW8ta6OiDQQBQoRaVqpbIGB\nWIKR7DBzO31NMWONZdv0jqYYTY9iOkt0NNE6Go2kUK7gdniaagXyVGZs7YlwQAP7ReToKFCISFOy\n968YPZQeoi3saprVsAciKUbTcXJWmq423UWulVLJwmU2VwtFIl2k1RNWdycROWoKFCLSlIZiGUbT\ncQp2tmnu4keSWUaSSWL5CN3tXswmaHFpROWKhWGYeJxOnE0yy1OpbFEoQMgTpDWooCoiR6c5zoQi\nIm9RLFXoG00wmBmip6M5ujpl8kUGokmGM8N0tHqabjBwIymUKngcnqZp9YIDg7FDtIV8TTMLmogc\nOwoUItJ09g4nGE6P4vdBwNf4XVLKlQp9I0mGMyMEAyaBJpmpqlHlCxZepxe/t3kGwyfTJcLeMO2h\n5lmjRUSOHQUKEWkq8XSe4USSeCFKd3tzdN3oj6QYzUYxHSXaQs3RfauR5QtlvE4vAU9zTNWbL1aw\nLAchT4AWLWYnItOgQCEiTcOybPYNJxhMD9LV5sHpaPxTXDSVI5JOky4l6WzTxV6tVSoW5YqBz+XF\n2yQDspPpImFPC+0tzdE9UESOvcb/tBUR2a8/kmI4FcU2C7S1NP7Fd75UZiiWYiQzQkfYg6NJBgA3\nsmyhgs/lI+B1Nc3FdzJdosWj7k4iMn36dBKRppArlBiIJBnNjdDT0fgXRrZt0z+aYiQTwe81mmaF\n70aXLZTxO/0EfY0fWAGSmSIu00fY5yfga54xISJybClQiEhT2DuUYDgzTDBg4vU0/uw7w/EM0UyC\ngpWhLawLvXpQsW3yBQu/y0fQ1xzjJ6KJIh2+dua0B2tdFRFpYAoUItLwRhNZRlIJ0uVkUyz2li2U\nGImnieQidLVpvYl6kc2V8Tp9BH0enI7GD625fJlK2UGrr0XdnUTkHVGgEJGGVqlY9I0kGUwP0t3u\nwdHgc+jbts1gNM1oPkIo4MDjavwL12aRyZUIugKEA40fWgEiyQLtvja6WgNae0JE3hEFChFpaEOx\nDKOZGKazTEug8bsGRVM5YtkUxUqO1lDjv55mUalYFEsQdAcI+Rv/71IqW+RyNq3eVrpa/bWujog0\nOAUKEWlY5YrFUCzNaG6U7ibo6lQqVxiJZ4hkI3SEPRg0zl1jGxuH6cBhOrCxa12dqkvnfjcYuxlm\n24omCoQ9rXSGA7i06rqIvEOaNkREGtbA/gXfvB4bXxPMgjQUSxPNxXB77IaY1cnGJlfM0ZfsY09s\nD4OpQQB6Cj0sbVvK/Jb5+Ny+hgpGh5LOlujwdRAONv7sThXLJpEusbS1jTltgVpXR0SaQP1/YomI\nTKJYquy/AI+woKfxWyfSuQLRdJZUMcn8rvofIFuxK+wa3sVTv32KX4z8YtIyv9/1+1xwwgWc2H0i\nDqNx74LnChWwnQTdPoLexu/ulEgVCbhCtAUD+JpktW8Rqa2qt9t+4xvfYMmSJfh8PlavXs1zzz1X\n7V2IiNAfSRHJRvD7DLzuxr1Yhf0DsWNjXZ3CQReOOl/hu2JXeLnvZW7dceshwwTAL0Z+wa07buWV\nvleo2JVjWMPqSqaLtHjCtDXJStLRRGFsqli1TohIlVT1U+uRRx7hb/7mb/jc5z7HK6+8wh/+4R9y\n3nnnsW/fvmruRkRmuXyxzEg8TTQfbYppYuPpPIlcmjJ5wsH6vgNuY7NreBd3/vxOynb5iOXLdpn/\n+/P/y67hXQ05tqJYrlAo2bR4grQFG/9YS2aKOA0vrf4g4SZ4PSJSH6oaKG677TY+9KEP8ZGPfIST\nTjqJ22+/nblz53LXXXdVczciMsv1jSQZyY7SEnTictb33fwjsWyb0USWWC5KW0v998/PFXM89dun\nphQmDijbZZ5+7WnypfwM1mxmpNJlWtwttAZ9TTIYu0iHv51utU6ISBVV7exYLBb5z//8T9atWzdh\n+7p163j++eertRsRmeUyuSKjyTSJQpzOcP1fgB9JNJUjkUthOCoEGmAgdm+y97DdnA7lleFX6E30\nzkCNZk7Fskjny4Q8IdpDjX83P7t/Ibs2X5iOFk0VKyLVU7VAMTo6SqVSYc6cORO2d3d3Mzg4WK3d\niMgs1zeaYiQ7QluLC2eDt05ULItoIkssH6ctVP/hyMbm9djrhy80fPIhH9oT29NQ3Z6SmRJBZ5Bw\nwIfbVf9h70iGo3k6/Z10t2khOxGprpqeIV966aVa7r4h6T2TamukYyqdL7FnKMFAoY8FXS5GBhv7\noiiaLjKQiJMjQTFf/xesDtMxPjXsIY2cDN2/nvShwdQge/fupWLV/wBty7IZjlbo9nYTKJVIjTb2\nwP9s3iIWh0WhCsF8ir7XG+//nUY6V0lj0DE1dcuWLTvs41X7BOvs7MThcDA0NDRh+9DQEHPnzq3W\nbkRkFhtNFoiVooQDZsPfYbUsm1S2SKqUoj3c2BerwFjLxMjJ8OtLx37u+vUhg0UjSGUt/E4/Ia8b\nj6vx/z6xVJk2TzcdLZ6G/39HROpP1QKF2+3mtNNO41//9V+59NJLx7f/6Ec/4rLLLpv0d1avXl2t\n3Te9Ayla75lUS6MdU8lMgYKvn0oals4PNvxFUSSZJecexltx0NPRGP3ZbWx6Cj2TP9j9lgCx4slJ\ni/SEeli4cGHdL3RXrlj0jeRYEFrAsvmdeBq8u1MiXcQfhJO6j2fF4q6Gm/q20c5VUv90TB29RCJx\n2Merepb8xCc+wQc/+EFOP/10/vAP/5C7776bwcFBrrnmmmruRkRmoaHY2DSxbS3uhg8Ttm0TS+VI\nFOK0het7mti3MjBY0rbk8IW6Dt0qsbRtad2HCYBYqkjYHaY9FGj4MGHbNiOxPPOCC5nbHmy4MCEi\njaGqZ8rLL7+cSCTC3/7t3zIwMMApp5zC008/zXHHHVfN3YjILJMvlomms6SLKebMCda6Ou9YKlcg\nVchhG2X83vofjP1WC1oW8Ptdv3/omZ4O0c1pVfcqFoQXzGDNqqNYrpDLW3S2hOkKN0bL0eHEU0U8\npp+OQAsdTfB6RKQ+Vf3Wy7XXXsu1115b7acVkVlsKJomlovSEnTiaPDWCYBoMk8iH6/7Rewm43P7\nuOCEC3h19NUpr0XhNJycf/z5eF31P/VqNFGg1dtKe4sfl7Oxx05Ylk0kUWRBcBHzOkO1ro6INLHG\nnnNRRJpeuWIRSWaJ5+O0tzTeBfjbZQslkrkchUqeoL/xutMYGJzYfSIfP+3jOI0j199pOPn4aR/n\nxO4T6767UzpXGlunwRumswnu5keTBXyOIB2hEK1aFVtEZpAChYjUtZF4hlgujs9r4G6C2Xbi6TzJ\nQpJQwFn3F9iH4jAcrJq/ik1nbGJV96pDllvVvb/M/FU4jPr+21Vsm1iyuH+dhiDOBl8Vu2LZRBNF\nuvxdzFfrhIjMsMa7PSYis4Zt24zEs0RyUeZ2N9ZYg8lYtk0qWyBTSjO3wVf5dhgOTp5zMovaFtGX\n7GNPbM/4GhU9oR6Wti1lQXgBXpe3IYJTPFnE7wjS6g82xd38SDxPiztMZ0uQkL+xjzURqX8KFCJS\ntyLJHLFsAtNRxu/11bo671g6VyBdzOJ00vD982Gs+5Pf7WdZ5zJO6DyBvXv3AjTE1LBvVShVyOYs\n5ofa6Olo/EH/5bJFPFVmaWsn8ztbal0dEZkFFChEpG4NxzJEczHaW5vjDmsiUyBTzBD0Nd+p18AY\nXwG7kcIEwGg8T5u3k65wAG+DTxMLMBTN0+Ztoyscwu911bo6IjILNHYnURFpWslMgVgmTdHK0hJo\n/IuismWRyhbIljMEmjBQNKp4qoATL23+EJ2tgVpX5x3L5Mrk8tAd6GJBl1onROTYUKAQkbo0HM8Q\nzUdpbXE3xWJcqUyBTDGL12XiaPABv82iUKyQzFTo9HcytyOE2eDHmW3bDEZy9ATmMK+zpSkmMRCR\nxqBPNRGpO/limUgqQ7qYoq2lObo7pXIFMuUMgQacKrYZWbbNSDxPh6+D7nCQgLfxpySOxAt4DD9d\noTbmtDV+a4uINA4FChGpO5HE2LoTLYHmWMjOsm2y+RL5cg6fR3eN60EsUcRrBugIhOlqgq5OxVKF\nWLJET7CHhXPCTdGqJyKNQ4FCROrO/9/e3QdJUtf3A393T0/3PHTP89PO7OztHncHd4cIgqJn5CER\n6kAwVZGUcgZNUpVoUZGHGJLiV1eRVJCqKEYgCUXMHxZWoobEvzTloakoiDlBUErhMIAg3AP7vDM7\nT/38/f2xdyvnHXfcMLs90/t+UVs727t0f/Zurrvf/X1abPWwbC0jrY/+2AkA6JoOeq6FqCKxu9MQ\n6JouuqZAIZnHWMEIxc339EIPuXgB5WwKenz0W1uIaLTwykZEQ6XVtbDc68KHjXgsHN2DOqaNntNl\n68QQ8Dwf8w0LpWQR5awRilmdljs2XEdBWS9wIDYRBYKBgoiGyuJyD02ribQenqesXdNBzzERU0f/\n5grrw2YAACAASURBVHWUCQjMLJlIaxnkdB05Y/TXNvF9gdlFC2N6BbViCkqEl3UiWn888xDR0BBC\nYKltomUth2KqWADwfB8924EjbGgqT7lBWmhYiCCGgp4LzYJvc0smkoqBgpFGIZ0Iuhwi2qB4dSOi\nodHsWFg221CiApoaju5BluPB9mxEFWnkpyUdZa2uA8uSUD66PkMYxrKYtofltodysoxN5XTQ5RDR\nBjb6Z1QiCo2FZhfLVjM0rRMAYNkubM+GqvB0GxTL9rC4bKOULKOaT4Vi3AQATM/3UEyUMJZPIa6F\n598MEY0eXuGIaCh4no9G20TLboUrUDgebNdGlIEiEJ7nY3bJRDFeRCljIJ2MBV3SQCwtW4CnomTk\nUM0bQZdDRBscr3BENBSW2iaWrRZimgQlRDffluPC9h2uWhwAXwhML/ZgqBkUjDTKIVhvAlhpcZlf\nslE1qqiX0pBDsFYLEY228Fy1iWikLS73sByy2Z2AlS5Pjm9DVXjTt54EBGYXe4hJOkp6DrViKhTr\nTQghcGSuu9LVKZdGRg9HiwsRjTYGCiIKnO14aHR66LgdGInwdHfyfB+250EIHxFO57mu5hsWJF9D\n2SiiXkxBCcEgbGDl94oigXKqgIkSB2IT0XAIxxmWiEbaUquHlrUMPa6EqvuG5/nwhY9IJDy/0yhY\nXLbgWBFUjArqpTTUkAzC7poumi0PY8YYJiuZUP1bIaLRxkBBRIFrdiy07BaMZDhu/I7xfAFfeLzx\nW0fLHRvdLlDRyxgvpEKzmKDvr3R1qiQrGC9koMfD1TWQiEYbAwURBcr3BVpdC12ni2Q8PN2dgJUu\nT57wEQlB3/1R0O45aLY8VPQyaoV0qG66pxd60JU0SqksxvJ60OUQER2HgYKIArXctdB2OtBUGZGQ\nPcn3fAHf9yGzy9Oa65gOlpouynoFY/lwDVZudRz0ehIqRhlTY9lQDC4nonBhoCCiQC13LHTsDvRE\nOLqmvJ7nC/jwuEL2GuuYLhYaDsp6BbVcGoVUIuiSBsZ1fUwv9FAzqpgoZULThYuIwoWBgogC1eyY\naNtt6CHr7gQAsiRBggSIoCsJr47pYKFho5ysoJpNo5AOx1oTxxyZ7yKr5VHOZFAMyToaRBQ+DBRE\nFBjTdtGxTPhwENPCt/CbJAESZPhMFGui3XOw2HBRTlZQy4XvhnuxacF3VFSMEiYrmaDLISJ6QwwU\nRBSYVtdCx+4iEQtnNw5ZliBJKys202C1ur8eMzGeD1+YsGwPC42V1bA3VTJQuI4JEQ2xcF7FiWgk\ntLo2um4XST2cpyIJEiRJBvygKwmXRstCqyNQ0cdQzYdrzASwMvbm0GwXpWQFVa6GTUQjIJxXcSIa\nCe2eja7dQSEWzhsmWZYgSzI8tlAMhIDAQsOCbcmoGivrMYTxZvu1uS6SkTTG0nnUuRo2EY0ABgoi\nCoRpu+jaJoTkQY2Gb/wEAKiKjKiswHEZKN4qXwjMLZqAr6KaKqFeTEOPa0GXNXDzSyY8R8Vkbgxn\nVXNcFJGIRgIDBREFIuzjJwBAiUQQjSiAkOD5PiIy+8H3w/N9zCyaUJFA2SiiXkojroVvVrB210Fj\n2cNUdgJTY9nQBm0iCp/wXsmJaKh1TAc9t4tEMtw3TVpUQVSOwnEFIuFZuHndWI6H2UUTRjSNopHH\nRDEFNRq+S5fteHhtzsR4qo6JUhapZPhaX4govMJ3ViaikdCzHFiuhYwaTKAQQsAXK6OlZUles9WH\ntWgEWkSF7ViIBfS7jqp2z8Fi00Y+XkBBz2C8lIISwlYe3xc4NNNFMVFCNZtDJacHXRIR0RlhoCCi\nQJi2C8uzoarrf/M025rFgZkDeOTgIwCAS+uXYkd5B0pGaeDHiqkKVEVDz+4hFa6ZTdeMgMBi00av\nB1T0KkopA5WcvmahL2hH5ruIRwyMpYtcb4KIRhIDBRGtO8t2Ybk2IrJAZJ0Hnc62ZnHf4/dh38v7\nVrd988VvYvfUbtx08U0DDxV6XEUiGsdiawECYmXlbHpDx8ZLRISGWqqEaj4VypmcjlloWnAtBRO5\nKs6qZjkIm4hGUvjajolo6PVsF5ZrQVvnLkBCCByYOXBcmDhm38v7cGD2AMSAp3iNKhEkNQ1RSUXP\n9Aa677DpWR6OzPWQkFMYT49hqpINdZjo9FwsNV2Mp8axeSwLTeUzPiIaTQwURLTuepYD07Ogqet7\nCvKFv9rN6WQeefWR1XEVg2QkVCTVBAPFGxAQWGhamF+ykY+XUM0UMTmWDeVMTsc4ro8jc11UjRrq\nxSzSIQ5ORBR+fBxCROuuZ620UOiJjTFIWU9oSEaTONJuICtUyCEdC9APy/Uwv2hCkeOoGQWUszoK\n6XAPNlkZhN1BPl7CWCaLasEIuiQioreELRREtO56lgPLW/8uT7Ik49L6pW/4/UsnLoUsDf60GIsq\nMOJxxJQEWh1n4PsfVc22jZl5Eyk1j3p6DJvHcqEPEwBwZK6LmGxgLFXEFAdhE1EIMFAQ0boSQsC0\nXdieBS26vqcgSZKwo7wDu6d2n/C93VO7saO0Y81mEiqkE8jEMljuOPAHPE5j1Diuh9fmu+h0JFT1\nGibyRUyFvIvTMa/NdSFcDfV0DVtrOUQivAwT0ehjlyciWlfHpouNKmu39sOplIwSbrr4Jrx/6v14\n5NWj08ZOXIodpbWZNvYYPa4iHU9gyYyj1XGQ1jfeKncCAo2WjVbHRTqWRd7IYCyvQ49vjEXc5pdM\nWGYEk9lxbKnlOAibiEKDZzMiWlfHxk+s94Ds1ysZJRT1It439T4Aa7uw3esV0nE0e1lMt48gGVeg\nbKCn013TxULTghZJoKZXkE8lUcomEQnhQnUn02jZaLR8TGUmsaWaRzK+8QIlEYUXAwURrSvLcWH7\nNrRosAOyJUlCRFrfGvS4hryuo+dmMbvUQLWQWNfjB8HzfMwvW7AtCflECdmEgbGcviG6Nx3T7jqY\nX3IwkdqEzWN5zuhERKHDQEFE68rzBTzfQ3SDLuA1ltdh2g56jR4abQsZPZzdfTzfR6PloN1zkVbT\nqGSyKKYTyBnx0K54fTI908WRORMTqQlsKuVQSIc/RBLRxsNAQUTryvV8eMKDtkEDRUSWMZY3YNoO\nDrcPQ1VcJGLhORULIdBoWWh2XOiKjnE9g6yRQDmbhBLZGNMEH2M7Hg7NdlHVaxjP5zg9LBGFVniu\nYkQ0ElzPh+97UCIbM1AAQDKmopw14IoyZhrTKGYlxLXRvtkWEOj0fLS7HlKGhqpeRlZPoJhOIrYB\nBx+7no9Xpzsoxiuo5QqYKKeDLomIaM1svLM8EQXK83y4vrdhBuO+kWImCe/o9LEzS9MoZLSRbKnw\nfB+tjoNW14XdiyKnZjGRHUMpm0RiA42TeD3fFzg43UFGzaOWLWLzWHZDdfMioo1n9K5eRDTSjnV5\nkuXRfiI/CJWsvvp6tjELM+Ehm1IhYfhvPm3Xw3LbQcf0oCs6yskU5CSQSaqY3MCLtQkhcHi2i7ic\nQi1TwZZaDvIG7d5HRBsHAwURrTkhBCzLw7PPunjsaROHeiZ6ZwNbt0ahRiMb+ultJatDichQZAXz\n3XkcmeuimI1BVYYvcAkIdE0XrY4D2wFSWhrjho5MMo5cKoGo2Qi6xMC9Nt+D5MVQz60sXLeRpgYm\noo1rYIFiaWkJf/3Xf43//u//xiuvvIJCoYBrrrkGd955J3K53KAOQ0QjRgiBp582cc89EXz1qxrc\nWBQoyJBdDVdf5eEj11s4e5u2oUNFIZVAUositqBisdPAa/OLSCUVpHQVkSH4c+lZHjq9ldYITY5B\nV/MwEklkjDhyegxqlM+mgJVVsB0riskMF64joo1lYGe7I0eO4MiRI/j85z+PHTt24NChQ7jxxhtx\n/fXX4+GHHx7UYYhohBwLE9deq+HwYRmAD0geAMD3ZHzrWzIefyKCL37Rwjlnb+y5+eNaFJvHskgs\nRhFfjqNpNnG404aeUJDWo+s65kRAwLR8dE0XnZ4LRYoiqaUwbiShx2JIJTWkk9qGHwfzetPzPdhW\nFJsydWyrF5CIbczxI0S0MQ0sUOzcuRPf+MY3Vr/evHkzPv/5z+Oaa65Bu92Gruun+L+JKIwsy8M9\n90SOhgkAkg/IHiB+/dR9blbG178Wwe3/z93wT3RlSUI1byCrxzC/nECz3UPDbODQbBsxVUYipiAR\ni6zJjbzlejBND6btwbR9RCUViWgSFT2JpBZDJqkhldDYGnES0ws9mL0IJrN1bBsvQOcq2ES0wazp\nlaHZbELTNCQSXMiHaCN69lkXX/3q6xZuk8TRForju/Hs26fgwx+2sX07b1aBldaKejGNYjqJ+WYc\njY6JntNDp9vB4nIPUUVCTI0gqshQozKiigz5TXaN8jwftitgOx4c14ft+rAdH4oURVyJQVdiKBhx\nJDQVeiwKI6FtqFWtz9TMQg9mV8ZkdgJbawUYiXAuVEhEdCqSEEfnLRywRqOBd77znfjABz6Ae+65\nZ3V7s9lcff3CCy+sxaGJaEg8//wkPvrRwq83yA5gHAIyrwD28Yt83XlnAxObjqxzhaPB83x0bQ9d\ny0XPctHzLDi+A1e4cD0HLlxIEiDLgCStxLVjY1J8ISB8wPNX9iVBhiIpiEYURCUVUVlZ+VpREFdl\nxNQI4tEIIhxMfFqLyy7MnoJKvIxNRQM6uzkRUUht3bp19XU6feK6Oqd9HLh3717cddddp/yZ73//\n+7jkkktWv26327j22mtRr9fxuc997kzqJaIwExIA3qieqUhEhhGXYcSj8H0B046vtCx4PlzXh3N0\nbQ9fCAisJAcfAkIIRGQZshKBDAmyJEOWJSgRCZoSQVSRoCoRqIrMqU3P0OKyC7MbQSVRxqYCwwQR\nbWynbaFYWFjAwsLCKXdSr9cRj8cBrISJq6++GpIk4dvf/vYJ3Z1e30JxsoRDJ/fkk08CAC666KKA\nK6GwWI/31FNPmXj3uzW47tGbVckDjMNA9peAnVr9OUUR+PKXbWzfzu4i/XI9D76/EieEL1bChQCU\niAxZWgklaz2I+sBzBwAAO7bvWNPjBG36aDenifQEto0XkNY39oQCa43XPxo0vqfO3Onu30/bQpHP\n55HP59/UwVqtFq666qo3DBNEtLHs3Klgzx4HX/nK0UGqQgKE/JtDKLB7t4vNZw3fugujRIlEAP4R\nrrnp+WMDsCewpZpnmCAiwgD7HrRaLVx55ZVoNBr48pe/jFarhenpaUxPT8NxnEEdhohGiKZFcMst\nHmq1ox34IR3t9vTrhtFiycdHrvc2/AxPNPxem+vCMpXVAdgME0REKwYWKJ566ik8/vjjeO6557Bt\n2zZUq1VUq1XUajXs379/UIchohEiSRLOPz+Gb37Twsc/bkNRgGOnHUURuOYaB1/8oo2zt7GrEw23\nI3PdX68zMV5AKsn3LBHRMQN7JHjZZZfB9/3T/yARbSiSJOGCC+J44AEXn/qUhR/81MbBnou3b7ew\nZYsCTeVTXhpevi9weLYLeBqmshPYOp7nOhNERL+BfQyIaF3EYgouvFBBNBPDgVkNU+MqFE5NSkPM\n9XwcmulCk3TUszVsqeWQZJggIjoBAwURrStZliBJMtZmBRyiwbAdDwdnukhFsxjPjGFrLcdxPkRE\nb4BnRyJaV7K0sh6C5wtw5n4aRqbl4dBsF4VYCdVMEVvH82xNIyI6BQYKIlpXWjQCNaLCdlzEVM5z\nGhZCCESV6OrrYyt1j5p218FrcybG9Cqq2TzOqua46B8R0WkwUBDRuoqpCrSICtu2gWTQ1dAgzLZm\ncWDmAL7/yvcBAJdJl2FHeQdKRinYws5Qo2VjbtHGeKqO8Xwem8rpkQ1GRETriYGCiNZVXItCjWho\nO8tBl0IDMNuaxX2P34d9L+9b3fatl7+F3VO7cdPFN41MqJhvmGgs+9iUnsREMYtaMXX6/4mIiAAM\ncB0KIqI3Y6WFQoNle0GXQm+REAIHZg4cFyaO2ffyPhyYPQAxAqPvp+d7aLWAqcwktlQLDBNERGeI\ngYKI1lVMVaApKmzXH4mbTXpjvvDxyMFH3vD7j7z6CHwxvOsTCSFwaKYD24xiKjuJbeNFFDPsh0dE\ndKbY5YmI1pUsS4ipUShyFLbjQ+PAbAqA6/o4NNuFKunYlKtiS40L1hER9YstFES07mKqglhEg+0M\n79NrOj1ZknFp/dI3/P6lE5dClobvMtM1XfzqtQ50JYfJ7DjOmSgyTBARvQXDd6YnotCLqwrUiAbL\n4TiKUSZJEnaUd2D31O4Tvrd7ajd2lHYM3SxJi00Lh2dMVJI1bC5UsX1TETEuWEdE9JbwLEpE625l\nHIWGlt0MuhR6i0pGCTddfBPeP/V+fP/l7wMALpu6DDtKwzVtrO8LTC/0YJkyJjOTqBc4kxMR0aAw\nUBDRutPjKpLRBGab3kgvgkYrSkYJRb2Iml8DAGzZvGWo/k4d18ehmQ402cDm7BimxrLIGvGgyyIi\nCg0GCiJad5qqQI/FEF3W0DU9JOM8FY06SZLguM7q62HR6bk4MtdFPl7CWKqIs6pZxLVo0GUREYUK\nr+JEFIiMHoPeNNDuNhkoaE0sNC0sNV3UjAmMZbKYqmQQiXDoIBHRoPHMSkSByOgxGKqBVtcJuhQK\nGd8XODTbQWsZmExP4qxyCVtqOYYJIqI1wseCRBSIZFyFrsWBZQWm7SHG9ShoAGzHw6GZLuIRAxO5\nKjaPZZHWY0GXRUQUagwURBSYjB6D0TTQ7nQYKOgta7RszC1aKCZKqKQKOKuW45SwRETrgGdaIgpM\nOqnB0AzMdBsoZPkUmfrjej6mF3pwrAgm0pOoZNKYrGQgy8MzOJyIKMwYKIgoMKmkBkNL4lBTguP6\niCrs405npt11ML1gwohmMJErY1M5g1yKU8ISEa0nBgoiCowkSUglNKQ0A41WD0W2UtCbJITAzKKJ\ndtvHmDGOciqDqbEs1Ci7zhERrTc+DiSiQJWzSeQTeSwt2/B8EXQ5NAJMy8PLh9vwrBg2ZzdjW7WC\nsycKDBNERAFhCwURBSoZV5HTdcx1U1haNlHIsJWC3th8w8RS00UpWUHZyGFqLItEjAvVEREFiYGC\niAI3ltex0CrgleWXkEtpHExLJ3BcH4dnu5B8DVOZOqr5NGqFFN8rRERDgIGCiAJnJDTk9CTmugaW\nWjbyaS3okmiINNs2Zhcs5OIFVIwiJisZpJJ8jxARDQsGCiIaCmN5A/OtPA4tv4JcSoUk8cnzRmc7\nHqYXevAcBfXUJoxlM5gop6FwxWsioqHCQEFEQyGV1JA3DMx3E2i0bGRTfAK9UQkhsNCwsLTsIBcv\noJwvYLyYQj6dCLo0IiI6CQYKIhoaldzKWIpDjVeQ1lX2j9+AOj0X0ws9aHISU5k6ytkUxosptkoQ\nEQ0xBgoiGhoZPYacbmDRTGF2sYdKgQuUbRSu62Nm0UTPBCrJKopGFhPlNPS4GnRpRER0GgwURDRU\nJisZdC0bLy6+hHbXgZ7glKBht7RsYW7JQjaWw3iuiGohhXI2yXE0REQjgoGCiIZKXIuiXsyg51Rx\naP5VTNUi7O4SUqa1Muha8jVsSk+hnE6hXkpzgToiohHDQEFEQ6eUTaLZyaBtt/HaXBP1SjLokmiA\nPF9gbslEu+OjmCijqGdRL6WR0bmoIRHRKGKgIKKhNFnJoGs6eHGhg6Vli7M+DSkhBGzHw0u/9PDq\nK1UAgAQLm8+KQI1Gjuu2JITA4rKNxaYFI5rG5kwJ1XwKY3mDA/CJiEYYAwURDaWoEsGmSgZdu4ZX\nll5GIqZAU9kVZpgIIfB/z1v42lcj2LdPheethL5IROCqq1x85HoLZ2/TIEkSGi0b80smYoqOiVQV\nBcNAvZRCXOMYGSKiUcdAQURDK6PHUM2l0XXKODw7g01VHRE+yR4Kx8LErbeqmJs9foyL50n41rei\nePyJCO68q41MAYgijpoxgbyeQq2Q4krXREQhwpGORDTU6qU0Kqk8kkoGB6c78H0RdEmElVWsv/bV\nyAlhYpXsYK7Rwde+JiEXGcO24hR2TlSxfVORYYKIKGQYKIhoqMmyhG31POqZMWiSjkOzHQjBUBG0\nl37pYd++kzRySy4QbQOyC7TH8Ng3z4bUKWLHZBFZg+uKEBGFEbs8EdHQiyoRbBvPQwjgV0sHcWim\ni/FygusUBGh2bqVr0yrJAxRz5XWnBJhZwNbhOkl0Ghb/roiIQoyBgohGgqYq2DqegxACrzQO4eBM\nB+OlJGcHCprkAooFSALoFoBeFrANwE6CjeBERBsDAwURjYy4FsXZEwVIkoSDjcN4dbqFeiXJgdrr\nTAiBpO5AjtnwXQXo5gErA9j6SpgQvw4S0ahArRZgsUREtOb4+IiIRkpMVXB2PY9NuXEk5Ax+daQN\n0/KCLmtD8HyBhaaFXx5sIZNV8P6Li8DiFmB5AmhXACt9XJgAgD17HOzcyWdXRERhxrM8EY0c7Wio\nkCUJM8sxHJyeRjatoJDhSstrwXY8LC7bWG470NUUxo0xpOMJ/NWNCp75QQZHDp98fZBazcfNN3uI\nxdR1rpiIiNYTAwURjaSoEsH2TQUYcyoSC3Ecbh1Bp9dGtZhAVGHj6yB0TReLyxZ6PYFMLIPNmSxy\nRhLlrI5UUoOYEvjWN03ce28E//ZvUbjuStezaFRgzx4HN9/s4fzzGfKIiMKOgYKIRpYkSaiX0kgn\nY4hPa5huzeFXh+dRLmhIJflUvB+u56PVcdBsO/DcCHLxPMbzGRRSSZSyyeNWtpYkCRdcEMcDD7j4\n1Kcs/N//tQEAZ5+tY+dOhS0TREQbBAMFEY28VFLDjskiktNRJBtJHF44jHa3i3I+zgHbb4LvC7S6\nDpbbDnqWD101UIgVkYkZKGZWgoQSeeNWn1hMwYUXKhDiGQDAhRdetF6lExHREGCgIKJQUCIyzqrl\nkNZjiM9oeK01g5cONZA1VGTTGoPFSbS7DpY7DtpdF3ElgbRWxnhSR1aPI5eKI6PHuH4EERGdFgMF\nEYVKIZ2AEVehz2hYaOWw0JvHL5eXkTGiyKW1Uz5p3whMy0OjbaPVcRCVYkjHcihlU8gkVkJE1ohv\n+D8jIiI6MwwURBQ6mqpgWz2Pds/Aaws6FlptLHQX8dKhJtK6gnxag7KBBm53TRednovljgP4CtJa\nCptSaaTiKyEiZ8ShqbwcEBFRf3gFIaLQ0uMqto7nUTNTeG3BwPxyGwu9Rbx0uIFUUkFajyIeC99p\n0HV9tHsu2j0H3Z6HqKxCV3XUkgaMWHI1RCRi0dPvjIiI6DQGfiUVQuDqq6/Gww8/jP/4j//Ahz70\noUEfgojojCRiUZxVy6FaMI4GizyWekt4ba4FT3RhJKLQEwqScWUkxwy4no+u6aLb89AxXXiuhKSa\nhB7NoJLVoWsa0noM6aQGI6EFXS4REYXMwAPFF77wBUQiK4scjeKFmYjCK65FsbmaRbVgYK6RQqNt\nom2aaNktzC+0cMRvIRGPHA0Y0aEcyO35ArbtwXJ8mJaHrunCcYFkNIGEmkImmUBSi8OIq0glNaST\nMajRky88R0RENAgDDRQ//vGPcd999+Gpp55CuVwe5K6JiAYmpiqol9Kol9LoWQ4abRONtonlnom2\n1Uar2cL0fAuaKkOLytDUCNSojJgaWbexF0IIWI4Py/aOfqy89nwJWkSFpmjQlBgyyTgSahx6XIWR\n0GDEVSRiUT7QISKidTOwQNFqtbBnzx78y7/8C4rF4qB2S0S0puJaFHEtirG8Advx0GibaHZWPnqu\nCdu1YHYttD0blteFLzxoagRaVIaqRqAqMmRZgiwB0tHPsiStvn79jb0QAp4n4PlHP4577cP3V7ov\nWY4Px/WhRjRoEQ2aoiMb1aDFNWiKipiqrNStKkjGVSQZIIiIKECSEEIMYkcf/ehHUSgUcO+99wIA\nZFnGf/7nf+L3fu/3jvu5ZrO5+vqFF14YxKGJiAbO8wVM24PterBcH5bjwXZ82J4Lx3dg+w4c34br\nu/Ah4AsfEAI+xNH/fIijXx+715eEBEmSEYEMWYogIq18liUZMmRE5JVtihSFKkehRiPQohHEojK0\n6NEQo7D7EhERra+tW7euvk6n0yd8/5QtFHv37sVdd911ygN873vfw6uvvoqf/exnePLJJwGsPIV7\n/WciolETkSUkYwqSv3GadD0ftrvyYToeXNeHLwBfiJUAIXDCZ1/4K/uUZERkCZGIBFmSoLzudUSW\noERkyJIENSpDU2S2OhAR0Ug4ZQvFwsICFhYWTrmDer2OG2+8EV/5ylcgy7/uW+x5HmRZxq5du/Do\no4+ubn99C8XJEg6d3LGwdtFFFwVcCYUF31Prx/dXTrPyEA7yHiS+p2gt8H1Fg8b31Jk73f37KVso\n8vk88vn8aQ/y2c9+Frfddtvq10IIvO1tb8MXvvAF/O7v/u6Z1EtEFDphDxJERLSxDWRQdrVaRbVa\nPWF7vV7H5OTkIA5BRERERERDaH3mPyQiIiIiolAa+MJ2x/i+v1a7JiIiIiKiIcEWCiIiIiIi6hsD\nBRERERER9Y2BgoiIiIiI+sZAQUREREREfWOgICIiIiKivjFQEBERERFR3xgoiIiIiIiobwwURERE\nRETUNwYKIiIiIiLqGwMFERERERH1jYGCiIiIiIj6xkBBRERERER9Y6AgIiIiIqK+MVAQEREREVHf\nGCiIiIiIiKhvDBRERERERNQ3BgoiIiIiIuobAwUREREREfWNgYKIiIiIiPrGQEFERERERH1joCAi\nIiIior4xUBARERERUd8YKIiIiIiIqG8MFERERERE1DcGCiIiIiIi6hsDBRERERER9Y2BgoiIiIiI\n+sZAQUREREREfWOgICIiIiKivjFQEBERERFR3xgoiIiIiIiobwwURERERETUNwYKIiIiIiLqGwMF\nERERERH1jYGCiIiIiIj6xkBBRERERER9Y6AgIiIiIqK+MVAQEREREVHfGCiIiIiIiKhvDBREaheO\nVgAACBlJREFURERERNQ3BgoiIiIiIuobAwUREREREfWNgYKIiIiIiPrGQEFERERERH1joCAiIiIi\nor4xUBARERERUd8YKIiIiIiIqG8MFERERERE1DcGCiIiIiIi6ttAA8UTTzyBK664AoZhIJVK4b3v\nfS8WFhYGeQgiIiIiIhoiyqB29Pjjj2P37t34y7/8S9x7771QVRXPPPMMotHooA5BRERERERDZmCB\n4tZbb8Wf/dmf4fbbb1/dtmXLlkHtnoiIiIiIhtBAujzNzs7iRz/6ESqVCn7rt34L5XIZl1xyCf7n\nf/5nELsnIiIiIqIhJQkhxFvdyY9+9CPs2rULuVwOd999Ny644AI89NBD+NznPoennnoK55133urP\nNpvNt3o4IiIiIiIKQDqdPmHbKVso9u7dC1mWT/nx6KOPwvd9AMAnP/lJ/OEf/iHe/va347Of/Sze\n+c534oEHHlib34aIiIiIiAJ3yjEUt956Kz72sY+dcgf1eh3T09MAgB07dhz3ve3bt+PVV199iyUS\nEREREdGwOmWgyOfzyOfzp93J5OQkqtUqfvGLXxy3/fnnn8fb3/7247adrJmEiIiIiIhG00BmeZIk\nCbfddhs+85nP4LzzzsP555+Phx56CE888QTuv//+QRyCiIiIiIiG0MCmjb355pthWRY+/elPY2Fh\nAeeeey6+/e1v421ve9ugDkFERERERENmILM8ERERERHRxjSQdSho7XzpS1/C5ZdfjkwmA1mWTzrI\nfWlpCTfccAMymQwymQw+9rGPcXpeOiOXXXbZCTO47dmzJ+iyaMTcf//9mJqaQjwex0UXXYTHHnss\n6JJoRN1xxx0nnJOq1WrQZdGIefTRR/HBD34Q4+PjkGUZDz744Ak/c8cdd6BWqyGRSODyyy/HgQMH\nAqh09DFQDLler4fdu3fjb/7mb97wZ/bs2YOnn34aDz/8MPbt24ef/OQnuOGGG9axShp1kiThj//4\njzE9Pb368c///M9Bl0Uj5N///d9xyy23YO/evXj66aexa9cuXHXVVTh48GDQpdGIOuecc447J/38\n5z8PuiQaMZ1OB+eddx7uvfdexONxSJJ03Pf/7u/+Dn//93+Pf/zHf8SPf/xjlEolXHHFFWi32wFV\nPLrY5WlEPPnkk3jXu96FX/3qV5iYmFjd/txzz2Hnzp344Q9/iPe85z0AgB/+8Id43/veh1/84hfY\ntm1bUCXTCLn88stx7rnn4h/+4R+CLoVG1MUXX4zzzz//uCC6bds2XHfddbjrrrsCrIxG0R133IFv\nfOMbDBE0MIZh4J/+6Z9Wl0MQQqBareKmm27C7bffDgAwTROlUgl33303/vRP/zTIckcOWyhG3P79\n+6Hr+mqYAIBdu3YhmUxi//79AVZGo+brX/86isUizj33XNx22218QkNvmm3b+MlPfoIrr7zyuO1X\nXnkl/vd//zegqmjUvfTSS6jVati8eTOuv/56vPzyy0GXRCHy8ssvY2Zm5rjzViwWwyWXXMLzVh8G\nNssTBWN6ehrFYvG4bZIkoVQqrS44SHQ6e/bsWV1P5plnnsHtt9+On/3sZ3j44YeDLo1GwPz8PDzP\nQ7lcPm47z0PUr3e/+9148MEHcc4552BmZgZ33nkndu3ahWeffRa5XC7o8igEjp2bTnbeOnLkSBAl\njTS2UARg7969Jww2+82PRx99NOgyacSdyfvsT/7kT3DFFVdg586d+PCHP4yHHnoI3/3ud/HTn/40\n4N+CiDai3bt347rrrsO5556L3/md38F//dd/wff9kw6qJRq03xxrQafHFooA3Hrrrat9+N5IvV5/\nU/uqVCqYm5s7bpsQArOzs6hUKn3XSKPvrbzP3vGOdyASieDFF1/EBRdcsBblUYgUCgVEIhHMzMwc\nt31mZgZjY2MBVUVhkkgksHPnTrz44otBl0IhceweaWZmBuPj46vbZ2ZmeP/UBwaKAOTzeeTz+YHs\n6z3veQ/a7Tb279+/Oo5i//796HQ62LVr10COQaPprbzPfv7zn8PzPN4M0puiqiouvPBCfOc738GH\nPvSh1e3f/e538fu///sBVkZhYZomnnvuOfz2b/920KVQSExNTaFSqeA73/kOLrzwQgAr77PHHnsM\nd999d8DVjR4GiiF3bLq8559/HgDw7LPPYnFxEZs2bUI2m8X27duxe/dufOITn8CXvvQlCCHwiU98\nAtdeey22bt0acPU0Cl566SX867/+Kz7wgQ8gn8/jwIED+PSnP413vOMdeO973xt0eTQi/vzP/xw3\n3HAD3vWud2HXrl144IEHMD09jU9+8pNBl0Yj6C/+4i/wwQ9+EPV6HbOzs/jbv/1b9Ho9fPzjHw+6\nNBohnU4HL7zwAgDA93288sorePrpp5HP51Gv13HLLbfgrrvuwjnnnIOtW7fizjvvhGEYXIepH4KG\n2mc+8xkhSZKQJEnIsrz6+cEHH1z9maWlJfEHf/AHIpVKiVQqJW644QbRbDYDrJpGycGDB8Wll14q\n8vm80DRNbNmyRdxyyy1iaWkp6NJoxNx///1icnJSaJomLrroIvGDH/wg6JJoRH3kIx8R1WpVqKoq\narWauO6668Rzzz0XdFk0Yr73ve+dcA8lSZL4oz/6o9WfueOOO8TY2JiIxWLisssuE88++2yAFY8u\nrkNBRERERER94yxPRERERETUNwYKIiIiIiLqGwMFERERERH1jYGCiIiIiIj6xkBBRERERER9Y6Ag\nIiIiIqK+MVAQEREREVHfGCiIiIiIiKhv/x+Y+rOF95W6EwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff67ce84208>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the sigma points lie between the first and second deviation, and that the larger $\\kappa$ spreads the points out further. Furthermore, the larger $\\kappa$ weighs the mean (center point) higher than the smaller $\\kappa$, and weighs the rest of the sigma points less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know *how* these weights and sigma points are selected yet, but the choices look reasonable."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Handling the Nonlinearities"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I explained at the beginning of the chapter that there are two places for nonlinearities to occur. The first is in the state transition function, and the second is in the measurement function. For the linear Kalman filter we use the equation\n",
      "\n",
      "$$ \\mathbf{x}^-=\\mathbf{Fx}$$\n",
      "\n",
      "to propogate the state from one epoch to the next. As you remember F defines a set of linear equations that performs this calculation. However, suppose we are tracking a ball or missile in flight. Air drag causes the behavior to be nonlinear, and therefore there are no linear equations that will compute the state.\n",
      "\n",
      "The linear Kalman filter uses the measurement function in this equation\n",
      "\n",
      "$$\\hat{\\mathbf{x}} = \\mathbf{K}(\\mathbf{z-Hx}^-)$$\n",
      "\n",
      "to incorporate the measurements into the state. The term $\\mathbf{Hx}$ converts $\\mathbf{x}$ to a measurement using the linear equations implied by \\mathbf{H}$.\n",
      "\n",
      "The UKF assumes that both the measurement function and state transition function are nonlinear, though in some problems only one or the other are nonlinear. If they are nonlinear we can not represent them with a matrix. Instead, we will define a function $h(x)$ for the measurement function and $f(x)$ for the state transition function. We will implement these as Python functions that take a state $x$ and return either a state $x$ for the state transition function, or a measurement vector $z$ for the measurement function. The functions will look something like:\n",
      "\n",
      "    def hx(x):\n",
      "        z = # do something to compute z\n",
      "        return z\n",
      "        \n",
      "    def fx(x, dt):\n",
      "        x_est = x propagated forward in time by dt\n",
      "        return x_est"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Tracking an Aircraft"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far we haven't been very concrete, so let's jump into solving a problem. In the *Multivariate Kalman Filter* chapter I presented an example of tracking an aircraft with two radar stations. This is a nonlinear problem so we were not able to construct a Kalman filter for that situation in that chapter. We are now able to do so.\n",
      "\n",
      "Assume we want to track an aircraft in 2 dimensions. We will ignore altitude to simplify the exposition and code. There are two radar stations on the ground, each which provides a range (straight line distance) and bearing to the aircraft from the station's position. The radars have a $1\\sigma$ error of $0.5^\\circ$ in the bearing measurement, and a $1\\sigma$ error of 0.1km for the range.\n",
      "\n",
      "We will assume that the aircraft does not engage in high dynamic flight, so we will chose a constant velocity process model for it. In other words, our state will contain the position and velocity of the aircraft in the $x$ and $y$ coordinates, like so.\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x} \\\\ y \\\\ \\dot{y}\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to design our state transition function. With a linear Kalman filter, for a constant velocity model we would set\n",
      "\n",
      "$$\\bf{F} = \\begin{bmatrix}\n",
      "1&dt&0&0 \\\\\n",
      "0&1&0&0 \\\\\n",
      "0&0&1&dt \\\\\n",
      "0&0&0&1\n",
      "\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "so that $\\bf{Fx}$ computes the next position with the Newtonian equation $\\bf{x}^- = \\bf{x} + \\dot{\\bf{x}}\\,\\Delta t$.\n",
      "\n",
      "We are assuming linear behavior for the aircraft over short time periods in this problem so this formulation suffices. However FilterPy's UKF implementation is designed to handle nonlinear problems, so we need to implement this as a function. The state transition function has the signature\n",
      "    \n",
      "    def fx(x, dt)\n",
      "    \n",
      "where x is the state variable (a one dimensional numpy.array), and dt is a float specifying the time step. Note that the name `fx` is not required, you may name it anything you like. We might implement this function as"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fx(x, dt):\n",
      "    \"\"\" state transition function for a constant velocity aircraft\"\"\"\n",
      "    \n",
      "    F = np.array([[1, dt, 0,  0],\n",
      "                  [0,  1, 0,  0],\n",
      "                  [0,  0, 1, dt],\n",
      "                  [0,  0, 0,  1]])\n",
      "    return np.dot(F, x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively, if `dt` is always a constant we might take advantage of the fact that functions can own variables, and do something like this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fx(x, dt):\n",
      "    \"\"\" state transition function for a constant velocity aircraft\"\"\"\n",
      "    return np.dot(fx.F, x)\n",
      "\n",
      "dt = 0.1\n",
      "fx.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": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is perhaps not as readable, but it is faster since we only construct `F` once instead of for every call of `fx()`.\n",
      "\n",
      "Finally, for such a simple problem we might just compute the positions directly as in the next code block."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fx(x, dt):\n",
      "    x_est = x.copy()\n",
      "    x_est[0] += x[1]*dt\n",
      "    x_est[2] += x[3]*dt\n",
      "    return x_est"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It doesn't matter which you choose, just do whatever is most useful for your situation."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The next step is to design the measurement function. As in the linear Kalman filter the measurement function converts the filter's state into a measurement. So for this problem we need to position and velocity of the aircraft and convert it to the bearing and range from the radar station.\n",
      "\n",
      "If we represent the position of the radar station with an (x,y) coordinate computation of the range and bearing is straightforward. To compute the range we use the Pythagorean theorem:\n",
      "\n",
      "$$range = \\sqrt{(x_{ac} - x_{radar})^2 + (y_{ac} - y_{radar})^2}$$\n",
      "\n",
      "To compute the bearing we need to use the arctangent function.\n",
      "\n",
      "$$bearing = \\tan^{-1}{\\frac{y_{ac} - y_{radar}}{x_{ac} - x_{radar}}}$$\n",
      "\n",
      "As with the state transition function we need to define a Python function to compute this for the filter. Our first attempt might look like this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, atan2\n",
      "def hx(x):\n",
      "    dx = x[0] - hx.radar_pos[0]\n",
      "    dy = x[2] - hx.radar_pos[1]\n",
      "    \n",
      "    rng = sqrt(dx**2 + dy**2)\n",
      "    brg = atan2(dy, dx)\n",
      "    \n",
      "    return np.array([rng, brg])\n",
      "    \n",
      "hx.radar_pos = np.array([0., 0.])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we used the ability of a function to own a variable to store the radar's position. However, we have a problem. We have two radar systems, not one, and FilterPy's UKF code does not have a way to provide it with multiple measurement functions. Instead, we have to define the measurement function to return all of the measurements at once. So, our second attempt, incorporating both radar systems at once, might look like the following."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def hx(x):\n",
      "    dx = x[0] - hx.radar1_pos[0]\n",
      "    dy = x[2] - hx.radar1_pos[1]\n",
      "    \n",
      "    rng1 = sqrt(dx**2 + dy**2)\n",
      "    brg1 = atan2(dy, dx)\n",
      "    \n",
      "    dx = x[0] - hx.radar2_pos[0]\n",
      "    dy = x[2] - hx.radar2_pos[1]\n",
      "    \n",
      "    rng2 = sqrt(dx**2 + dy**2)\n",
      "    brg2 = atan2(dy, dx)\n",
      "    return np.array([rng1, brg1, rng2, brg2])\n",
      "\n",
      "hx.radar1_pos = np.array([0., 0.])\n",
      "hx.radar2_pos = np.array([200., 0.])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I chose the ordering (range 1, bearing 1, range 2, bearing 2) for the return values somewhat arbitrarily. When we pass the measurements to the UKF they will have to be ordered the same way. If you use a different order for `hx` just change the ordering for the measurement.\n",
      "\n",
      "All that is left is to define the measurement error matrix $\\bf{R}$, the process noise matrix $\\bf{Q}$, and the covariance $\\bf{P}. These are always linear, so the process is the same as for the linear filter.\n",
      "\n",
      "The measurement function used the ordering (range 1, bearing 1, range 2, bearing 2), so $\\bf{R}$ will need to use the same order. The bearing $1\\sigma$ error is $0.5^\\circ$ and the range error is 0.1 km, so we have to set\n",
      "\n",
      "$$ \\mathbf{R} = \\begin{bmatrix}0.001745^2&0&0&0 \\\\\n",
      "0&0.1^2&0&0 \\\\\n",
      "0&0&0.001745^2&0 \\\\\n",
      "0&0&0&0.1^2\n",
      "\\end{bmatrix}$$\n",
      "\n",
      "The design of Q is the same as for the linear Kalman filter. We will not focus on it here, and just use the computation that FilterPy provides.\n",
      "\n",
      "So let's construct the filter. FilterPy's UKF is named `UnscentedKalmanFilter` and is in the `filterpy.kalman` module. Let's look at the help."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "help(UKF.__init__)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Help on function __init__ in module filterpy.kalman.UKF:\n",
        "\n",
        "__init__(self, dim_x, dim_z, dt, hx, fx, kappa=0.0)\n",
        "    Create a Kalman filter. You are responsible for setting the\n",
        "    various state variables to reasonable values; the defaults below will\n",
        "    not give you a functional filter.\n",
        "    \n",
        "    **Parameters**\n",
        "    \n",
        "    dim_x : int\n",
        "        Number of state variables for the filter. For example, if\n",
        "        you are tracking the position and velocity of an object in two\n",
        "        dimensions, dim_x would be 4.\n",
        "    \n",
        "    \n",
        "    dim_z : int\n",
        "        Number of of measurement inputs. For example, if the sensor\n",
        "        provides you with position in (x,y), dim_z would be 2.\n",
        "    \n",
        "    dt : float\n",
        "        Time between steps in seconds.\n",
        "    \n",
        "    hx : function(x)\n",
        "        Measurement function. Converts state vector x into a measurement\n",
        "        vector of shape (dim_z).\n",
        "    \n",
        "    fx : function(x,dt)\n",
        "        function that returns the state x transformed by the\n",
        "        state transistion function. dt is the time step in seconds.\n",
        "    \n",
        "    kappa : float, default=0.\n",
        "        Scaling factor that can reduce high order errors. kappa=0 gives\n",
        "        the standard unscented filter. According to [1], if you set\n",
        "        kappa to 3-dim_x for a Gaussian x you will minimize the fourth\n",
        "        order errors in x and P.\n",
        "    \n",
        "    **References**\n",
        "    \n",
        "    [1] S. Julier, J. Uhlmann, and H. Durrant-Whyte. \"A new method for\n",
        "        the nonlinear transformation of means and covariances in filters\n",
        "        and estimators,\" IEEE Transactions on Automatic Control, 45(3),\n",
        "        pp. 477-482 (March 2000).\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "With that we can construct our filter and initialize it. As with the linear Kalman filter $\\bf{x}$, $\\bf{P}$, $\\bf{Q}$, and $\\bf{R}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.common import Q_discrete_white_noise\n",
      "dt = 1.\n",
      "kf = UKF(dim_x=4, dim_z=4, dt=dt, hx=hx, fx=fx, kappa=0)\n",
      "\n",
      "# initialize position at (100,100) with a velocity of 100m/s\n",
      "kf.x = np.array([100, 0.1, 100, 0.1])\n",
      "\n",
      "range_var = 0.1**2\n",
      "bearing_var = math.radians(0.5)**2\n",
      "\n",
      "kf.R = np.diag([range_var, bearing_var, range_var, bearing_var])\n",
      "kf.P = np.eye(4)\n",
      "\n",
      "q = Q_discrete_white_noise(2, 0.02)\n",
      "kf.Q[0:2, 0:2] = q\n",
      "kf.Q[2:4, 2:4] = q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'math' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-30-42652386d07c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mrange_var\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m \u001b[0mbearing_var\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mradians\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[0mkf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mR\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mrange_var\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbearing_var\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrange_var\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbearing_var\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mNameError\u001b[0m: name 'math' is not defined"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We need to simulate the Radar stations and the movement of the aircraft. By now this should be second nature for you, so I will present the code without much discussion."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.linalg import norm\n",
      "\n",
      "class RadarStation(object):\n",
      "    \n",
      "    def __init__(self, pos, range_std, bearing_std):\n",
      "        self.pos = asarray(pos)\n",
      "        \n",
      "        self.range_std = range_std\n",
      "        self.bearing_std = bearing_std\n",
      "\n",
      "    \n",
      "    def reading_of(self, ac_pos):\n",
      "        \"\"\" Returns actual range and bearing to aircraft as tuple. \n",
      "        Bearing is in radians.\n",
      "        \"\"\"\n",
      "        \n",
      "        diff = np.subtract(self.pos, ac_pos)\n",
      "        rng = norm(diff)\n",
      "        brg = atan2(diff[1], diff[0])      \n",
      "        return rng, brg\n",
      "\n",
      "\n",
      "    def noisy_reading(self, ac_pos):\n",
      "        \"\"\" Compute range and bearing to aircraft with simulated noise\"\"\"\n",
      "        \n",
      "        rng, brg = self.reading_of(ac_pos)      \n",
      "        rng += randn() * self.range_std\n",
      "        brg += randn() * self.bearing_std \n",
      "        return rng, brg\n",
      "        \n",
      "   \n",
      "class ACSim(object):\n",
      "    \n",
      "    def __init__(self, pos, vel, vel_std):\n",
      "        self.pos = asarray(pos, dtype=float)\n",
      "        self.vel = asarray(vel, dtype=float)\n",
      "        self.vel_std = vel_std\n",
      "        \n",
      "        \n",
      "    def update(self):\n",
      "        \"\"\" compute next position. Incorporates random variation in\n",
      "        velocity. Returns new position.\"\"\"\n",
      "        \n",
      "        vel = self.vel + (randn() * self.vel_std)       \n",
      "        self.pos += vel\n",
      "        \n",
      "        return self.pos"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we just need to run the filter. As with the linear filter, we implement a loop where we collect the measurements and then call the predict and update functions of the filter.\n",
      "\n",
      "For ease in reading I'll repeat all of the code from above into the code block below.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import asarray\n",
      "from math import radians\n",
      "import book_plots as bp\n",
      "\n",
      "dt = 1.\n",
      "\n",
      "def hx(x):\n",
      "    r1, b1 = hx.R1.reading_of((x[0], x[2]))\n",
      "    r2, b2 = hx.R2.reading_of((x[0], x[2]))\n",
      "    \n",
      "    return array([r1, b1, r2, b2])\n",
      "    pass\n",
      "\n",
      "def fx(x, dt):\n",
      "    x_est = x.copy()\n",
      "    x_est[0] += x[1]*dt\n",
      "    x_est[2] += x[3]*dt\n",
      "    return x_est\n",
      "\n",
      "range_std = 0.1\n",
      "bearing_std = radians(0.5)\n",
      "\n",
      "f = UKF(dim_x=4, dim_z=4, dt=dt, hx=hx, fx=fx, kappa=1)\n",
      "aircraft = ACSim ((100,100), (0.1, 0.1), 0.0)\n",
      "\n",
      "R1 = RadarStation ((0,0), range_std, bearing_std)\n",
      "R2 = RadarStation ((200,0), range_std, bearing_std)\n",
      "\n",
      "hx.R1 = R1\n",
      "hx.R2 = R2\n",
      "\n",
      "f.x = array([100, 0.1, 100, 0.1])\n",
      "kf.R = np.diag([range_std**2, bearing_std**2, \n",
      "                range_std**2, bearing_std**2])\n",
      "kf.P = np.eye(4)*1000\n",
      "\n",
      "q = Q_discrete_white_noise(2, 0.2)\n",
      "kf.Q[0:2, 0:2] = q\n",
      "kf.Q[2:4, 2:4] = q\n",
      "\n",
      "xs = []\n",
      "track = []\n",
      "ps = []\n",
      "\n",
      "for i in range(int(60/dt)):   \n",
      "    pos = aircraft.update()\n",
      "    \n",
      "    r1, b1 = R1.noisy_reading(pos)\n",
      "    r2, b2, = R2.noisy_reading(pos)\n",
      "    \n",
      "    z = np.array([r1, b1, r2, b2])\n",
      "    track.append(pos.copy())\n",
      "\n",
      "    f.predict()\n",
      "    f.update(z)\n",
      "    xs.append(f.x)\n",
      "    ps.append(f.P.diagonal())\n",
      "\n",
      "xs = asarray(xs)\n",
      "track = asarray(track)\n",
      "\n",
      "time = np.arange(0,len(xs)*dt, dt)\n",
      "\n",
      "plt.figure()\n",
      "bp.plot_filter(time, xs[:,0], label='UKF', lw=3)\n",
      "bp.plot_track(time, track[:,0])\n",
      "plt.legend(loc=4)\n",
      "plt.xlabel('time (sec)')\n",
      "plt.ylabel('x (m)')\n",
      "\n",
      "plt.figure()\n",
      "bp.plot_filter(time, xs[:,2], label='UKF')\n",
      "bp.plot_track(time, track[:,1])\n",
      "plt.legend(loc=4)\n",
      "plt.xlabel('time (sec)')\n",
      "plt.ylabel('y (m)')\n",
      "plt.show()\n",
      "\n",
      "plt.figure()\n",
      "\n",
      "plt.subplot(211)\n",
      "bp.plot_filter(time, xs[:,1], lw=2)\n",
      "plt.title('velocity')\n",
      "plt.legend(loc=4)\n",
      "plt.xlabel('time (sec)')\n",
      "plt.ylabel(\"x' km/sec\")\n",
      "\n",
      "plt.subplot(212)\n",
      "plt.title('velocity')\n",
      "bp.plot_filter(time, xs[:,3], lw=2)\n",
      "plt.ylabel(\"y' km/s\")\n",
      "plt.legend(loc=4)\n",
      "plt.xlabel('time (sec)')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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k06kAeHp68vLLL/Pqq6/i6+tbYnMUKa0UckRERERus6ycDGb98A6Z2WkAuDl7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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff67ca77828>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EXMJm4hI2A+BXpxGhDVvRrEFrgvyal9kdrdhSzCcrpnIi7WiZz+jQojd3tHuw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\nEREREZFZYZFDRERERERm5V/noG7wTkDXqAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff67e9b4f98>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sMHfTBCNKL0jUfXnEpp8yc2tuUalVxGeepaii5Te1d3I2eR+VNWV4OvrTx3dY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WVHuKwCKuu95/fHhRsIKstli/fz8eDhw3M/53M+5x6497zP5/N5f0SrCg4O5s0332TlypU88sgj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       "text": [
        "<matplotlib.figure.Figure at 0x7ff67ce045c0>"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Sigma Point Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As I already said there are several published algorithms for choosing the sigma points. I will present the method first chosen by the inventors of the UKF. \n",
      "\n",
      "Our first sigma point is always going to be the mean of our input. We will call this $\\mathcal{X}_0$. So,\n",
      "\n",
      "$$ \\mathcal{X}_0 = \\mu$$\n",
      "\n",
      "Tne corresponding weight for this sigma point is\n",
      "$$\n",
      "W_0 = \\frac{\\kappa}{n+\\kappa}\n",
      "$$\n",
      "where $n$ is the dimension of the problem, and $\\kappa$ is a scaling factor that will be discussed in a moment.\n",
      "\n",
      "The rest of the sigma points are defined to be\n",
      "\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "\\mathcal{X}_i &= \\mu + (\\sqrt{(n+\\kappa)\\Sigma})_i\\,\\,\\,\\, &\\text{for}\\text{ i=1 .. n} \\\\\n",
      "\\mathcal{X}_i &= \\mu - (\\sqrt{(n+\\kappa)\\Sigma})_{i-n}\\,\\,\\,\\,\\, &\\text{for}\\text{ i=(n+1) .. 2n} \\\\\n",
      "\\text{and the corresponding weights are} \\\\\n",
      "W_i &= \\frac{1}{2(n+\\kappa)}\\,\\,\\,\\text{for i=1,2..2n}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "$\\kappa$ (kappa) is a scaling factor that controls how far away from the mean we want the points to be. A larger kappa will choose points further away from the mean, and a smaller kappa will choose points nearer the mean. Julier and Uhlmann suggest using $\\kappa + n = 3$ if the distribution is Gaussian, and perhaps choosing a different value if it is not Gaussian. \n",
      "\n",
      "It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to 1 standard deviation. However, there is an $n$ term in there - the more dimensions there are the more the points will be spread out and weighed less."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Unscented Transform"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The unscented transform is the core of the algorithm yet it is remarkably simple. Given a set of sigma points and a transfer function we need to compute the new mean and covariance of the points after they have passed through the function. In other words, loop through the sigma points and compute their new position after passing through your nonlinear function. Then just compute the mean and covariance of these points.\n",
      "\n",
      "In other words, we just compute the mean and covariance from the equations above:\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mu &= \\sum_i w_i\\mathcal{X}_i\\;\\;\\;&(2) \\\\\n",
      "\\Sigma &= \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\\;\\;\\;&(3)\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Unscented Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can present the entire Unscented Kalman filter algorithm. Assume that there is a function $f(x)$ that performs the state transition for our filer - it predicts the next state given the current state. Also assume there is a measurement function $h(x)$  - it takes the current state and computes what measurement that state corresponds to. These are just nonlinear forms of the $\\mathbf{F}$ and $\\mathbf{H}$ matrices used by the linear Kalman filter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Predict Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For the predict step, we will generate the weights and sigma points as specified above.\n",
      "$$\\begin{aligned}\n",
      "\\mathcal{X} &= sigma\\_function(\\mu, \\Sigma) \\\\\n",
      "W &= weight\\_function(n, \\kappa)\\end{aligned}$$\n",
      "\n",
      "We pass each sigma point through the function f.\n",
      "\n",
      "$$\\mathcal{X_f} = f(\\mathcal{X})$$\n",
      "\n",
      "Then we compute the predicted mean and covariance using the unscented transform. I've dropped the subscript $i$ for readability, and switched to the roman letters x and P for the mean and covariance.\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{x}^- &= \\sum W\\mathcal{X_f} \\\\\n",
      "\\mathbf{P}^- &= \\sum W{(\\mathcal{X_f}-x^-)(\\mathcal{X_f}-x^-)^\\mathsf{T}} + \\mathbf{Q}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This corresponds with the linear Kalman filter equations of\n",
      "$$ \\begin{aligned}\n",
      "\\mathbf{x}^- &= \\mathbf{Fx}\\\\\n",
      "\\mathbf{P}^- &= \\mathbf{FPF}^T+\\mathbf{Q}\n",
      "\\end{aligned}$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Update Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can perform the update step of the filter. Recall that Kalman filters perform the update state in measurement space. So, the first thing we do is convert the sigma points into measurements using the $h(x)$ function.\n",
      "\n",
      "\n",
      "$$\\mathcal{X_z} = h(\\mathcal{X})$$\n",
      "\n",
      "Now we can compute the mean and covariance of these points using the unscented transform.\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{x}_z &= \\sum w\\mathcal{X_z} \\\\\n",
      "\\mathbf{P}_z &= \\sum w{(\\mathcal{X_z}-x)(\\mathcal{X_z}-x)^\\mathsf{T}} + \\mathbf{R}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The $z$ subscript denotes that these are the mean and covariance for the measurements.\n",
      "\n",
      "All that is left is to compute the residual and Kalman gain. \n",
      "\n",
      "The residual is trivial to compute:\n",
      "\n",
      "$$ \\mathbf{y} = \\mathbf{z} - \\mathbf{x}_z$$\n",
      "\n",
      "\n",
      "The Kalman gain is not much worse. We have to compute the cross variance of the state and the measurements, which we state without proof to be: \n",
      "\n",
      "$$\\mathbf{P}_{xz} =\\sum W(\\mathcal{X}-x)(\\mathcal{X_z}-\\mathbf{x}_z)^\\mathsf{T}$$\n",
      "\n",
      "And then the Kalman gain is defined as\n",
      "$$K = \\mathbf{P}_{xz} \\mathbf{P}_z^{-1}$$\n",
      "\n",
      "Finally, we compute the new state estimate using the residual and Kalman gain:\n",
      "\n",
      "$$\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n",
      "\n",
      "and the new covariance is computed as:\n",
      "\n",
      "$$ \\mathbf{P} = \\mathbf{P}^- - \\mathbf{PKP}_z\\mathbf{K}^\\mathsf{T}$$\n",
      "\n",
      "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. We convert the mean and covariance into measurement space, add the measurement error into the measurement covariance, compute the residual and kalman gain, compute the new state estimate as the old estimate plus the residual times the Kalman gain, and then convert both back into state space. The linear algrebra is slightly different from the linear Kalman filter, but the algorithm is the same."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using the UKF"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We are now ready to consider implementing a Kalman filter. All of the math is above is already implemented in FilterPy, and you are perhaps a bit lost at this point, so lets just launch into solving some problems so you can gain confidence in how each the UKF actually is. Later we will revisit how the UKF is implemented in Python.\n",
      "\n",
      "Let's solve the 'bearing only' target tracking problem. Here the idea is that we have a ship or other platform tracking a moving target. Our sensor only provides the bearing to the target relative to the ship.\n",
      "\n",
      "This is a nonlinear problem because the conversion between a target position and the bearing is:\n",
      "\n",
      "$$\\theta = \\tan^{-1}\\frac{y_{ship} - y_{target}}{x_{ship} - x_{target}}$$\n",
      "\n",
      "If we were solving this problem using and EKF we would need to compute the Jacobian of this transform to linearize the filter. With the UKF we do not have to do this - we will see how this works as we work the example."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Define State"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, lets define our filter state. Let's assume a constant velocity model for the target, so a reasonable state would be\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x} \\\\ y \\\\ \\dot{y}\\end{bmatrix}$$\n",
      "\n",
      "\n",
      "where $x$ and $y$ are the position of the target, and $\\dot{x}$ and $\\dot{y}$ are its velocity. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Define State Transition"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to tell the filter how to perform the state transition - how to predict the next position from the current position. In the linear Kalman filter this is the equation $\\mathbf{x}^- = \\mathbf{Fx}$ but the unscented Kalman filter is intended for nonlinear problems. We cannot implement nonlinear behavior using linear algebra, so instead of providing the filter with a matrix we need to provide the filter with a function that computes the transition.\n",
      "\n",
      "As it turns out our state transition is linear. We model the target movement using the standard Newtonian equation\n",
      "$$x_k = x_{k-1} + \\dot{x}\\Delta t$$\n",
      "\n",
      "However, the UKF code in FilterPy does not differentiate between linear and nonlinear versions, so we will need to write a Python function to perform this computation. The signature of the function required by `filterpy.UnscentedKalmanFilter` is\n",
      "\n",
      "    def fx(x, dt):\n",
      "       return x\n",
      "       \n",
      "The filter implements the state as a one dimensional array, so our function can be implemented as"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fx(x,dt):\n",
      "    # pos = pos + vel\n",
      "    # vel = vel\n",
      "    x[0] += x[1]\n",
      "    x[2] += x[3]\n",
      "    return x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> FilterPy's KF and EKF code uses a 2D array to store the state. Due to implementation details the UKF uses a 1D array. I am not enamored of this inconistency, but for now this is how it is."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Define the Measurement Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we define our measurement function. In the linear KF this is implemented with the $\\mathbf{H}$ matrix, but because the UKF is nonlinear we need to provide a function. We have already given the computation of the bearing from position as\n",
      "\n",
      "$$\\theta = \\tan^{-1}\\frac{y_{ship} - y_{target}}{x_{ship} - x_{target}}$$\n",
      "\n",
      "so all we have to do is compute that in a function. The signature of this function is required to be\n",
      "\n",
      "    def hx(x):\n",
      "       return measurement\n",
      "       \n",
      "The filter state does not includes the ship's position, so we will assume a global variable `ship_pos` is defined that specifies the (x,y) coordinate for the ship."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "def hx(x):\n",
      "    \"\"\" measurement function - convert position to bearing\"\"\"\n",
      "    return math.atan2(ship_pos[1] - x[2], ship_pos[0] - x[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And those two functions are the crux of the problem. All that remains is defining the noise in the system, and running the filter.\n",
      "\n",
      "**Important Note**: There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Design Noise Parameters"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have spent a lot of time designing the $\\mathbf{R}$, $\\mathbf{Q}$, and $\\mathbf{P}$ matrices in past chapters, and nothing changes for the UKF filter, so I will just choose some arbitrary values without much discussion. Let's assume the standard deviation in the bearing measurement is $\\sigma=1^\\circ$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implement the Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So let's implement a filter given the design above. I'll just present the code; it should look very similar to the linear KF to you. The main difference is how we construct the filter:\n",
      "\n",
      "    f = UKF(dim_x=4, dim_z=1, dt=dt, fx=fx, hx=hx, kappa=0.)\n",
      "    \n",
      "When you construct the filter you have to provide the state transition function, the measurement function, and the value for $\\kappa$ along with the usual dimension and time step values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "\n",
      "\n",
      "def fx(x,dt):\n",
      "    # pos = pos + vel\n",
      "    # vel = vel\n",
      "    x[0] += x[1]\n",
      "    x[2] += x[3]\n",
      "    return x\n",
      "\n",
      "def bearing(ship_pos, target_pos):\n",
      "    return math.atan2(target_pos[1]- ship_pos[1], target_pos[0] - ship_pos[0])\n",
      "\n",
      "def hx(x):\n",
      "    \"\"\" measurement function - convert position to bearing\"\"\"\n",
      "    return math.atan2(x[2] - ship_pos[1], x[0] - ship_pos[0])\n",
      "\n",
      "\n",
      "dt = 0.1\n",
      "ship_pos = [-40,20]\n",
      "target_pos = [0,0]\n",
      "\n",
      "std_noise = math.radians(1)\n",
      "\n",
      "f = UKF(4, 1, dt, fx=fx, hx=hx, kappa=0.)\n",
      "f.x = np.array([target_pos[0], 0., target_pos[1], 0.])\n",
      "Q = Q_discrete_white_noise(2, dt, .01)\n",
      "f.Q[0:2,0:2] = Q\n",
      "f.Q[2:4, 2:4] = Q\n",
      "\n",
      "f.R *= std_noise**2\n",
      "f.P *= 100\n",
      "\n",
      "N = 300\n",
      "xs = []\n",
      "for i in range(N):\n",
      "    target_pos[0] += 1 + randn()*0.0001 # add some process noise\n",
      "    angle = bearing(ship_pos, target_pos) + randn()*std_noise\n",
      "\n",
      "    f.predict()\n",
      "    f.update(angle)\n",
      "    xs.append(f.x)\n",
      "\n",
      "xs = np.asarray(xs)\n",
      "plt.plot([i/10 for i in range(N)], xs[:,0])\n",
      "plt.xlabel('time')\n",
      "plt.ylabel('target X position')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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B0xHqO4ErpbUjhhwiIiIiosdUV1+LorLbuCW7gaOpe1FWebdRjavDAMyM/CPsbVz00GH3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\n2c+aeCAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f07904d75f8>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we look at only the target's estimated position in x, the results look very good. After running for several seconds the filter appears to settle down and produce a reasonably linear output for the target's position. However, let's look at the 2D plot of position. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "book_format.equal_axis()\n",
      "\n",
      "plt.xlabel('target X position')\n",
      "plt.ylabel('target Y position')\n",
      "plt.plot(xs[:,0], xs[:,2])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6jR8/Xvfff79v9Yt9+/Zp4cKFWr9+vVauXNntb3ntj0B2cmt7iz7bt1Ebtq/U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\nAFgQlgEAAAALwjIAAABg8f8AvvZGJj5e05cAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d429a20>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we can see the actual performance is abysmal. This is not an indictment of the UKF, but of the difficulty of the problem we are trying to solve. There are an infinite number of solutions for each measurement. For example, if our ship is at (0, 20), a bearing reading of 0 could reflect a target position of (0, 20) or (100, 20), or (1e300, 20). The Kalman filtering literature has many treatments of this problem; a common solution is to have the ship perform manuevers while tracking. This allows the filter to reduce the range of possibilities to something managable. This is rather outside the scope of this book so I will leave it to you to search the literature if you are interested in this specific problem.\n",
      "\n",
      "Instead, I will make the problem tractable by introducing a second sensor. The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. In the chart the width of the circle is intended to denote a different amount of sensor noise."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "circle1=plt.Circle((-4,0),5,color='#004080',fill=False,linewidth=20, alpha=.7)\n",
      "circle2=plt.Circle((4,0),5,color='#E24A33', fill=False, linewidth=5, alpha=.7)\n",
      "\n",
      "fig = plt.gcf()\n",
      "ax = fig.gca()\n",
      "\n",
      "plt.axis('equal')\n",
      "plt.xlim((-10,10))\n",
      "plt.ylim((-10,10))\n",
      "\n",
      "plt.plot ([-4,0], [0,3], c='#004080')\n",
      "plt.plot ([4,0], [0,3], c='#E24A33')\n",
      "plt.text(-4, -.5, \"A\", fontsize=16, horizontalalignment='center')\n",
      "plt.text(4, -.5, \"B\", fontsize=16, horizontalalignment='center')\n",
      "\n",
      "ax.add_artist(circle1)\n",
      "ax.add_artist(circle2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ia+5gZH3x23DOmKv5eLSpAU1P/wzBYwcNjoy6w8QzDl243IK/+Z/3UFVn/B6d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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0776b99278>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can compute the bearing between a sensor and the target as follows:\n",
      "\n",
      "    def bearing(sensor, target):\n",
      "        return math.atan2(target[1] - sensor[1], target[0] - sensor[0])"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So our filter will need to receive a vector of 2 measurements during each update, one for each sensor. We can implement that as:\n",
      "\n",
      "    def measurement(A_pos, B_pos, pos):\n",
      "        angle_a = bearing(A_pos, pos)\n",
      "        angle_b = bearing(B_pos, pos)\n",
      "        return [angle_a, angle_b]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The design of the measurement function and state transition function can remain the same as nothing has changed that would affect them. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "\n",
      "\n",
      "def bearing(sensor, target_pos):\n",
      "    return math.atan2(target_pos[1] - sensor[1], target_pos[0] - sensor[0])\n",
      "\n",
      "\n",
      "def measurement(A_pos, B_pos, pos):\n",
      "    angle_a = bearing(A_pos, pos)\n",
      "    angle_b = bearing(B_pos, pos)\n",
      "    return [angle_a, angle_b]\n",
      "\n",
      "\n",
      "def fx(x,dt):\n",
      "    x[0] += x[1]\n",
      "    x[2] += x[3]\n",
      "    return x\n",
      "\n",
      "\n",
      "def hx(x):\n",
      "    # measurement to A\n",
      "    pos = (x[0], x[2])\n",
      "    return measurement(sa_pos, sb_pos, pos)\n",
      "\n",
      "\n",
      "def moving_target_filter(std_noise):\n",
      "    dt = 0.1\n",
      "    f = UKF(dim_x=4, dim_z=2, dt=dt, hx=hx, fx=fx, kappa=2.)\n",
      "    f.x = np.array([target_pos[0], 1., target_pos[1], 1.])\n",
      "\n",
      "    Q = Q_discrete_white_noise(2, dt, 1.1)\n",
      "    f.Q[0:2,0:2] = Q\n",
      "    f.Q[2:4, 2:4] = Q\n",
      "\n",
      "    f.R *= std_noise**2\n",
      "    f.P *= 1000\n",
      "    \n",
      "    return f\n",
      "\n",
      "\n",
      "def plot_straight_line_target(f, std_noise):\n",
      "    xs = []\n",
      "    txs = []\n",
      "\n",
      "    for i in range(300):\n",
      "        target_pos[0] += 1 + randn()*0.0001\n",
      "        target_pos[1] += 1 + randn()*0.0001\n",
      "        txs.append((target_pos[0], target_pos[1]))\n",
      "\n",
      "        z = measurement(sa_pos, sb_pos, target_pos)\n",
      "        z[0] += randn() * std_noise\n",
      "        z[1] += randn() * std_noise\n",
      "\n",
      "        f.predict()\n",
      "        f.update(z)\n",
      "        xs.append(f.x)\n",
      "\n",
      "    xs = np.asarray(xs)\n",
      "    txs = np.asarray(txs)\n",
      "\n",
      "    plt.plot(xs[:,0], xs[:,2])\n",
      "    plt.plot(txs[:,0], txs[:,1])\n",
      "    plt.show()\n",
      "   \n",
      "    \n",
      "np.random.seed(123)\n",
      "\n",
      "sa_pos = [-40, 0]\n",
      "sb_pos = [40, 0]\n",
      "target_pos = [40, 20]\n",
      "\n",
      "std_noise = math.radians(1.)\n",
      "f = moving_target_filter(std_noise)\n",
      "plot_straight_line_target(f, std_noise)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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evXqKj48npAIAYGdXsi8rZvtird2xSHuONtSKja/KZnM39fRoHa+RzwTK2zNK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\nBQAAgMf5fyAXJ++LrhXEAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0772610cc0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This looks quite good to me. There is a very large error at the beginning of the track, but the filter is able to settle down and start producing good data.\n",
      "\n",
      "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors with the same y-coordinate. This will cause a nonlinearity in the computation of the sigma means and the residuals."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(12330)\n",
      "target_pos = [0, 0]\n",
      "f = moving_target_filter(std_noise)\n",
      "plot_straight_line_target(f, std_noise)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rNCjcy5MB1RfFGACAasRluLR171qt2pqqmyU3THmL+2I1IuEJPRDTzoLpgOqN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\nAAZjIiIiIiIAwP8DJWrbJF/ZX4YAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d42f7b8>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we seed the random number generator just right we can get the filter to eventually lock onto the signal and converge to a solution, but of course this is untenable behavior for a real world filter. I will deal with this nonlinearity later; I bring it up now in case you are experimenting with the code above and you start to see this sort of behavior."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Track a target moving in a circle"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Change the simulated target movement to move in a circle. Avoid angular nonlinearities by putting the sensors well outside the movement range of the target, and avoid the angles $0^\\circ$ and $180^\\circ$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your solution here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have a few choices here. First, if we know the movement of the target we can design our filter's state transition function so that it correctly predicts the circular movement. For example, suppose we were tracking a boat race optically - we would want to take track shape into account with our filter. However, in this chapter we have not been talking about such constrained behavior, so I will not build knowledge of the movement into the filter. So my implementation looks like this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_circular_target(f, std_noise, target_pos):\n",
      "    xs = []\n",
      "    txs = []\n",
      "    radius = 100\n",
      "    for i in range(300):\n",
      "        target_pos[0] = math.cos(i/10)*radius + randn()*0.0001\n",
      "        target_pos[1] = math.sin(i/10)*radius + randn()*0.0001\n",
      "        txs.append((target_pos[0], target_pos[1]))\n",
      "\n",
      "        z = measurement(sa_pos, sb_pos, target_pos)\n",
      "        z[0] += randn() * std_noise\n",
      "        z[1] += randn() * std_noise\n",
      "\n",
      "        f.predict()\n",
      "        f.update(z)\n",
      "        xs.append(f.x)\n",
      "\n",
      "    xs = np.asarray(xs)\n",
      "    txs = np.asarray(txs)\n",
      "\n",
      "    plt.plot(xs[:,0], xs[:,2])\n",
      "    plt.plot(txs[:,0], txs[:,1], linestyle='-.')\n",
      "    plt.axis('equal')\n",
      "    plt.show()\n",
      "\n",
      "sa_pos = [-240, 200]\n",
      "sb_pos = [240, 200]\n",
      "\n",
      "np.random.seed(12283)\n",
      "std_noise = math.radians(0.5)\n",
      "target_pos = [0, 0]\n",
      "f = moving_target_filter(std_noise)\n",
      "plot_circular_target(f, std_noise, target_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/FlyctYvjvD2gpLz+xw3sqo34nnpeW4fCc7fC9YMh0M++n6dzn6MTpfnMXfUF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\nB+5/ffh8Ply5cgUulwupVAqnTp1CbW0t+vv7tTx+l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       "text": [
        "<matplotlib.figure.Figure at 0x7f0776b682b0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Discussion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The filter tracks the movement of the target, but never really converges on the track.  This is because the filter is modeling a constant velocity target, but the target is anything but constant velocity. As mentioned above we could model the circular behavior by defining the `fx()` function, but then we would have problems when the target is not moving in a circle. Instead, let's tell the filter we are fare less sure about our process model by making $\\mathbf{Q}$ much larger."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def circular_target_filter(std_noise):\n",
      "    f = UKF(dim_x=4, dim_z=2, dt=0.1, hx=hx, fx=fx, kappa=2.)\n",
      "    f.x = np.array([target_pos[0], 1., target_pos[1], 1.])\n",
      "\n",
      "    Q = Q_discrete_white_noise(2, dt, 10.1)\n",
      "    f.Q[0:2,0:2] = Q\n",
      "    f.Q[2:4, 2:4] = Q\n",
      "\n",
      "    f.R *= std_noise**2\n",
      "    f.P *= 1000\n",
      "    \n",
      "    return f\n",
      "\n",
      "std_noise = math.radians(0.5)\n",
      "cf = circular_target_filter(std_noise)\n",
      "target_pos = [0, 0]\n",
      "plot_circular_target(cf, std_noise, target_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fn2PPYduBW+v5BnHLiH+wftcyfl/3Y5WPH+AbzDWX3E67Zt0xDIONu6HTxNLt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\nC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DMHCrcdiN+Br0cQHs4+7D+xvVrnX7F5PokpCYwf/Dg21rYllrmpl0bBesWdL8GJRH1l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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d385470>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The convergence is not perfect, but it is far better. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Sensor Position Effects"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Is the behavior of the filter invariant for any sensor position? Find a sensor position that produces bad filter behavior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your answer here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have already discussed the problem of angles being modal, so causing that problem by putting the sensors at `y=0` would be a trivial solution. However, let's be more subtle than that. We want to create a situation where there are an infinite number of solutions for the sensor readings. We can achieve that whenever the target lies on the straight line between the two sensors. In that case there is no triangulation possible and there is no unique solution. My solution is as follows."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "std_noise = math.radians(0.5)\n",
      "sa_pos = [-200,200]\n",
      "sb_pos = [200,-200]\n",
      "plt.scatter(*sa_pos, s=200)\n",
      "plt.scatter(*sb_pos, s=200)\n",
      "cf = circular_target_filter(std_noise)\n",
      "target_pos = [0, 0]\n",
      "plot_circular_target(cf, std_noise, target_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2FJ7uc26gMCtJdY4kWa3OZr9+dW26JGnrnlPkdsdp2forvfq75q5QSVmBstO3ani/95Sb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\nfdqmnOW9+Wyh7xNyARxj+17fttF9KwK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PZegTERdwkxiAQyPQAjhqyX2P09XTfhtQntR3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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d325d30>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I put the sensors at the upper left hand side and lower right hand side of the target's movement. We can see how the filter diverges when the target enters the region directly between the two sensors. The state transition always predicts that the target is moving in a straight line. When the target is between the two sensors this straight line movement is well described the bearing measurements from the two sensors so the filter estimate starts to approximate a straight line. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Compute Position Errors"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The position errors of the filter vary depending on how far away the target is from a sensor. Write a function that computes the distance error due to a bearing error. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your solution here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Basic trigonometry gives us this answer."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def distance_error(target_distance, angle_error):\n",
      "    x = 1-math.cos(angle_error)\n",
      "    y = math.sin(angle_error)\n",
      "    return target_distance*(x**2 + y**2)**.5\n",
      "\n",
      "d = distance_error(100, math.radians(1.))\n",
      "print('\\n\\nError of 1 degree at 100km is {:.3}km'.format(d))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Error of 1 degree at 100km is 1.75km\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Discussion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is an inherent physical limitation that is extremely difficult to deal with when designing filters. We can see that a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. For example, here is a scatter plot that shows the error distibution for a $1^\\circ$ standard deviation in bearing for a $30^\\circ$ bearing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = 100\n",
      "xs = []\n",
      "ys = []\n",
      "\n",
      "for i in range (3000):\n",
      "    a = math.radians(30) + randn() * math.radians(1)\n",
      "    \n",
      "    xs.append(d*math.cos(a))\n",
      "    ys.append(d*math.sin(a))\n",
      "    \n",
      "plt.scatter(xs, ys)\n",
      "plt.show() "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KzGEfJAKQuzwej773vahKSoKy2aQdOwzddps3PVZpyhSfFi0K6rPPgho61Cen\n05nligEAhYJOJ5Bn3G63zjnHLdO01LNny+0vdXVONTUZ2rQpxBB5AEC7IXQCecjlcumUU7wqK7M0\nb95Xy+3TpkW1dKlDH39s6LPPDG3cGFY0Gs12uQCAAkDoBPKUy+XSCScUa+jQJi1aFFR1dUwLFzo1\nfXpUS5Y4tWOHoYYGQ2vWRBQOh7NdLgAgz7GnE8hjhmGorMxUUVGDXK64Bgxo0u9+59RVV8X1u985\nNWVKVKZpaM2amE4+OaHi4uJslwwAyFN0OoECYJqmBg2yVF5uafz4VOD893+P6447vHr6aaf27jW0\nerWlYDCY7VIBAHmK0AkUCNM0VVVlqW9fS5MmRTVzplsTJ8ZVW+vStdf6tWePXe+/n9C+ffuyXSoA\nIA8ROoECcqDj2bmzNGZMQnPmuNO3F02e7NOSJW4tW2bn9iIAQJsjdAIFxjRNnXqqpZEj4y2eNTba\ndPPNXr3zjsGpdgBAmyJ0AgXINE2dc45NCxY0H6f05z+nhsV/8omht96KqbGxMcuVAgDyBafXgQJV\nVFSksWMjevzxRkWjNt16q1cul/TAA2H97ndOjR8fV2OjpWHDuK8dAHD0CJ1AAfN4PBo+3Kb16yOa\nPz+srVuN9Eile+91a8yYhOz2uIYMIXgCAI4Oy+tAgXO73aqs9CmRkE44ITVS6d57Uyfbly51aNky\np1atMrRjR4Msq+W1mgAAtAahE4CcTqdGjvTr+OOTKiuzNGZMQgsXOtMjlSZM8GvVKrtWrdqvRCKR\n7XIBAB0Qy+sAJKVuLzr++E7q3LlBdnvqZPuBkUqSNGWKT0uWBPXee0FVVnrkdruzWS4AoIOh0wmg\nGdM0NWSIpdGjW45Uqq+Xtm+3a9WqqCKRSBaqAwB0VIROAC0cCJ7z5n01Umnu3LAee8ylPXtsikZt\nev11gicAoPUInQAOyjRNjRzZpCVLgvrNb4J64gmHvv/9hB580K21aw15vYbeeSem/fv3Z7tUAEAH\nQOgE8I1Stxcl1dRk08UXJ3TvvW7V1ERUXi6NH+/XZZcV6YUXDK7NBAAcEqETwLfq1KmTRo82dOKJ\nTRozJqEuXZKaOtWbvrN96lSv1q+30fEEAHwrTq8DOCSfz6dBg4JqbIzLcZCvGpZl07p1SZ18MkPk\nAQAHR6cTQKv4/X6de64hj8fSnDnh9AGjOXPC+vLLpDZutOvtt20stQMADopOJ4BW8/v9GjQoqP37\nmzRrVlgc1cUQAAAgAElEQVSSVFRkqabGJ0n6xS8ieuutpM46i44nAKA5Op0ADovf79cFFzjVt6+l\nXr0s1dR4tXu3oYkT47rpJp+uusqv5cvtdDwBAM0QOgEcNq/Xq+HD3fL5ktq719C4cfH07UWBgKEp\nU3xau9bQzp3c1w4ASCF0AjgiLpdLZ57p0bx5IRUVJVs8f/ppp958064NG/YrHm95uxEAoLCwpxPA\nEXO5XLr0UptOOCGk4cMTmjw5tbdz2rSoHnnEKbc7qWOPTerdd0M65RSnfD5flisGAGQLnU4AR8Xp\ndOq000x997tNevLJoKqrY3rkEacmT47p6aedeuEFh/bsMbRqVULBYDDb5QIAsoTQCaBNpG4vsjRs\nWEKXXJLQf/yHS9dfH9OiRW5dc41f69Y59Ne/WopGo9kuFQCQBSyvA2gzqfvaG3Tssak9nr/8pUeB\nQOpn29mzPaqujqlbt6gqKy15vd5slgoAaGd0OgG0KdM0VVlpadSogx8eCoVsevvtuBobG9u5MgBA\nNtHpBNDmTNNUVVWD5s8PpQ8X1dRE1KOHpZdecigctmnfvrguuCDE4SIAKBCETgAZYZqmLrpov/70\np0Zt3GiXy5XUP/5h02OPuVVSYumCC+JasyahgQO5vQgACgHL6wAypri4WKef7lDnzknFYjb9/Ode\nxWLSxIlxXXedX+PGFamuzsHtRQBQAAidADLK5/Np1CjphBOaJKnF7UU33+zV2rWG9u3bl+VKAQCZ\nROgEkHFFRUUaPNimBQu++fail14y6HgCQB4jdAJoF8XFxRo5MqlLL41q3ryQSkstlZZamjYtqtdf\nt6u+3qa1awmeAJCvOEgEoN0UFxfrrLPC2rIlpiefDOrpp52qrXVo6tSYbr89NbfzoYfCGj68QYZh\nyLKsLFcMAGgrdDoBtCuv16uKCp+6dbN09tkJ3XBDKnB+fY/nJ58Y8vv7yOHg52IAyBd8RQfQ7pxO\np044wa9gMKguXVr+7Lt5s6GdOw116dJbiUSC8AkAeYBOJ4CscDgcqqz0KZm09NBD4fQezwceCGv2\nbLduucWr7dsdevvtkBKJRLbLBQAcJdoHALLG6XTqnHP82ro1qCVLgtq82dDMmW59/LFDpaWp/ZzR\nqE1vvhlSVZVXTqczyxUDAI4UoRNAVjkcDvXrZ6pbtwZ9/rmhYNBQaamlOXPC+s53Evr0U4ficamh\nIaKRIy253e5slwwAOAKETgA5wTRNjRrVoD/9qVHxuE02m6XPPnOopiZ1qn3evJDefz+iAQOauK8d\nADog9nQCyBmmaaqy0qb6eptiMUO33vrVqfYpU3x64gm3XnjBUjAYzHapAIDDROgEkFOKi4s1YkST\nPJ6WNxc1Nto0ZYpPa9Y0MUQeADoYQieAnGOapnr12tvi5qJ33zU0a1ZYoZBNb70lgicAdCCETgA5\naffu3RoyZI9+97ugHn44pLo6u265JaYHH3Rr6VKnEglD69cTPAGgoyB0AshZu3bt0llnWSora9KM\nGVHdc49bEyfGVVvr0rXX+hUI2PXBBzaCJwB0AIROADnNNE2deqpDNltSY8YkNGeOO3246Kc/9WjD\nBrtWrDAIngCQ4widAHKe3+9XZaU0cmQ8/b4uXSzdcENMM2Z4de21fr38sp3gCQA5jNAJoEPo1KmT\nhg2ztGBB6nDRhAkxzZ7tSXc9J03yaf16ltoBIFcROgF0GKZp6rvftfSnPzVq7Nh4i+cbN9pVV+cg\neAJADiJ0AuhQOnXqpMGDXXI6Ld1/fzg9UqmmJqLPP7dp3z5p3Tr2eAJAruEaTAAdjsfj0ZAh0t69\ncVVXxyRJJSWWjjnGpmnTUtdmPvRQWMOHN6h792IZBj9fA0C2EToBdEgej0ejR9vUtWtUDQ027dpl\naNq01LWZknTzzV49/nhQlrVfZWUETwDINkIngA7L7XarqsqpnTv3q6io5fPt2w05ndKXXzbqlFN8\ncjj4kgcA2cKP/gA6NMMwVF5uqrLS0kMPfbXHc86csCwrqfHj/Ro7tkjPPRdRMBjMdrkAULD4sR9A\nXjBNU6NGNejxx4P65BNDW7fatGDBV8vtP/6xT0uWNKqyskGmaWa5WgAoPHQ6AeQN0zQ1eLCl/v0t\nnXdeU4vnoZBN27ZxXzsAZAOhE0BeSV2bacluT+rhh0Pp5fZp06KaOjXV+Xz/fYInALQ3ltcB5B3T\nNDVwYIMsy1J1dUyNjTbdd59bLpf02msO9e5tKRi0VFXFUjsAtBc6nQDykmmaOuWUpIYNS+i555xy\nuaTp0yPq3j2pGTO8uvpqv5Yv5752AGgvhE4Aecs0TY0c2aRFi4Kqro5p506b7r33q/vap0zxad06\n7msHgPZA6ASQ10zTVFWVpfHjY7rookT6/V26WLr66qgsy6YNG9jjCQCZRugEkPdM09RJJyXl91ua\nPz+kioqEfv7ziBYtcuuKK/x66y2nXn+d+9oBIJMInQAKgmmaOvFE6dhjm3TbbdFmy+yzZ3v0yitO\nrVhB8ASATCF0AigYpmmqstKmnj2tgz5fvtyptWsJngCQCYROAAWlU6dOGjIktcx+YIZnTU1E/fo1\nqaTEUjQqrV3L4SIAaGuETgAFxzRNffe7Tfrznxv1+ONBNTRIDof0yCMe3XSTV7t2GVq1io4nALQl\nhsMDKEimaeq000LasiWuCy6Qxo/3KxaTJk6M62c/82jMmISkuIYMYYA8ALQFOp0ACpbP51O/fi7F\nYklJ0rhxcS1c6NTEiXHV1ro0YYJfL7/MAHkAaAuETgAFzev1asgQQ488ElJRUVJjxiQ0Z447fbJ9\n0iSfVq40tHNn6lpNAMCRYXkdQMErKirSqFFh9e4d1a5dhmprXc2e19U5ZVlxffnlfp1ySrEMg5/X\nAeBw8ZUTAJTqeA4Y4FN5uaUFC7462T5tWlRLlzq0c6ehffsMffTRfkWj0WyXCwAdDp1OAPhfTqdT\n/fr5ZVlBLVoUVF2dUwsXOjV9elT33uvW3r2G5s8P6R//iGjQoKQ8Hk+2SwaADoPQCQBf43A4dNJJ\nxSop2S/LimvAgCbde69bmzalvlxOnuxTdXVMu3cnNHZsTC6X6xCfEQAgsbwOAC0YhqGyMlPDhlk6\n8URLe/c2/1LZ2GjTjTf69N57EUUikSxVCQAdC6ETAL5B6tpMS/PmNd/j+e67hn75y5D27bNpxYqY\ngsFgtksFgJzH8joAfAvTNDVyZIP++MdG7d5t6NFHXbrjjqg+/9zQnXem9nT++tchXXghQ+QB4NvQ\n6QSAQ0jdXpSUy5XUT34S1cqVDs2e7UnP8vzxj31ascJQY2NjtksFgJxF6ASAVjBNU+efb8npTB70\n+fLlTr33nsVSOwB8A5bXAaCVTNPUySc3aNeuhHr1sjR7dmp5fcaMsObNc0uSPv+8SWPG7FdxcXE2\nSwWAnEPoBIDDYJqmRoxo0AcfNGnJkia98YZd8+a5NXFiXPfd51ZtrdS1a1CDBrHHEwC+juV1ADhM\npmlq4EDJ6bQ0fHiTxoxJ6L77Up3OG2+MyG6X1q+3qaGhIcuVAkDuIHQCwBEwTVMnnSQlk5bOOqtJ\n3bpZmj07LNOULr/cr8suK9Ly5XaCJwD8L0InAByh1Kl2qUuXhBYsCGvjRnuzU+1Tpvi0cqVB8AQA\nEToB4KiYpqkhQySP5+Cn2uvqnCy1A4BaETpnzpwpwzCavfXo0aPFx5SVlcnn8+mCCy7Qhg0bMlYw\nAOQa0zR1yik2jRgR1/33h5vdXrRihV1ffmmj4wmg4LWq01lRUaFAIJB+e//999PPfvnLX+pXv/qV\n5s+fr9WrV6tbt24aOXIkQ5IBFJTi4mKNHOnWyScn9F//FVR1dUz//d8OTZkS0w03+HX11X69/DJ7\nPAEUrlaFTrvdrm7duqXfvvOd70iSksmk5s6dq7vuukv/+q//qoEDB2rx4sXav3+/nnjiiYwWDgC5\nxuVyacAAp2Kx1O8nToxp2jRveo/npEmpm4sIngAKUatC5yeffKKysjL16dNH1dXV2rp1qyRp69at\n2rVrly666KL0x3o8Hp177rlasWJFZioGgBzm8/n03e/adNllMR1/vNXsWUmJJYdDWreO4Amg8Bwy\ndFZVVWnx4sWqq6vTo48+qkAgoGHDhqm+vl6BQECSdOyxxzb7M926dUs/A4BCU1RUpMGD3Uokkpo3\nL6TSUksVFQnNnBnVVVf5NX68X8uWOQieAAqKLZlMHvzI5TcIhULq3bu3ampqNGTIEJ199tnavn27\njjvuuPTHXHvttfr888+1dOnS9Pu+/sX1o48+aoPSASC3uVwuBYO9tHevIYdDuuoqvwKB1M/6paWW\nliwJqk+fffr888+zXCkAHFq/fv3Svz6SG9cOe2SSz+fTwIEDtWXLFnXv3l2StGvXrmYfs2vXLpWW\nlh52MQCQT2KxmL7znV0qKbHk8bR8Xl8vrVplpr+WAkA+O+y71yORiDZu3KgLL7xQvXv3VmlpqV58\n8UUNHjw4/fyNN97QnDlzvvFznHHGGUdeMb7V22+/LYnXOJN4jdtHPr3OkUhEH34Y1dy5YU2d6pUk\nzZ0b1qxZHu3cadeiRUlVVRW1+13t+fQa5zJe58zjNW4fR7sl6JChc9q0abrkkktUXl6u3bt3a9as\nWQqHw5owYYIkaerUqbrvvvtUUVGhfv366Z577lFxcbGuvPLKoyoMAPKFx+NRRYWhYDCsJUuCqq+X\nZs3y6J13nKqoSGjHDkMulzRoUEO7B08AaC+HDJ07d+5UdXW1vvzyS3Xt2lVDhw7VypUrVV5eLkm6\n4447FA6HNWnSJO3Zs0dVVVV68cUX5ff7M148AHQULpdLgwYl9eGHEX3xhV07d9pVUZHQ9OlR3X57\nqvu5YEFIZ53VoB49imUYXBgHIL8cMnTW1tYe8pPcfffduvvuu9ukIADIV263WyedZJdlBbVoUVA7\ndhi6/XZv+nDRpEk+Pf54UPv379eJJxI8AeSXw97TCQA4cg6HQ6ecUqxjjtkvl6vl8+efd+rssxPq\n1Gm/yspYageQP/gxGgDamWEYKiszNWiQpQULQs3ual+82KVJk3xat87Qhg0Nih243ggAOjhCJwBk\niWmaGjGiSY8/nrqr/b773KqvT31ZXr7cqX/8w9Crr4YVCoWyXCkAHD1CJwBkkWmaGjzY0tlnJ+Ry\nKd3xXLrUoVhMcrsNrVsXV2NjY7ZLBYCjQugEgCw70PF87LFUx3PhQqdmzoxq+nSPrrjCr1WrnHrp\npSQdTwAdGgeJACAHmKapYcMaVFQU15gxcc2Y4dGqVU717ZuQ35+UzSa9/35cp58ek+tgJ5AAIMfR\n6QSAHGGapiorLSWT0rZtdvXtm9DMmVHNmOHVDTf4tWOHXe+/zx5PAB0TnU4AyCGmaWrIkAYtWBBS\nfb2t2RzPKVN8mjUrrC+/bFJVFbcXAehY6HQCQI45sMezf3+r2ftLSlK/r6tz6tVXjaO+BxkA2hOh\nEwBykGmaOvVUSw89FFZpqaWKioR++tPUUnttrUt79hhav17at29ftksFgFZheR0AcpRpmho1qkG1\ntY2y2Wy64gp/eqn9rru8WrQoqA0bLA0YsE+dOnXKcrUA8O3odAJADjNNU6efnpTTmWzx7PXXHdq7\n19DKlTaW2gHkPEInAOQ40zQ1cGCy2ZWZ06dH1L17Utdc49eECX69/LKd4AkgpxE6AaADOHC4aNGi\n1AD5nTttuvdejwIBQ4GAoUmTfHr3XQ4XAchd7OkEgA7CNE0NHbpPNltc27e37BkkEtJ779l0+umM\nUwKQe+h0AkAH0qlTJw0ZYql//yb96lfh9HJ7TU1EN93k1dq1Dr3+Oh1PALmH0AkAHUxqnFJSJSVN\n+uMfU8vtv/iFR5s2OTR7tkevvOLU2rUETwC5hdAJAB1Q6q72pAwjqdpal+rrU1/OS0osDRjQpA8/\nNBggDyCnEDoBoINK3dWe1MMPh1oMkJ8xw6s9ewytWSOCJ4CcwEEiAOjATNPURRc1aMmSRkk2jR/f\nfID8H/4Q1Lp1SVVWcrgIQHbR6QSADs40TZ12mk12e8sB8n/5i1PjxxfpxReZ4wkguwidAJAHiouL\ndcopNv3616FmJ9oXL3YpEDB0000+rVvHzUUAsofldQDIE8XFxbrwwgYtXhzU9u2GHnzQnT5gJElP\nPeXSF18kNGIES+0A2h+dTgDII6ZpasgQSxUVTbrzzmi663nnnRFZlvTGGw69/TYdTwDtj04nAOQZ\n0zR1yikN2rPH0qxZYX38sSGHQ3rySZckqbKySR5Pk8rLu2n37t1ZrhZAoaDTCQB5yDRNnXuupV69\nmjRsWKLZPe133eVVKGTTli2ddeyxx2a7VAAFgtAJAHnKNE1VVdn0ne+0PNW+dKlTP/iBX2++2YWl\ndgDtgtAJAHmsuLhYgwa59MgjBz/VfvPNXq7MBNAu2NMJAHnO4/Fo7NiY/vjH1AD5G27wNrs288MP\nDYXDUlUVp9oBZA6dTgAoAC6XS8OH+1RcbOnnP4+mr82cPj11bebVV/v10ksMkAeQOXQ6AaBAOBwO\nnXyyV6FQWI8/HtQnnxi6/XZv+trMyZN9WrQoSMcTQEbQ6QSAAuJyuXTmmR7FYkkde6zV4nldnVPr\n1rHHE0DbI3QCQIFxu90aMcKr3r0tLVjw1QGjadOiWrHCrkhEWrmS4AmgbRE6AaAAOZ1OSTt02mlN\nWrQoqOrqmP77vx265ZaYrrrKr6uv9uvll9njCaDtsKcTAApUJBKRYezUCSeUyeeLa8yYuK66yp/e\n4zlpkk9PPBHUoEHs8QRw9Oh0AkABC4VCKi/3qqTEkvVPWzxLSizZbGKPJ4A2QegEgALncrnUv79H\nxxxjad68UHqc0syZUVVX+zV+vF/LljkIngCOCsvrAAC53W4NHJjUF1/E9PvfB+VwSNXVXy21T53q\n1ZIlQVVWstQO4MjQ6QQASErdXDRihFelpZbs9ubPSkosRSLSu++y1A7gyBA6AQBpTqdTFRV+HXOM\npblzw82W2q+6yq8rr/Srro6ldgCHj+V1AEAzDodD/fr51alTUEuWBBWJqNmp9ptvZqkdwOGj0wkA\naMHhcKiszFSfPpYcB2lPbN5s0PEEcFgInQCAb9S9e7H697f00EPh9M1FDzwQ1hNPOLVvX2qc0s6d\nDUokEtkuFUCOY3kdAPCNDMNQ9+7FGj58v5YsCWrzZkOPPebUtdfGdfvtXknS3LlhnXVWUMcd5/vf\nm44AoCU6nQCAb2UYhsrKTFVWWurUSbryylTgDAQMBQKGpk71avt2Q3//e4iOJ4BvROgEALSKaZoa\nNSqhE0+0WjyLxaQdOwy9/35Q8Xg8C9UByHWETgBAq5lmquN5YJxSaWnq1zfd5NXll/u1datdH3xA\nxxNAS+zpBAAcFtM0NXp0g/74x6BiMemmm7zatCn17WTSJJ8WLQrK7w/q+OPZ4wngK3Q6AQCHzTRN\nnXaaJbdb2ru3+beSSEQKBAx9+mlI0Wg0SxUCyDWETgDAETFNU6eeamnBglCzpfb77/foqaec2rLF\n0IcfRtjjCUASoRMAcBRM09SIEU1atCio3/wmqP/3/1z6/vcTqq116dpr/frwQ7s2bw4RPAEQOgEA\nR8c0TVVVWerSRRo2rElz5rjT45QmT/Zpzx5DH3xA8AQKHaETAHDUDpxqHzmyZbCsr5fq6w29/TbB\nEyhkhE4AQJswTVPDhlmaP7/lHs/nn3dq715D77/POCWgUBE6AQBtxjRNffe7TVqy5OB7PD/91K6P\nPw5mu0wAWUDoBAC0qQNL7Z06tdzjOWmST9u2Gdq5s4GOJ1BgCJ0AgDZnmqYGDTr4Hs9ly5zavNnQ\n5s1B5ngCBYTQCQDIiAN7PL8+x3PatKiWLnXo+eed2rTJrtdfjygSiWS7VADtgNAJAMiYA3M8Fy8O\nqro6poULnZo4Ma7Fi12aPNmnpiZD770XJXgCBYC71wEAGWWapoYMaZDDkVpqv+8+t+rrDQ0ZEpfd\nLiUShjZsiOqUU+zc1Q7kMTqdAICMM01TgwdbGj48IZdLGjIkrltuiemqq/y67jqvdu0ytGZNmMNF\nQB6j0wkAaBepcUoNWrw4KJtNuuoqv2IxadKkmJYvT3U4P/ssrDFj3HK5XFmuFkBbo9MJAGg3qaV2\nSx5P6vc/+lFMTU1Sba1LtbUuffqpXe+9F2aPJ5CHCJ0AgHZ1YI7n3LlhnXxyk2bP9qTneM6e7VEw\naOill+IETyDPEDoBAO3ONE2NHp3QgAFNLZ7t2GEomZTWro2yxxPII4ROAEBWmKapgQOTmjfvqzme\nDz4Y1iOPuPTKK041NBj65JOgLMvKdqkA2gChEwCQNaZpauTIJj3xRFCzZoX18MNf3dU+YYJf69bZ\n9dFH++l4AnmA0AkAyKoDV2aWl1st7mqfMsWnQMDQO++EuDIT6OAInQCArDNNU1VVlkaPbn5Xe0mJ\npb17pSefdOmFF+KKxWJZqhDA0SJ0AgB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tW1df7VB5eYWys2s3kI+JkV56yalp06p08GBA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\nAAAg5AidAAAACDlCJwAAAELu/wPfWHZnWbhSLQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d3964a8>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Explain Filter Performance"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that for even very small angular errors the (x, y) positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer this for the one sensor problem as well as the multiple sensor problem. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> This is **very** important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you really need to revisit some of the earlier Kalman filter material in the Multidimensional Kalman filter chapter.\n",
      "\n",
      "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible psoitions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target to form an intuition."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pos = [5, 5]\n",
      "for i in range(5):\n",
      "    pos[0] += 0.5\n",
      "    pos[1] += 1  \n",
      "    \n",
      "    actual_angle = math.atan2(pos[1], pos[0])\n",
      "    d = math.sqrt(pos[0]**2 + pos[1]**2)\n",
      "\n",
      "    xs = []\n",
      "    ys = []\n",
      "\n",
      "    for i in range (100):\n",
      "        a = actual_angle + randn() * math.radians(1)\n",
      "        xs.append(d*math.cos(a))\n",
      "        ys.append(d*math.sin(a))\n",
      "    plt.scatter(xs, ys)\n",
      "\n",
      "plt.axis('equal')\n",
      "plt.plot([5.5, pos[0]], [6, pos[1]], c='g', linestyle='--')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h1bszefjwYU2dOlXdunXT2LFj1b9/f61Zs0YpKSnxqA8AmiXLsnTHK3fonjfv\nUaeFnfT7t38v35kfqGvX6tXef/pTpXbtMvTww25NnBhWYaFb48alafXqsEKhkN3lA2hG6t2ZHDNm\njMaMGROPWgAA/1G0rSh62o0/4tcTu5/QFZlX6LqBF2vfPr+83iqlp1sKBh2aP98TnUc5eXKqWrSo\n0OWXO5lDCaBRcDY3ACSYI8/grjE4Y7ByW+bKMAx16JCmDh2kvXsrVVVV3ZU80iuvOHX66ZU66yyn\nOnZ0EyoBNCjeYQAgwRzZlawxMXdina9r396rtDRp0aLK6Kk5v/lNQLm5VXrhhRT9/e9VWr+ehTkA\nGhadSQBIMG9/9nat26O6jVJuy9w6X2cYhvr1S1NpqV8rVlTo5ZddKi+XvF6H0tMt3XOPR/n5EYXD\nAQ0eXH1sIwDEG51JAEgwdw2+S/+48R8a032MDIdxwjO4DcNQdnaaLr88TePGmerZs0rbtqXooYdq\nL8x58cWgPv20khNzAMQdYRIAElCP9B56eszT2nPznpM6g9swDPXo4VWrVtWnj+XnR6ILc8rKDE2e\nnKq33jK1Zk2lIpFIQ5cPoBkhTAJAAstqlXXSX1s97O3VD38YUd++dQNjZaVDoZClt96qZB4lgLgh\nTAJAE+J0OjV0aKouusjQkiXfLsy55x6//H5p0qQ0jR7dQqtWBdmPEkBcsAAHABJAuCosV0p8FsgY\nhqGOHVPVrl1YaWkVKi019NFHhpYt+3Y/yilTUnXWWRW66CKLE3MA1AudSQCwmWVZ6re8n8a+MFbb\nv9wet8d1uVwaPNirLl1M+f2OOvevWePUunUh7drFwhwAsSNMAoDNirYV6e3P3tZj7z+mrku6atwL\n41RlVsXlsV0ul/r29enyyyP64x/90WHv3/42oLPOsjRhQpouucSrNWsCBEoAMWGYGwBsdPRpN6Zl\nqjxUrhQjJW7P4XQ69aMfpaq01K+nnqrQCy+4tH27oaefdkeHvSdM8GrVqgqdd55PTid/GgCcPDqT\nAGCjY512c6J9JWNVsx/lRRe5lZdXpZRjZNXCQpdeeCHI1kEATgkfPwHAJsc6g3tUt1Enta9krDwe\nj666yqGMjIAuuKBKt97qkyRNmxbU3LkeFRZK3/teQL168ecBwMmhMwkANglEAsrrkCd3ijt6rSG6\nkkdzu926+OJUtW9v6bHHKlRQENLcuR599VX1n4Rg0FRJSZA5lABOCh89AcAmPpdPS65YotsuvU3z\nNs7TwcAb5Uu/AAAgAElEQVTBBu1KHsnpdOrSS1P12WdBHTpUpcJCKSPD1MKFfk2dWr1V0N13V+j0\n0w117+5hHiWA4+LdAQBsltkyU4uHLZZlWY36vIZhKCvLp3btIurSJaBg0NTUqR598YVDc+YEdf31\naZKkRYv8uuoqSy5XfPbBBNC0MMwNAAnC4ai7F2RjcDqd6tUrVenpLpWUpOjWW0OaPt0XPdf7ppt8\nev31AAtzABwTYRIAIEnKynJp+fKg3O66HdIdOwxt2MA8SgB1ESYBoBFZlqV3971rdxnHZBiGhgzx\naOhQQwsXfrvB+Z/+5NfSpW4VFaWotDRsd5kAEgxhEgAaUdG2IvX+c2/lP5GvTXs32V1OHTXzKK++\n2q3CwgrddZdfixe7NWZMRC+9xDR7AHURJgGgkRy5r+TLO15W37/01dzX5tpb1HG4XC716+dT587S\nxRdXaelSl+67L6ysLJdMs3rrILYPAiARJgGg0RzrtJvh3xtuUzXfzel0auBAn26+2aGXX67SkCHV\nWwYVFweVl+dSXp5LxcUESqC5I0wCQCOw47SbeKg+htGj7GyPDMNQaWlY48d7oiu9x4/36MMPAwRK\noBkjTAJAI2isM7jt8Oijhlav9rN1ENBMESYBoBFcmn2p5gyYo1aeVpKSoyt5LDXbB9Ws9J42LagV\nK9y64QYfWwcBzRRhEgAaQWtva80eOFt7btmjOQPmJG1Xsmb7oDVrAnXO9GbrIKB5IkwCQCOqCZXJ\n2JWsYRiGevTwatCgKrndinYo2ToIaJ74zQcAnDLDMJSf79ETT/hVVJRyxNZBHrtLA9DICJMAgJhU\nbx1k6Oyzw7r55iplZVWv+AbQvBAmAaCBbCjZoK+DX+uK3CvkcDjsLqdB1GwdBKD54iMkADQAy7J0\n65pbdWXhlbrgkQtUtK1IlmXZXRYAxB1hEgAawOrtq7Vl3xZJ0pZ9W3Rl4ZX615f/srkqAIg/wiQA\nxJllWZqzfk6ta6O6jVLXM7vaUxAANCDCJADE2ZFdyRrJuq8kAHwXwiQAxNmft/y51u1kPe0GAE4G\nYRIA4uyZMc/ogWEPKLNlpiS6kgCaNrYGAoA48zg9uvGCGzXhvAlat3sdXUkATRqdSQBoIB6nR/m5\n+XaXAQANijAJAACAmBEmAQAAEDPCJADUk2VZGvPMGC1/d7nCVWG7ywGARkWYBIB6Wr19tf768V81\nYdUEdV3SVY++96jdJQFAoyFMAkA9HH3aza6Du/TithftKwgAGhlhEgDq4Zin3fRnX0kAzQdhEgBi\ndKwzuK/pdo2+n/F9ewoCABsQJgEgRgcqDihYFax1ja4kgOaGMAkAMWrboq3en/S+nhnzjHqk96Ar\nCaBZ4jhFAKgHw2FodPfRuqbbNfo6+LXd5QBAo6MzCQBxYDgMtfa2trsMAGh0hEkAAADEjDAJAKfA\nsiyVh8rtLgMAEgZhEgBOQdG2IuUsyNHdG+8mVAKACJMAcNIsy9KcV+foS/+XmrF2hnIW5GjlP1fa\nXRYA2IowCQAnqWhbkbbu2xq9/aX/S3U6vZONFQGA/QiTAHASarqSRxrVbZR6te1lT0EAkCAIkwBw\nEo7uSkrSrAGcdgMAhEkAOAkZLTI0KGdQ9DZdSQCoRpgEgJNwQYcLtG7sOq0fu16DcgbRlQSA/+A4\nRQA4BQNyBmhdzjq7ywCAhEFnEgAAADEjTAIAACBmhEkAOI5/7P+H9pfvt7sMAEhohEkAOAbLsjRu\n5Th1WthJ04qnESoB4DgIkwDixjRNlZQEVVISlGmadpdTLzX7Svojft3z5j06e9HZOlBxwO6yACDh\nECYBxIVpmiouDiovz6W8PJeKi5M3UB7rtJsfnfMjpael21MQACQwwiSAuCgtDWv8eI/KygyVlRka\nP96j0tKw3WXFhNNuAODkESYB4AiWZenODXfWusZpNwBwfIRJAHGRleXS8uVBZWSYysgwtXx5UFlZ\nLrvLOmUOh0PLRy7XtedeK4cckuhKAsCJcAIOgLgwDENDhni0aVP10HZWlkeG8e3n1Ugkoo8/DkmS\nund3y+lM3LefHuk99NTopzSz/0z9beff6EoCwAkk7rs5gKRjGIaysz11rkciEb3wQlBTp/okSYsX\nV+r88w117OitFTgTTY/0HuqR3sPuMgAgoSXuuziAJuPjj0OaOtUXXZwzZUqqFi0ytGZNIGlXfAMA\nqhEmAdiivNyhCRO8SbviGwBQjTAJoMF17+7W4sX+6OKcadOCevbZ6sU5Dodl+0bnlmVp1iuztP3L\n7bY8PwAkM8IkgAbndDo1YoRbTzxRoUWLKrV0qUtut/TYY3599JEZ3eh89Wq/IpFIo9dXtK1Id224\nS12XdNXYF8YSKgHgFLAAB0CjcLlcGjgwRXv3hvTUUyG1bGlISlHfvm6VlVV/rr3hBp+efLJCl1zi\na7TV3keedmNaph57/zFVhiv1zJhnGuX5ASDZESYBNBrDqF7B3bFj9e2SkmCdr1m50qWDB4Pq3Tui\nzEx3g6/2PtZpNzP7z2zQ5wSApoRhbgC2ycpy6c9/rj2XctUqpzZsSFFxcZXWrWvY1d7HOoOb024A\n4NQQJgHYxjAM5ed79OSTFSooCOnBB1268cawCgvdmjnTp48+kvbuDTXY83/074/04YEPa13jtBsA\nODUMcwOwldPp1CWX+PT119VD3vPne6JzKB96yK0LLvDr88/DyshIifsm5z3Se2jnTTs1b+M8PbL1\nEV35vSvpSgLAKSJMArCd0+nUFVcYys72q7Cw+lqbNqYmTQrp5z/3KT8/ossvD2vfvm/Up0+qXK74\nnfmd2TJTi4ct1ox+MxSuYs9LADhVDHMDSAiGYahHD5+WLQsoI8PU2LEhPfSQWxMnVg97//znadqz\nx6n16/0KheI/9J3ZMlOdTu8U98cFgKaOziSAhGEYhoYO9WrTprD27avuEh457H3rrT4VFIT0zTch\nXXGFJY+n7jngAIDGRWcSQEIxDEPZ2R6df75XQ4bUHXYuL3do8uRUrV8f0qeffsPZ3gBgM8IkgITk\ncrk0eLBHDz5YecxjGN95J0W7dkmvvVahYLDufpXH8+K/XlT+E/natHdTQ5UOAM0KYRJAwnK73Rox\nIlWvvx7QihUV0WMY77zTr86dLRUUpOn669O0cmVEfr//Ox+vZl/Jl3e8rL5/6av8J/L10YGPGuEn\nAYCmizAJIKEZhqHOnVM1YIBbCxb4VVAQkssl/epXPpWVGSorM3TzzT69/XZEn31WccJh76NPu3l5\nx8uqsqoa48cAgCaLBTgAkoLH49GAAZaksAKBuvfv3euQaZratatcF17oqbM4h9NuAKBh0JkEkDS8\nXq8GD/aqUydTCxd+ewzjvff65XJJP/5xmq69toVeeCFSZx7lsc7g5rQbAKg/OpMAkorL5VKvXq2U\nm+tX27YV2r7dUChkacaM1OgWQrfc4lNmZrkuvNCIbnD+ReUXauVppcPBw5LoSgJAvNSrMxmJRHT7\n7berc+fO8vl86ty5s2bOnKmqKuYgAWhYPp9Pfft61KaNpXDYUef+w4cdeu01f7RDOf688dpzyx79\nbuDvdLr3dLqSABAn9epMzp07Vw8//LAee+wx9ezZU++//77GjRsnj8ejO+64I141AsAxud1uXXml\nQ2++Wan776/U1KmpkqRp04L61a+qj2E8eDCs88+PqGNHn1p7W2vWgFmafvF0+Vw+m6sHgKahXmHy\nnXfe0YgRI3TFFVdIkjp27Kjhw4fr7bffjktxAPBdXC6XLr44Te+9V6GCgpDKyx2aO9cjt7t6g/Mp\nU1J1111+dehQqR/+0Cun00mQBIA4qtcwd35+vtatW6d//etfkqSPP/5Yr7zyioYNGxaX4gDgZDid\nTv3gB2m6+OIqvfhi9V6UR25w/vHHKdq/36FNmyoViURsrhYAmhaHZVlWfR7g9ttv17x58+R0OhWJ\nRHTHHXfozjvvrPU1hw8fjv5/+/bt9Xk6ADgup9OpYDBThw55dMstPn0V+FLTJ5+mP/7RK7dbeuih\nCrVsKZ1xhl+m+TnBEgBOUm5ubvT/rVq1qnVfvTqTixYt0vLly/Xkk0/q3Xff1WOPPaYlS5Zo2bJl\n9XlYAIhJJBJRSsoedehQoocfrpD+K18zdvXXV2f+nyxZeu+9FJWWOnTwoE/l5Z3l9XrtLhkAkl69\nOpNt27bVHXfcoalTp0av/eEPf9Cjjz5aqwN5ZGfy6DSbCDZv3ixJ6tOnj82VgNcisSTz6/HCxy/o\n6meujt7Odp6vu7u+pIP/TtW2bSmSpEGDwrrsshSlpqbaVeZJS+bXoini9UgsvB4N70RZrl4LcCzL\nkmHUbm4ahqF6jpwDQL1YlqW7Nt5V69pZ7kx9sLWF0tMtFRa6JUnZ2aZSUyPKy6tQWlqaHaUCQNKr\nV5i86qqrNG/ePHXq1Endu3fXu+++q/vuu09jx46NV30AcMqOddrNDV1/I8d+UzNn+qKbm8+b59Vd\nd/kVCpm67LKQ3G63HeUCQFKrV5i877771LJlS02ePFn79+9Xu3btdMMNN2jWLDYDBmCP453B/ZPL\nvq+NG+seqLBzZ3WwfOutoLKyIurY0VtnxAUAcHz1esdMS0vT/PnztXv3blVWVmrnzp36/e9/z6d7\nALYxLVMTz5uozJaZ0WuzBsxSamqq+vd36YEHKqNnev/2twGdd16Vnn7apX/9y9DOnVXavPkbVnkD\nwCngbG4ATUqKkaIbL7hRE86boGXvLtMnX3wSPYPb6/XqyisjOueccv373w7t3evQ0qVu/exnYU2f\nXr2R+YIFfn3zTaUGDEiV08lbJAB8F94pATRJHqdHN15wY53rTqdTPXu2VCgU0ltvBXXttdVBsmYe\n5S23+FRYWKFNmyqVl0egBIDvwrskgGbJ7XYrL8+hSCRQ574dOwxVVDh0+HBAQ4d6CZQAcALMMgfQ\nbLlcLvXt69LChf7oPMo//cmvefM8mjfPq7VrnXr9dT9zKAHgBPi4DSDpWZal5z55TiO6jJArxXVK\n3+v1enXVVSFlZlbo448NzZnj0c6dTmVkmJKklStdOngwqOHDRYcSAI6BziSApLd6+2qNfma0uizu\nomXvLlO4KnxK31895J2mDh0cqqgwlJFhasaMgDp3NrVqlVMbNqTQoQSA4yBMAkhqlmVpzvo5kqTd\nh3br56t+rpteuumUH8cwDA0d6tUbbwT19NMVOnDAoQUL3LrxxrAKC926/vo0FRUFCZQAcBTGbAAk\ntdXbV2vLvi21rk3qMymmxzIMQ506+ZSVFdGXXwbl90c0f74nutL7xht9atGiQgMH+hjyBoD/oDMJ\nIGkd2ZWscU23a/T9jO/X63GdTqeGD/do5Mi6w+X/938ubdgQlGma9XoOAGgqCJMAktbfd/29Tldy\nVv/4HOfqdDp1ySU+Pfjgtyu9p00L6qWXnCoqSlFp6anNywSApoowCSBpXdb5Mj0z5hn1SO8hKT5d\nySPVdCgff7xCBQUhLV3q0sSJYb30EkPcAFCDd0QASctwGBrdfbSu6XaNnvvkOXU7s1vcn8PpdGrg\nQJ8MIyhJWrrUpfvuCysryyNJMk0z2qXMynLJMPiMDqB5IUwCSHo1obKhVAdKQ2efHdbNN1cpK8sj\nwzBkmqbWrQvo//6vOkAOGxbQ4MFeAiWAZoUwCQAnwTAMZWd7al3buzekjz6SCgvdkqTs7IC+972Q\nOnb02lEiANiCj88AEKNDh0zNm+dVWZmhsjJD8+Z5degQq7wBNC+ESQBJpXhnse7eeLfKQ+V2l6KW\nLeu+hbZsWT38XVISVEkJWwgBaPoIkwCShmVZum3tbZqxdoZyFuRo3sZ5+ib4jW31dOzo1rJlgejW\nQcuWBZSZ6dSaNQHl5bmUl+fSmjUBAiWAJo0wCSBpFG0r0tZ9WyVJX/q/1G1rb9PuQ7ttq6fmCMZN\nm8LatCmsoUO92rs3ogkTvh36njDBq08/DdlWIwA0NBbgAEgKlmVpzqtzal0b1W2UerXtZU9B/3H0\nwpyvv67bhTzWNQBoKuhMAkgKR3Yla8waEJ/TbuKpdWtDM2Z8O/Q9e7ZfksX8SQBNFp1JAEmheGdx\nrduJ0JU8lsxMt849N6CCgpB8PktnnikNHeqTJC1fHtSQIR72oQTQpPCOBiAp3D/sfq0fu16DcgZJ\nSsyupFQ97D14sFc33+zQdddZmjrVF50/OX68hzO9ATQ5dCYBJI0BOQO0LmedPjrwkc5NP9fuco6r\nZh5lSUnQ7lIAoMHRmQSQdBI5SB4pK8ul5cuD0fmTy5cHlZXlsrssAIgrOpMA0EAMw9CQIR5t2lQ9\ntF1zpjcANCWESQAJy7RMGY7kDl/HOtMbAJqS5H6XBtBkWZalAY8O0K/W/Epl5WV2lwMAOA7CJICE\nVLStSBs/3ah7N92rzgs7a1rxNJkW+zQCQKIhTAJIOEefduOP+LXn0J6kH/IGgKaId2YACSdZTrsB\nABAmASSYRD2DGwBwbIRJAAmlPFSuc9qcI4cc0Wt0JQEgcREmASSU0zyn6anRT+mDGz/QtedeqzHd\nx9CVBIAExj6TABJSj/Qeemr0U4qYEbtLAQCcAJ1JAAnNafCZFwASGWESAAAAMSNMArCdZVnadXCX\n3WUAAGJAmARgu6JtRcq9P1c/e/5n2vblNrvLAQCcAsIkAFvV7CtpWqYe/+BxdVvSTYvfXmx3WQCA\nk0SYBGCro0+7MS1T/bP721gRAOBUECYB2IbTbgAg+REmAdiGM7gBIPkRJgHYpne73pp8wWS5U9yS\n6EoCQDIiTAKwTYeWHbR42GLtvGmnJl8wma4kACQhjpYAYLvMlplaPIwV3ACQjOhMAgAAIGaESQAA\nAMSMMAmgUb1Z+qY27d1kdxkAgDghTAJoNJZlacpLU9T3L32V/0Q+oRIAmgDCJIBGc+S+ki/veFl9\n/9JXuw7usrkqAEB9ECYBNIrjnXbT+fTO9hQEAIgLwiSARsFpNwDQNBEmATSKBW8tqHWb024AoGkg\nTAJoFM9e+6x+N/B3au1tLYmuJAA0FYRJAI2itbe1Zg2Ypd0379aTo56kKwkATQRhEkCjau1tret6\nXGd3GQCAOCFMAgAAIGaESQAAAMSMMAmgQViWpfErx+vFf70oy7LsLgcA0EAIkwAaRNG2Ij363qMa\n8eQI9Xmkj4q2FdldEgCgARAmAZuZpqmSkqBKSoIyTdPucuLi6NNutu7bqkffe9S2egAADYcwCdjI\nNE0VFweVl+dSXp5LxcVNI1By2g0ANB+EScBGpaVhjR/vUVmZobIyQ+PHe1RaGra7rHo53hnc7CsJ\nAE0TYRJAXO39eq8OVByodY2uJAA0XYRJwEZZWS4tXx5URoapjAxTy5cHlZXlsruseslqlaUdU3fo\ngWEPKLNlJl1JAGjinHYXADRnhmFoyBCPNm2qHtrOyvLIMJL/M57H6dGNF9yoCedN0OHgYbvLAQA0\nIMIkYDPDMJSd7bG7jAbhcXqU7ky3uwwAQANK/hYIAAAAbENnEkgipmlGV3tnZbkSZkjcsixFzIhc\nKck93xMAcOoS4y8RgO9UsyflddcZ+tvfInrttQqFw4mxjdDq7avVZXEXLXt3mcJViVETAKBxECaB\nJFFaGtacOU5NmRLSzJk+XX99mlauDNoeKC3L0pz1c7T70G79fNXP1WVxF63dtdbWmgAAjYdhbiCJ\nTJwY0vTpPpWVVX8OnDo1VS1bVqhr1yplZrptGfZevX21tuzbEr29+9BunZl6ZqPXAQCwB51JIElk\nZbmUm1v3qMWXX3ZpwQLZchRjTVfySNd0u0bfz/h+o9YBALAPYRJIEoZh6OKLvbr//sroJufTpgX1\n0ktOlZc7bDmK8eiupCTN6s9pNwDQnBAmgSTicrk0cqRHjz9eoYKCkJYudWnixLCefdal7OwqHTgQ\n1gcfVCoSiTRKPT6nTz3Te0Zv05UEgOaHMAkkGZfLpcGD03TTTdKSJUEtXepSbm6Vbr01pBEjUjV0\nqFfPP984C3Mu63yZ3pv0nv465q/q1bYXXUkAaIZYgAMkIcMwlJPjVceOpl5+OawDB8IaMSI1ujDn\nppt8Sk+v0KWXpjT4ohzDYWhU91G6pts1cjgcDfpcAIDEQ2cSSGI1RzF6PLV/lVu3NnXokPThh4FG\nW5RDkASA5okwCTQB3bu7tWiRXxkZprp2jWjOnKAmTUrT0KFeW1Z5AwCaD4a5gSbA6XTqqqsspadX\n6NAhadKktOiQ9/jxHq1ZE1CrVilxOYJx25fb1P609mrhbhGP0gEASY7OJNBEuFwuXXppmjp1Sqlz\n3/PPKy5HMFqWpYJnC5SzIEd3b7xb5aHy+pQMAGgCCJNAE2IYhnr08Gr58mB0L8qZM/3q1s3UPfd4\n9PLLTm3cGNCePRUxDX0XbSvS1n1b9aX/S81YO0OdF3bWQf/BBvhJAADJgmFuoIkxDENDhni0aVNY\nhw9X6b33LM2e7dV//3dIDz/sVjDoUN++EW3fXqFBg3xyOk/ubcCyLM15dU6ta/2z++t03+kN8FMA\nAJIFnUmgCapZ5d2jh1fZ2Zby8yN6+GG3Jk4Mq7DQrVmzvAoEpDffrDzpYe+aruSRZg1gX0kAaO7o\nTAJNWM0RjIFAQJI0f75HoZA0cWJYN9yQJklasqRS+fkR+Xy+4z7OsbqSo7qNUq+2vRqsdgBAcqAz\nCTRxLpdLgwZ5NHRodQdy1Kiw5s/3qKzMUFmZocmTU7V+fUSffHL4uMcwOhwO3Tf0Pg3uNDh6ja4k\nAECiMwk0C263W4MGVXchN26s/WvfurWpzz4z5PNJe/dWqH9/rzweT53H6J/dX2t/tlYbSjZoQ8kG\nupIAAEmESaDZcLvdGjHCUG5uQP36RTR5cqpatzb1298GNX169RD3/fdXasuWgM4/X8cMlFJ1qOyf\n3b8xSwcAJDDCJNCMOJ1O9ezZQuec49eyZRX67DND06f7ohucT52aqoKCkPbvDys/37K5WgBAMqj3\nnMmcnBwZhlHn3/Dhw+NRH4AG4PP5NGiQS126VNW5r7zcoV/+MlWvvx5Wy5YtbagOAJBM6h0mt2zZ\norKysui/rVu3yuFw6LrrrotHfQAaiNfr1YUXerRggT+6wfm0aUE9+6xLkmSalha884wORZyc7Q0A\nOK56D3OfccYZtW4/8sgjatWqla699tr6PjSABubxeDRypKXMzHJ9/rmhWbO8crulGTMCeuTVYj3j\nukN/2fkHjfjw55p/9TRln5Ftd8kAgAQT1zmTlmXpL3/5i376058ed/I+gMTi9Xp1/vnSgQMR5edX\nbw3kdpt67uAfpXQpZPn1188Wa9/jZfr7pMfl9XptrhgAkEgclmXFbZZ9cXGxfvSjH+n9999Xz549\no9cPHz4c/f/27dvj9XQA4sjr9aq8PEvhsKGCOWv1Wf+ra91/xtPvqnDB2TrrrJ3H3Y8SANA05ebm\nRv/fqlWrWvfFddPyRx55RBdeeGGtIAkgOQQCATmd23XWWZ/JM+R3te5z7bhGrq96qbJSCgbb21Qh\nACARxW2Y+8CBA1q1apUeeOCBE35dnz594vWUcbN582ZJiVlbc8NrYb/Nn2/W7sD7ta613DpTM2YE\n9Mc/enXnnVKrVl103nkeud1um6psfvjdSCy8HomF16PhHTnKfLS4dSYfffRReb1eFRQUxOshAdig\nT/s++seN/9C13a+VQw719o7Uz4Z21f33uzVmTERjx6bpqqvS9PzzYYVCIbvLBQDYLC6dScuytHTp\nUl1//fVKTU2Nx0MCsNG56efqqTFPafSro6VIR930U7euvPLbM70l6ZZbfMrMrFBmZkhZWakyjLjO\nmgEAJIm4vPuvX79eO3fu1C9+8Yt4PByABNEprZPOPt2l5cuDatGi7lq9Z591aeNGh/72t3KFw2Eb\nKgQA2C0uYXLQoEGqqqpirgLQBJmmqSFDPLrppirdf39lrQ3OV6xw6/773fJ4HNq0KaBAIGB3uQCA\nRsbZ3AC+k2EYyslJU/v2IbVrV6Fnn3Vp7lyPTj/d1NSpIRUUpEmSFizw66qrguwzCwDNCJOcAGj1\nttX62fM/07Yvt53w69xut/r0ceuii6r+c1JOUNOm+VRWZigUkt56K0WbNwcZ8gaAZoQwCTRzlmVp\n1vpZevyDx9VtSTf97Pmfac+hPcf9+uojGFP017+Wq0uX6jO727QxdfvtQRUWujV6dAutXBliY3MA\naCYIk0AzV7StSFv3bZUkmZapxz94XF8Hvz7h93i9Xl10UapatjS1cKFfY8eGoiu9y8oMTZ3q09tv\n++lQAkAzQJgEmjHLsjTn1Tm1ro3qNkq92vb6zu91Op0699w0dewY0YABdUPjxx8bev75EIESAJo4\nwiTQjB3Zlawxa8Csk/5+p9OpPn3S5HY7NGNGILrS+557/HroIbc2bUrRO+8EGPIGgCaM1dxAM7bj\nqx1yp7gVqqo+yeZku5JHcjqdGjo0Vd27B9WnT4V27DB0771uFRREtPT/b+/eo6Oq772Pf2Zn9lyC\nEqESEBgDqEck4OUhTQl0JcrhgCCCPKKYVftAOBRBbkLhFFEsLdfa9iAguBA0gGjoZXl4EBHwEZFS\nDQpGvFBuCSBegosiFMjM5DL7+SOHlAB6dCdkz2S/X2u5VmYLO19W1iSffH/79/suNyVJp0+H1bNn\nQKZp1vu/AQDgLDqTgItNzJqo4vHFGvvDsQp4A9+rK3k+wzCUlhZUZmZAwaCUnV2l5ctNjRhRoYIC\nn4YNa6JXXonqyJGwYrFYPf8rAABOojMJuFzbpm21qN8i/fqOX6tZsFmd7mWapgYNktq2rT68/Pzx\ni2PGJCs3t1z/9m8R9ekTYPwiADQSfDcHIEl1DpLnmKapzMyg+vSpvfHmqqtiuv76mF5/3dCePXQo\nAaCxoDMJoN55vV717BnQkiVhPfxwUFddFdNjj0U1ZUpQkvTDH4Z1/HhY2dlBOpQAkOAIk4DLnCk/\no5nlfc0AABf0SURBVCt8V1z2z2Oapu6+26NmzcoUiVjKy2tSs+Q9aVJQCxeW6ejRqNLSgpe9FgDA\n5UNLAHARy7KUsyJHfV/sq8LPCi/75/N6vcrOTlbr1hd/q3nnHa8OH65kuRsAEhxhEnCRc+dKbjy4\nUVnPZanfi/1UUXV5DxU3DEOdOwf17LPhmnMoJ0+O6rXXvNq40aujRznUHAASGWEScIlLTbtJNpNl\nJl3+sx8Nw1Dfvn698MJZ5eaWa/lyUw89VK61a015PJaOHInqyJEoXUoASEA8Mwm4RF2n3dSV1+vV\n7bcHZRhRSdLSpT4tWlSuTz6Rhg8PSJLy86Pq3dvPphwASCCEScAF6jKDuz5VB0pD111XoQkTqmRZ\nhrKyfDUbc/Ly/CosrFBamr9B6wIA2Mev/4ALVMQqdM+N9+iqwFU11xqyK3m+6mk5fqWl+eXxeByp\nAQBQf+hMAi7gS/Jpes50jf/ReC3csVBHTh1p8K7kpYRCpvLzo8rLq+5E5udHFQrRlQSAREKYBFwk\nJZCi6TnTnS6jhmEY6t27emlbkkIhnpcEgERDmATgqHPL3gCAxEQLAAAAALYRJoFGyrIsvVHyhizL\ncroUAEAjRpgEGqn1+9er1wu9lLEsQ6/se4VQCQC4LAiTQCN0/rmS73/5vgasGaBf/L9fOFsUAKBR\nIkwCjdClpt08ePODDlUDAGjMCJNAIxMv024AAO5AmAQamQ0HNjg6gxsA4C6ESaCR6dWhl5656xmF\nmoYk0ZUEAFxeHFoONDJ+r1+jMkYp79Y85X+Qrx9f+2OnSwIANGKESaCROhcqAQC4nFjmBgAAgG2E\nSQAAANhGmAQagS2Htui5959TRVWF06UAAFyGMAkkOMuy9B+v/4dGvDJCNz59o54vep5QCQBoMIRJ\nIMG9euBV7fpylyTp0MlD+vd1/669x/c6XBUAwC0Ik0ACsyxLM7bOqHXt3pvuVZeWXZwpCADgOoRJ\nIIGd35U8h2k3AICGRJgEEtgfPvlDrddMuwEANDTCJJDAVt6zUn++78/qklq9rE1XEgDQ0JiAAyQw\nw2Po3k73atBNg1T4WSFdSQBAg6MzCTQChsdQ91B3p8sAALgQYRIAAAC2ESYBAABgG2ESSCCWZenO\n1Xdq3vZ5Oh097XQ5AAAQJoFE8uqBV7WpeJMefeNRtV/QXr/Z/htZluV0WQAAFyNMAgniwmk3fw//\nXe998Z48Ho9zRQEAXI8wCSQIpt0AAOIRYRJIAN80g5tzJQEATiNMAgng68jXaupvWusaXUkAQDxg\nAg6QAJoHm2vL0C3admSbfvXWr9Qs0IyuJAAgLhAmgQSSnZatN/7PGwpXhJ0uBQAASSxzAwkpaAad\nLgEAAEmESQAAANQBYRKIU5Zl6auzXzldBgAA34owCcSp9fvXK+2pNE3aNEmlZ0qdLgcAgEsiTAJx\nyLIszXhrhiKVEc0vnK/2C9pr1e5VTpcFAMBFCJNAHFq/f73e//L9mteRyohubXWrgxUBAHBphEkg\nzpzrSp6PaTcAgHhFmATizIVdSYlpNwCA+EWYBOLMv/zgXzQkfYg88kiiKwkAiG+ESSDO3Hj1jVoz\neI0+Gv2RhqQPoSsJAIhrjFNEoxOLxXT0aIUkKRQyZRiJ+TtTemq61gxe43QZAAB8q8T8KQt8g1gs\nps2bo+rWzVS3bqY2b44qFos5XRYAAI0WYRKNytGjFcrL86u01FBpqaG8PH9NlxIAANQ/wiQQB3Z+\nsVP7ju9zugwAAL43wiQalVDIVH5+VK1axdSqVUz5+VGFQqbTZX0ry7L00PqH1GlJJ/30v35KqAQA\nJBTCJBoVwzDUu7dfhYUVKiysUO/e/rjfgHPuXMmYFdPqD1crfUm6PvvHZ06XBQDAd8JubjQ6hmEo\nLc3vdBnfyaWm3dzT8R61bdrWmYIAAPie4rtlAzRyTLsBACQ6OpNwpXg5i3LeX+fVes20GwBAoqEz\nCde58CzKdevCOno07Mh5lH8c/EeN/eFY+ZJ8kuhKAgASD2ESrnPhWZSPPurXJ59Uatu2MlVWVjZo\nLW2attGifotUMr5Ey+5eRlcSAJBwCJNwtebNYxo1qlx5eU2Um5us115zZmJOm6ZtNOJ/jWjwzwsA\nQF0RJuE6oZCpZ58Nq1WrmIYOLde8eYGaLuXIkUEm5gAA8D2wAQeuYxiG+vb168UXy1RS4rno/1uW\npSNHopKc3ZwDAEAiIEzClbxer26/PVnXXRfV1VeHNXp0UJL0/PMRHT5sad26JElSv34R9ewZqLdA\naVmWJmycoNzOucoKZdXLPQEAcBItF7hW9eHmQQ0YEKyZmNO5s0e7d3tUUODT228nqbKySrt2na23\njTnr96/XoncXqfvz3XXn6jv1ztF36uW+AAA4hc4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VK2vGcqJhxGIxZWZmavbs2ZKkW265\nRQcOHNDixYs1ZswYh6tzt2XLlikzM1NdunRxuhTXWrhwofLz87VmzRqlp6erqKhIEyZMULt27TR8\n+HCny3OdF154QcOHD1fbtm2VlJSkrl27Kjc3V7t27XK6NFdxbZh85513dPz4caWnp9dcq6qq0l/+\n8hctXbpUZ8+elWmaDlbobozldE7r1q3VqVOnWtc6duyoTz/91KGKIElfffWV1q1bpyVLljhdiqvN\nnj1bjz/+eM0zq+np6Tpy5Ijmzp1LmHRAhw4dtHXrVoXDYf3jH/9Qy5YtNWTIEF133XVOl+Yqrl3m\nHjRokD7++GPt3r1bu3fv1gcffKCMjAzl5ubqgw8+IEg67NxYzmuuucbpUlynR48e2rt3b61r+/fv\nV7t27ZwpCJKkFStWKBAIKDc31+lSXM2yLBlG7R+dhmGwquWwYDColi1b6uuvv9bmzZs1cOBAp0ty\nFdd2JlNSUi6aGZ6cnKxmzZpd1JXB5Td58mQNGDBAoVBIX331lWbOnMlYTodMnDhR3bt315w5c3T/\n/ferqKhIixYt0ty5c50uzbUsy9Ly5cv1wAMPKDk52elyXO2ee+7RvHnz1L59e3Xq1ElFRUWaP38+\n36scsnnzZlVVValjx446ePCgpkyZoptuukl5eXlOl+Yqrg2Tl+LxeNiE4xDGcsaPjIwMrV27VtOm\nTdPMmTOVlpamWbNmafTo0U6X5lpbt25VcXGxXnrpJadLcb358+eradOmGjNmjI4dO6ZrrrlGI0eO\n1BNPPOF0aa506tQpPfroo/rss8/UvHlzDR48WLNnz+ac4gbGOEUAAADY5tpnJgEAAFB3hEkAAADY\nRpgEAACAbYRJAAAA2EaYBAAAgG2ESQAAANhGmAQAAIBthEkAAADY9v8BXfVhYO5uM84AAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0776de6518>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that each individual measurement has a very large position error. However, when we plot successive measurements we suddenly have a clear trend - the target is obviously moving towards the upper right. When the Kalman filter (whether a linear KF, an EKF, or UKF) computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately $45^\\circ$ degree line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this sort of noise distribution. Of course, this graph makes it look easy because we have computed 100 possible measurements for each position update and plotted them all. This makes it easy for us to see where the target is moving. In contrast, the Kalman filter only gets 1 measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n",
      "\n",
      "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose in the example above we told the filter that the initial position of the target was 1000km away from the sensor (vs the actual distance of 7.07 km), and that we were highly confident in that guess by setting $\\mathbf{P}$ very small. At that distance a $1^\\circ$ error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's consider the effect of adding a second sensor. Again, I will start by plotting the measurements so we can form an intuition about the problem."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin, cos, atan2, pi\n",
      "\n",
      "def isct(pa, pb, alpha, beta):\n",
      "    \"\"\" Returns the (x, y) intersections of points pa and pb\n",
      "    given the bearing ba for point pa and bearing bb for\n",
      "    point pb.\n",
      "    \"\"\"\n",
      "    \n",
      "    B = [pb[0] - pa[0], pb[1]- pa[1]]\n",
      "\n",
      "    AB = math.sqrt((pa[0]-pb[0])**2 + (pa[1] - pb[1])**2) \n",
      "    \n",
      "    ab = atan2(B[1], B[0])\n",
      "    a = alpha - ab    \n",
      "    b = pi - beta - ab\n",
      "    p = pi - b - a\n",
      "    \n",
      "    AP = (sin(b) / sin(p)) * AB\n",
      "    \n",
      "    x = cos(alpha) * AP + pa[0]\n",
      "    y = sin(alpha) * AP + pa[1]\n",
      "    return x, y\n",
      "\n",
      "\n",
      "def plot_iscts(N=4):\n",
      "    for i in range(N):\n",
      "        pos[0] += 0.5\n",
      "        pos[1] += 1  \n",
      "\n",
      "        actual_angle_a = math.atan2(pos[1]-sa[1], pos[0] - sa[0])\n",
      "        actual_angle_b = math.atan2(pos[1]-sb[1], pos[0] - sb[0])\n",
      "\n",
      "        da = math.sqrt((sa[0]-pos[0])**2 + (sa[1]-pos[1])**2)\n",
      "        db = math.sqrt((sb[0]-pos[0])**2 + (sb[1]-pos[1])**2)\n",
      "\n",
      "        xs, ys, xs_a, xs_b, ys_a, ys_b = [], [], [], [], [], []\n",
      "\n",
      "        for i in range (300):\n",
      "            a_a = actual_angle_a + randn() * math.radians(1)\n",
      "            a_b = actual_angle_b + randn() * math.radians(1)\n",
      "\n",
      "            x,y = isct(sa, sb, a_a, a_b)\n",
      "            xs.append(x)\n",
      "            ys.append(y)\n",
      "\n",
      "            xs_a.append(da*math.cos(a_a)+sa[0])\n",
      "            ys_a.append(da*math.sin(a_a)+sa[1])\n",
      "\n",
      "            xs_b.append(db*math.cos(a_b)+sb[0])\n",
      "            ys_b.append(db*math.sin(a_b)+sb[1])\n",
      "\n",
      "        plt.scatter(xs, ys, c='r', marker='.')\n",
      "        plt.scatter(xs_a, ys_a)\n",
      "        plt.scatter(xs_b, ys_b)\n",
      "\n",
      "    plt.axis('equal')\n",
      "    plt.show()\n",
      "\n",
      "pos = [4, 4]\n",
      "sa = [0, 2]\n",
      "sb = [8, 2]\n",
      "\n",
      "plt.scatter(*sa, s=100)\n",
      "plt.scatter(*sb, s=100)\n",
      "plot_iscts(N=4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4rsGGL8IUT5iA74038P3jH9hdu/KPwbcRT6SC3vZNBj/+cQ5QFzhNdu5MHfO8\n/edTt4i4iHx9+vVKREQaXN3uLXW3/aNHw913wxVXpOYiGgZmTQ0Dtj5Nu3Yeo0cnOP10m6lTY5SX\nB7jxxhw2bPDx7sdhnG9+k9VXjOFv7f+Jt5YHGDEizIgRYTZu9JFIQHW1ycyZWZSUJNJL9hQVHb5r\nWkS+HgVGERE5IXyhEFZOTmpR7oICTMvC9Dy+tftvFBc7TJgQT3cyV1ebvPWWSfv2Bqu+7MGuXQbV\n1SY///n+4zNnZjFiRDL9+tddl+T3v6+hVy+bzm28DGciIl+VhqRFRKRR1d+azzd9OvzoR6nboRDO\nmjX4EgkuvTmfd3N6AXDuuUn+3/+rZdMmH8OGpaqUkybFqK4+tGoYDnvk5bk8+GAtrcIOHdt4dJo3\nCzcaPWTRbxH5+lRhFBGRBlHXEZ1JctcuAIK5ufuXzPH78a1axbnf3MOiRXv5xS9iVFaaTJ58YDUx\nGjWYMmV/p/OUKTGGD0/wpz9FuLJqHr1/N53ObWwMbQUo0uBUYRQRkeNWv4p48BZ9dU0wyV27MGfM\nAMOg5qc/xXzqKcjNJXHGGawvvAKnEjZvthg7NgQc2shSW2swZ06A3/42gt8PrVt79MiN0KagAPvM\nUTjRKL5Q6JCGGxE5fqowiohIo7PCYcxgMNXw4nnw6qvgeSSuvpq3c77Dxo0+PvwwFRbrVxXrGlkm\nTYrx+us+ZsyIEQ57fCuyjDN+U4pv0SJqNm0iuWsX7oIF6dCqsCjSsFRhFBGR43a4pXQOFszNJVpa\nCk8+ibFjB5uvvoV1H/nTazE++mjNIc+57LIkwaBHnz42v/udTTDosWuXAb16pR/jrVyJuXQpGAZu\njx6H3SJQRI6PAqOIiDSIY6nq+fPy2HTdj9habcAOgzFjstMLbt99dxb33htl/PjUkPR990Xp1Mnl\nmmuS7Nrl8cknPpYvT/3Y2n5ZZwb+538SKC+HL75IVS4DAcySElUXRRqBAqOIiDQ613XZvDlKVZVD\nJGIyblyIYcPsAx6zebOPTz81eOKJGoJBj1DIo1Ur+PBDgy+/NPnyS5Py8tQC4EVFLh90bE+fvn3J\n+stfcEtL8bdtC6TmUyo0ijQszWEUEZFGZds2L71UywsvGNxwQ5gf/jCHW25J8uc/Wwfs7/yrX9Vy\nySVJunVz6b3nTXq1+5LcTSvIzvZo08Y7YI3GmTOz2L7d4C+xy4hddx1mMIgTjR6wh7WINBxVGEVE\npMG5rkuGKypAAAAgAElEQVRFRRLD8PjkE5u//MWivDyQHn6eNSvINdckeeSRAAsXRgCDrCyXXtYG\nsu6dS7JfP+yiIoJ/+hP9/72Adyq7HvIeb75p8dhjQX7723O54JlyzD17VAURaSQKjCIi0qBc12XJ\nkjijRgUZOTLBkX7UhMMe99yT6nou3rkCq7An3jvrSfbrh/+99/C/9x7xa66BHTs4v7vFnDld0g0y\nkyfHmDYti0AAkkmoOP8aejz2CygtTe0ooyFpkQalwCgiIg3GdV0++CDGqFGp4eNIxOD1132MGZNg\nypQYP/95FgBlZVG6dXPoX/08/leq4MYbMe+9Fzc3l2TfvqnX6tqVwIsvgmFgf+tbDDrvPBYu7E5t\nrcG4cSECAZg+Pcrnn5sEg2G63HUXbdq0OZmXL9JsKTCKiEiDqKssLlmyf2D46af9TJ0aY86cAN/9\nbpKFCyP4fBDeu5XT3vwD/PCHmMFgapvAfc+x/v537H79cPLzCVRXYzgO5hdfYM2dS98f/YiPAt2Y\nMCFOVZVB27Yeb71lsXq1jz17kgwaFCFcr7pYN5dRFUeR46PAKCIiDaKiIsmoUUESCZg8Oc6sWUEA\neveGRYtsDMOksDCMW1uLM/XXuPn5mL/8ZWpJnOnTobQUe+VKrFWr8AADSA4dirF1K/733sPz+bCW\nL+f0i3zsLCgkEDCoqjqwc/rtt20uvLCW7OzsjLvPiMhXo/nBIiLSoHbuNJkxIzV/cfHiGFdckUX3\n7lkUFQUxTTMV3EpLcTt0gHg8/TxfKIS5dStmZSXWqlW4HTrgtmkD7drhTp6MM2EC+HxkPfggAzqv\np3v3QzunIxGDt96ySSQSJ/FvQKT5UYVRREQaRGGhn3nzUs0uAEOGePTpk4VpHlqb8IVCsHYtbnEx\nZkkJAE40ivXBB6nh6OJigk88gWHbuD16YF56Kea990I8nprbuHQpeZd0AHIOeN0vvzQxTZdVq6Kc\nd14rnNJSQEPSIsdLgVFERBqEaZoMGRJk+fIkAIWFQdzaWlwODWx1Wwn6IL1+IgClpVBTg7l0KYbj\npLb769Bh/3BYMAg33ZR6/Ycf5jdzJnLrmFSjy6xZUWbPDjBggMPQoUkqPt1N3sNlANgakhY5LgqM\nIiLSYEzTpKgoVWE82hxCKxzGjkRwFyzAjMUgK9VBbf3qVxCLkRw4EHPDBoxt27BrajDHjwfA37Yt\nyUcewdy1i++supeFv/8pH//Dx+zZAb73PZtZs4KUlweYM6eWYe3bY+7ceeL+AkSaKQVGERE5qcyq\nqvTQdLpbOhjEyc+HPXtSDS/33ouXl4dZWUly8mQA7LPPxu3alX4991Ibbc2AAQ6zZgXTi4OPGZPN\n7347lkvO15C0yPFSYBQRkUZRN+ycvp3hMb76j5k+HScaJausDKdLFzzrwB9Vrm1jeh7Gjh2YgLVk\nCQPOOw+GXpPumK7z/At+en7DoKhVQ1+dSMuiLmkREWk0Vjh81OrewY+xwuFUUwzg27oVp18/vG7d\n4KabcCdPTg1ZJ5P4Kiqw3n8ft6AAq6qKS9b+moceqk3vTT1xYpxFi1QXEWkI+pckIiKnnLrKoxON\nYpWlGld8bdsCpIasA4HUf4aRHsoGuCYrizZtojz/vI+5c/3cd1+SwsLgSboKkeZDgVFERE5JdZVH\n++Bh7X1D2PUfV9/AgSY9eyYZO9ahsDB42GV9ROSrUWAUEZFT2mGX5Mmgfqe2iDQM/dolIiInnR2J\npPd9FpFTjyqMIiJyUmnPZ5FTnyqMIiIiIpKRKowiInJSHct6jUB6yFoVSJETT4FRREROuqOFQA1b\ni5xcGpIWERERkYxUYRQRkVPesQ5bi0jjUGAUEZEmQUFR5OTRkLSIiIiIZKTAKCIiIiIZKTCKiIiI\nSEYKjCIiIiKSkQKjiIiIiGSkwCgiIiIiGSkwioiIiEhGCowiIiIikpECo4iIiIhkpMAoIiIiIhkp\nMIqIiIhIRgqMIiItjB2JYEciX/mYiLRc1sk+AREROXHsSARn6tTUF9OnY4XDx3RMRFo2BUYRkWbM\ndV0qKpIAFBb6v9Jz6yqNCo4iosAoItJMua7LkiVxRo0KAjBvXpwhQ7Jh+nTg0CBohcPpY4CqjSKS\npjmMIiLNVEVFklGjglRXm1RXm4waFaSiIokVDh8xAGY6JiItlyqMIiItyO7dDps3xyks9GOaR64Z\n1K82KkCKiCqMIiLNVGGhn3nz4uTlueTlucyeHeXWW/088IDHX/8axbbtjM8/UrVRndQiLY8qjCIi\nzZRpmgwZEmT58iS7dzvcemuAH/wgyYYNJs8/7yMejzF0aHbGSuPB1Ekt0jIpMIqINGOmaVJUFGTj\n+r0MGmTgOFBeHgCgqMjlzDPjFBWFTvJZisipToFRRKSZsyMRusyfyZDLJ3Djv7WlujpVUZw5M4tz\nzqmhS7s9mKaJFQ6nKojRKL7QoSEyPURdb26jlt4RaRkUGEVEWgAjGqXr56uAy9P3tW3rEovBW+/B\n2ZG/YvXpA6++irViBU4wiN23L17r1vg2bsSsqsIpLT0gSB5tePrgNSC/ytC3iJxaFBhFRJq5uqpg\nN8/jN62j3HpriLZtXaZNi3PTTTkAzJ49kMHvvIhl22AYeAC2jX/pUpzCQpIXXYS/rIxkfj5mVRUA\n7vjxR+ycPPwakEGFRpEmSoFRRKQFqKv+DRtms3BhDTt3wujROenh6dtvz2b+/GFc0P5tvCuuwHjt\nNbBt7LPPxty2DWvZMtyCgv0v6Hm4L78M+fmYJSVY4fABFUXD8NJrQAKMGpVqvikqCp7YCxeRBqFf\n9UREWhDLsuja1WLbtkO//S9e7OejVufDK68A4Hbtim/NGszKStz8fNwOHQCw77gDNz8fa8UKAIxg\nkHXr9vLss7VccIGfCy7ws3q1Q9u27gGv7yYSjXx1ItJYFBhFRFqYoqIgRd0cfvWr2vQajf/1XzFC\nIY/aWoO/f+v72IWFWB98gOE4eD4fTp8+WGvXpkLjq69ibtwIwSCJkhLeXg07dsCYMdnpXWVuvTXE\nnDn714B8tGwzXfNO9pWLyNelIWkRkRagfjezW1vLgE1P8tE532fBghpefdUiK8vj0UezePTRIPfe\nG2V3h/O5JL6cZP/+OL16EVi+HHf8eKxf/hI3N5f48OF8cdpFrF9p8vLLfkIh75D3LC72sXx5EjeR\noGteR/ytWp3oyxaRBqIKo4hIM1fXzexMnZpeNgfDoNeHfyYnx6NnT5e77w6lq4Pjx4cIBg0qvjca\na9Uqsp54As9LBUK3oIDEN7/J2jYXs2Fj6rHl5QFycz3uuiuarig+/HCUbt0CFBUF6XFaK4VFkSbu\nmALj1q1bKSkpoVOnToRCIXr37s1rr73W2OcmIiKNxHr/fazKSvp030thoXvI8T/9yc+q90PEJ00C\nwEgmSX74IVXX/JCX7Cu54YYwJSU53HJLkkQC/ud/sti82eSxx2p44okahl1u49bWnujLEpFGctQh\n6V27dnHRRRdx6aWX8uKLL5Kbm8uGDRvo1KnTiTg/ERE5TlY4jFNamr4NkOzRA7dDBwKexwXnxHjw\nQYOf/CQbgIkT48yYEaS8HJ580uXsKVOgupo1tafBFwbjxoXS3c+zZgUZMSLJc8/5ufRSG9N0GXAO\ncPfdOKDtA0WaiaMGxv/93/+loKCA+fPnp+8rKipqzHMSEZEGZEciUFaWur1vlxZzyxbMjRtxt24l\na9s2vvPDH7JwYTHPPONnxozU0jcjRyYwDIgQ5uPdp7Fhg4/OnQ+tRobDHnPm1PLN02y6F7chuWMH\nbr31GkWk6TvqkPSzzz7L+eefz/e//306d+5Mv379mDNnzok4NxEROQE8AL+fzp0dvv1th06dXKZO\njRGLeXTu7LJypcnatRZ33hniP/8zxP3375+rOHt2LdddF2fQJVGKv9GO5I4dUFaWCoulpaouijQT\nR60wbtiwgYceeojx48czefJkVq1axe233w7AmDFjGv0ERUTk+By8/zOAM3ky9vPP47Vqhc8wyJoz\nh86DBtGr1yB+8xsXw3Dp39/giy9M/vY3P+XlgXRTzLRp8NhjNWRlQTjsUrz1DaznPyc6eDDuyy9j\nxWKQlXXY/ahFpGkyvLrWtyMIBAKcf/75LFu2LH3flClTeOaZZ1i3bl36vt27d6dvr1+/vhFOVURE\nGkq2adLtlVegQwfMzz/H69gRY8cOkqedRuSC77BmTWq5nG99y2H1al86MALk5bksWFBD7942rRc/\nQ2DlSjyfj8RllxFYupRk//580a8fXzrOSb5KETlWp512Wvp2mzZtDjl+1Apjfn4+Z5555gH3nX76\n6Xz22WcNcHoiItJYsvft21zrHjrvEFLzGJ19gZHPPyc+ZAjbel3Emrd9jBmTaoA57bQoAwbYFBW5\nzJyZBcCcObV8u/cegv/zPzhnnYVnWRi2jbV+PXaPHkcMi0c7HxE5dR01MF500UV89NFHB9z3j3/8\ng+7dux/xOf379z/uE2sqVq5cCbSsaxZ97i1RU/vM69ZeBPAdoVM52qkT1uOPYyQSxL7/fT7K6ke8\nyuDdd30kErBzp8n06SFuuy1G//6pPagDAS+1SHdNDTgO1vvvE7/6avyrV+OrqMCYPJmeXbt+rfM5\n1TS1z1yOX0v+zOuPFB/OUZte/uM//oPly5czY8YMPvnkE/7whz8we/ZszV8UEWmi7EiEaGUlrm2D\n5xH70Y94edu5XH99mO9/P4dOnTzuvjtG+/apSuAZZ7g4jkFxscv114d59VU/H+/qTPI738E++2ys\n1aux+/bFLSzEDAZP8tWJSGM4aoWxf//+PPvss0yePJl77rmHoqIi/vu//5vbbrvtRJyfiIh8DYdr\ndIFUWEw+8gjmxo0YPh/x736XD2p7cvvt2ek5ijNnZjFyZIKSkgQXX2zTqZNDp07QtWub9PGFCx32\nnH8+7R5/HLOqCnPrVpLDhhHY9x4HVxCPdD4i0jQc017SV111FVdddVVjn4uIiDSgIwUzt0MHzA0b\niF9/PYu/OI/ly32Hfdw11yTJzXUxTbjssgO39vvsMwNoRd/rryc4Zw44DubWrbgLFkBV1SELdtff\ny1pEmh7tJS0i0sKYgwcTu/Za3uU8xo4NsWBBgP/6r1h6bcVJk2JcdlmSc3rtoXjRbyhIbGT27Nr0\n8fvui/LppyaxmMFfPy4gPmECztlnY61ciXuY7sqD97IWkabnmCqMIiLS9NmRCMn77+eTc77LnjYD\n2PBhqmawc6fJPfdkceutcYYOtTFNj2/lrMf3xqe47dphbtnC4P5t+d3vOlBRYbJ3Lzz8cBYPPwyT\nJsVYX9CO3p99htOtG27XrrjDhhFUJVGkWVFgFBFpIVzXZckZt7NpvZ/Nm03efNPHL34R5ac/TS2w\n3a+fSyjkcvqWVwj+/hXsfv3wv/de6s+XXiL/36dhmgFGjsyhutqkfXuXzZtN+vUz2fLPo+n82fsE\nliyBl19Ob0EImr8o0hwoMIqItBAfbbL42xsm5eUBEgmYPDnOgw8GuOeeKMXFLkVFLoW5Bsl1u3HO\nPRffjh0AmNu3k7zySrrEPqPS/gYA7du7TJ4cZ9asIOXlAebMMRgU8MAwAEju2gVPPpnaIrCJLKMj\nIkemwCgi0gLt3GkyY0aQkpIEZ5zh0K+fRXZ2q1SH89q14Hm4EyZg2zZ2ZSX+ZcvwrVvHeadXMmfO\n5SxbZjFrVjDdWT1mTDYLF17KuaXfxgeYZWUQi+EWF3P4lhoRaUoUGEVEWogzzwxw2WWxA3ZtGTzI\n5sILw5immWpOiUZTD47HcV9+GXP7drI2bUoFyB49sM46i0H+3XTs2Jry8sABrx+NGvx9U4CzTzdx\nAbKyMEtKVF0UaQYUGEVEWgjLsrj66iw++ijOgAG1dOzoo6goe39Y3LcTS3LMGIylSzG3bsXz+8Hz\n8Hw+3O99j2DHjlhTp9Lle2MoK8ujtDQ1/3HixDhjx4a4994on+9wydOcRZFmRYFRRKQFsSyLPn2O\n/K3fzc/H/+CDkEhg9++PNXw4dk0NpmWR07Ur8W3bIBaj8OmH6TH8TkaOTBCJGMyYESQQgJdf9hMO\nJ+nU3iXQuvUJvDIRaUxah1FERLDCYXzTp2OWlKQaV4JBrOHDCebmktO9O6F9+0P7QiHc4mLsCy+k\n/2kRLr7Y5rnn/AQCqSrjokUWsRisW++d5CsSkYakwCgiIkAqNAZzc/FNn45v+nSCubmHfQw33oj/\nlVewfv5zhlwS5dFHaxg5MsHcuX6mTYvzyCMBErZ+vIg0JxqSFhGRAxxt3qEZDKZv+4G+fSEcTjJs\nWJJHHgnw3e/adMnXjxeR5kT/okVE5CvxhUIkJ0/GDAYJ5ubSxXVZvz7K5s0wbJhNQQEUFASP/kIi\n0mQoMIqIyDGr66Y2Ad++TmjTNLn00hA9eiQBKCz0Y5oakhZpThQYRUTkqOxIJONx0zQpKjqwqui6\nLhUVCpEizYECo4iIZFR/jca6hhjIPNfRdV2WLIkzalQqRM6bF2fIkKBCo0gTpX+5IiLylVjh8FEb\nYyoqkowaldo6sLraZNSoYLraKCJNjyqMIiKSkRUOw1fcucVNJEj1UItIc6AKo4iIHNWxVBXr2JEI\nXebP5NGyzeTlueTlucybF6ewUAFSpKlShVFERBqcEY1y+fq5vPnaJMxAgMJCzV8UacoUGEVEpEHV\nH8LucYxVSRE5tSkwiohIgzvW4WsRaRo0PiAiIiIiGSkwioiIiEhGCowiIiIikpECo4iIiIhkpMAo\nIiIiIhkpMIqIiIhIRgqMIiIiIpKRAqOIiIiIZKTAKCIiIiIZKTCKiIiISEYKjCIiIiKSkQKjiIiI\niGSkwCgiIiIiGSkwioiIiEhGCowiIiIikpECo4iIiIhkpMAoItJE2ZEIdiRysk9DRFoA62SfgIiI\nfHV2JIIzdWrqi+nTscLhk3tCItKsqcIoIiIiIhmpwigicpLVDSt/lSqhFQ7D9Olf+XkiIl+HAqOI\nyEmQTCZ5//04nuvR5/Vf46uq+spDywqKInKiaEhaROQESyaTPPNMgmuvzea663N4vnA0Tn5+g7y2\n67ps3hxn8+Y4rus2yGuKiCgwioicYO+/H2fs2BDV1SbV1SZjx2Wz6sIf4wWDwP7u56/aBe26LkuW\nxLngAj8XXOBnyRKFRhFpGBqSFhE5gexIBM/1Drn/6af9bN0a5+rBtZh3342bn49ZVZU6eAxD1a7r\n8sEHMZYsMUkkYOdOk1GjgixfnqSoKNgYlyIiLYgqjCIiJ0jdUjh9Xv81DzwQJS/PJS/PZeLEOAsW\nBLj99mxeW24e0/B0/epjXWVx6NAsyssDTJ4cp317VRZFpOGowigicgLYkQhONAqAr6qK635kU/BU\nDU8/7WfGjCA7d5rk5bksXuyn1Q23ct5ZBoZhpJ9zyGvtW4PRuesu3vu7yZIl/nRlcdasICUlCYYM\n8SgsVHVRRI6fAqOISCM7YJHt0lJ8oRBWOMz55yfZujVOeXmAvDyXKVNibNliEI8bfLHLpWNWAsrK\nSObn45SU4MbjAJjBIG5+Pk7r1iz+i4+f/CQbgMmT48yYkQqIP/yhS58+WZimBpJE5PgpMIqInCR+\nv5++fWuZP7+G115LfTuePz/I/PlBZs+uZbD1BoGOHTE3bMCbMQP3zDMBMNetwznjDN47fSRvPGsd\ntrKosCgiDUmBUUSkkdUtsp3ctQuzrAwHcPZVGouLc9i+vYYePVzuvDNEQYHD5MlxfD6PTwsvp9fu\n3RjbtoHnYezYgeF5xAYM4GVjGLd//9DK4j//c5Lzz89RWBSRBqXvKCIijSw9f/HJJ3E7dsTt0gV3\nwYLUMHUsRkFn6NrV5ayzbH760wRTpmTxt7/52bbNZPd3voN94YXYffpguC6JXr14v9NQ3nzT4ppr\nkiQSpCuLc+bU0u8M95Cw+FWX5xEROZgCo4hII0rPXywrw+3QAWPrVoy65XL2yc2KkJPt8rOfxZk2\nLcgdd8QJBj0qKkw++qgVznnnYa1aReLaa/l7l++wbZtJeXmA557zM3lynLZtXa69Nknf8Hq4++4D\nwmHd+ztTpyo0isjXpsAoInKiXH45huNgxOMkzzkH+447sMJhfIEAfSNv4PN5jByZwHEMnn3Wz7p1\nPnbuNHnzow7EJ0zglX9056mngtx+e3Z60e9Zs4I88EAUv98l/+NlJ/sKRaSZ0hxGEZFGVDd/EYBo\nFLdHDzzHwb98OeZTTxG/+26CubnEi4tpu3svAwe25sc/DnHLLUlmzQpSXh7gxRf3UhntgM/nceWV\nST74wKS6OpB+j3DYo3dRBF+vG/GFQkCqsmiFwwe8v/aeFpGvSxVGEZFGlg5qZWVgGNjXX49ZWQlA\ncs8eajZtwv/HP9L93T8RCHgMG2Yza1aQRAJGjYrTqRN88IHF6NE5lJTk8P/9f0kGD06Ql+dy//1R\neht/J+vnP8d+/nmcaPSQIeh0cBQR+ZpUYRQROYHMqir84TB2v354bdrg++MfMT77DK9LF/D7OcP8\niKFDz2DRIotbbkly440JNmwwGTcutfc0wLhxIRYurMHni9E7vAnr7Q9wu3bFzcvDrqnRN3YRaXD6\nviIicgLUHxoOhsPEr78eu6YGPvkEp29fzG3b8K1di11czAWn7+SBB9rTu7fL22/7WLbscN+qPXp3\nrCY45/9wCwpwOnUi8Nxz8NxzJCdMIKtzZ1UVRaTBaEhaROQEqRsaTg8V5+Tg9OqFb80azMpK3Px8\nAu+8A3v30ru3y5o1JmPGZLNgQYCJE+Ppvafvvz9K3x57CD74IPFrr8W3aRN4Xvp9jKVLSe7apa5o\nEWkwqjCKiJxA6WV24nHs/v3x8vLAdcEwcIqL8Tp2hHbt2LTJ4OWX/UBqF5cZM1JrLf7TPyUpKHDx\n/fnP4DhYGzaQHDgQp0cPvHbtMFwXY/du3Jdfxlm7FqZPV6VRRI6bKowiIidaXTXQtjFqa4n/4Ack\nzzmHwF//ihePs/rTMK5rsGiRla4sBgJw0UU22dkuo0eH+PjbP8ArKMD3/vt4QPDxxzFcF/9f/4pv\n3TrMHTtO5hWKSDOjwCgicgJZ4TDuhAm4BQVYq1bhtmtH1m9/C56H06kTn3QawLZtPu65J8i0aXHm\nzvUzcmSCRx+toWNHhxdf9LF2rcWOHQaJa6/F8DysTz/FvvhiPMNINdMUFGCWlODbV13UTi8icrw0\nJC0icoL527YlGQjg9OiBuWEDnmnif+89toyfzvZPTX7yk9TC3Dt3GsycGaVNG8jJcYnH4aGHspky\nJcaGDSbt2hXSa/Bgsl5+GTwPzzTB58OsqsIXCqXDojN1auqNNTwtIl+TKowiIieBuWUL5mefYXge\nTt++xMaOZf2nQRYv9qcf8+67fkaPziEahfx8+Ogji3/+5wR33ZXF3XeHiP3/7d1vjJX1nffxzzkz\nwIA1p3QVq7tdkF2nygCVmz8KtrFuXbrUSqgpNiZtWPvAmIKZwiN3iuiaW8aYNt5KQVnWkN0aU+zW\n0GZjuzaBtbBAE1cw/lkpG3bVVrFL1CGdyr85537ADZXb3R8gzJxxeL0SErhmgO/knMz1nt/1u87Z\nX83rn/yz9I0de+R1HVtaUjl0KPXzz8+BvXutKgJnjBVGgGaoVFLp60ujVkvfwYN57s2L8k//NOzY\nvsVvf3tEkmTlyt9lVvtv8m+vnZ877vj9azF+/OP1HDrUyJ43q7noqqtS/9M/TWXq1NT/9V9T3bUr\nrffdl0Pjx2fYrbemxTu9AKdJMAIMoKOrfi13352+d99NNcm/PNuW/W/n2It1H923+PnPH8qVl76V\nEd/+P7nsL/8yDzxwaTo7j7z13wMPvJuVK0dk7NhG3v705fnCs92pbN6cvgsuSMurr6b+R3907P8U\nisDpckkaYIAc3U94dE/hiPPPz0v/eeQy9MqVv7/JZc6cw/n85w9l4oR9aX3qqRz6i79I5Z138qnJ\nB/P44735+7/vzbp1rZk1q56/+7vhWbhwVF6bfn2SpFKvp9HSkr5PfrKZXyowxFhhBGiSer2eAwcr\nx1YWH3lkWO6999189KPJH/xBPaN/sC6V/fvT8vzzqRw+nD/8X/+RV/54fqrVasaObWT58hF5661q\nPv7xev7znI788V13pXrwYA739qblH/4h1ddfb/aXCAwRVhgBBkjrRz6SlrvvTsvdd6c6alSeeupA\nnnyyNQsXHszf/u2wTJxYz8GDlfzud42M/+matPz7v6d+4YVJS0uSpOU3v8kVI3bk3HPrmT69L8OH\nH9nLePvt+/PP/9ya53dVj9wd/eCDR2Lxr/7K5WjgjLDCCDCAjgbcK68cyM03j8jBg8lf//X+zJt3\nKH/yJ/V87KP1zPivf0zL668nbW1p/eIX0zJ/fg69806qI0akLUnbr5K77x6R668/lCR5+OHhmTPn\ncPbtO7JqeVTLyJHN+BKBIUgwAjTRW29Vc+edbVmw4GAmT6rn8suSanVuMndukt8H5ntfU7H9Yx/L\nPf/7m1m4aFSS5Pbb9+fCC+vp6mrL3/zNoUxwVzRwhglGgCb4xCeGZe3aI6uMSTJ7diPTpp+TavXE\nO4Wqb72VL/55PX+4/rfZt6+S11+vpKurLb291SSHhCJwxglGgCaoVquZPXtEtm07cln5E58YccJY\nbP3IR5L3rB5OnXo469cfyO23H7n0vGLFu5kwYUT/Dg6clQQjQJMcudv51ALvvauHra2tmTcvaW/f\nnySZMGFEWlt9WwfOPN9ZAD7EWltbM3myb+VA//KyOgAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQA\noEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlG\nAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECR\nYN8vTCAAAA2hSURBVAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgw\nAgBQJBgBACgSjAAAFJ1SMHZ3d6darea2227rr3kAABhkTjoYt23bljVr1mTy5MmpVCr9ORMAAIPI\nSQVjT09PvvrVr2bt2rUZPXp0f88EAMAgclLBeMstt2T+/Pm5+uqr02g0+nsmAAAGkdYTfcKaNWuy\ne/fuPPbYY0nicjQAwFmm0igsGe7cuTOf+cxnsnnz5rS3tydJPvvZz2bSpElZsWLFcZ/b09Nz7Pe7\ndu3qp3EBADjTLrnkkmO/r9Vq7/t4cYVx69at2bt3bzo6Oo4d6+vry6ZNm7J69er09vZm2LBhZ3Bc\nAAAGm+IKY09PT379618f+3Oj0cjNN9+c9vb2dHV1ZcKECcd97lH/XZkOVc8880ySZNq0aU2ehIHk\ncT/7eMzPPh7zs8/Z/JifqOOKK4y1Wu19f2nUqFEZPXr0cbEIAMDQdcrv9FKpVNz4AgBwFjnhXdL/\nv40bN/bHHAAADFLeSxoAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLB\nCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAo\nEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEA\ngCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQY\nAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABF\nghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIA\nUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQj\nAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBI\nMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAA\nigQjAABFghEAgCLBCABAkWAEAKBIMAIAUCQYAQAoEowAABQJRgAAigQjAABFghEAgCLBCABA0QmD\nsbu7O9OnT0+tVsuYMWMyd+7cvPjiiwMx26DXaDTS1taWtra2NBqNZo8DAHxAzullrSf6hKeffjqL\nFi3K9OnTU6/Xs2zZslx77bV56aWXMnr06IGYcdBpNBp5/vkD2bYtWb++PUkyb96BzJyZTJw4IpVK\npckTAgAnwzn95JwwGH/6058e9+fvfe97qdVq2bJlS6677rp+G2ywajQa2bhxf264oS09Pb9/Ev3k\nJ0mt1sgTT+zPNde0eYIBwCDnnH7yTnkP4759+1Kv18/a1cXnnz/wvifWUT09ldxwQ1teeOFAEyYD\nAE6Fc/rJO+Vg7OzszJQpUzJz5sz+mGdQazQa2bYt/+0T66ienkp+8YvY/wAAg5hz+qk54SXp91qy\nZEm2bNmSzZs3F5dnn3nmmdMebDBqa2s7tr+h5Iknqrnyyhezf//+AZiKZhqqz3X+Zx7zs4/HfGhy\nTj/eJZdcUvz4SQfj4sWL8/jjj2fjxo0ZN27c6c4FAMCHxEkFY2dnZ37wgx9k48aNaW8/cY1Pmzbt\ntAcbjBqNRubNO5Cf/KT8eTfcUE9HR4dNskPY0RWHofpc5/085mcfj/nQ5px+vJ6enuLHTxiMCxcu\nzKOPPpr169enVqtlz549SZJzzz0355xzzpmZ8kOiUqlk5swjd079T3searVGrrgiQ/6JBQAfZs7p\np+aEN7089NBD+e1vf5vPfe5zueiii479+s53vjMQ8w06EyeOyBNP7E+t9v4NsEdvwZ84cUQTJgMA\nToVz+sk74QpjvV4fiDk+NCqVSq65pi2bNh3IL35xZDNscmTJ+oorkokTvV4TAHwYOKefvFO6S5oj\nKpVKJk1qy8SJjVx55ZG3STwb9jcAwFDjnH5yBONpqFQqx26z98QCgA8v5/SyU37hbgAAzi6CEQCA\nIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgB\nACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWC\nEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQ\nJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMA\nAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgw\nAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACK\nBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQA\noEgwAgBQJBgBACgSjAAAFAlGAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFAlG\nAACKBCMAAEWCEQCAIsEIAECRYAQAoEgwAgBQJBgBACgSjAAAFFUajUbjTPxDPT09Z+KfAQCgiWq1\n2vuOWWEEAKBIMAIAUHTGLkkDADA0WWEEAKBIMAIAUCQYT9OqVaty8cUXZ+TIkZk2bVo2b97c7JHo\nJ93d3Zk+fXpqtVrGjBmTuXPn5sUXX2z2WAyg7u7uVKvV3Hbbbc0ehX72xhtvZMGCBRkzZkxGjhyZ\njo6O/PznP2/2WPSTw4cPp6urK+PHj8/IkSMzfvz43HHHHenr62v2aIOGYDwN69atyze/+c0sXbo0\nO3bsyKxZszJnzpy89tprzR6NfvD0009n0aJF2bp1azZs2JDW1tZce+21efvtt5s9GgNg27ZtWbNm\nTSZPnpxKpdLscehH77zzTq666qpUKpU8+eSTefnll/Pd7343Y8aMafZo9JPly5dn9erVWbFiRXbu\n3JkHHnggq1atSnd3d7NHGzTc9HIarrjiilx++eVZvXr1sWPt7e358pe/nOXLlzdxMgZCb29varVa\nfvSjH+W6665r9jj0o56enkydOjWPPPJI7rrrrkyaNCkPPvhgs8ein3R1dWXTpk3ZtGlTs0dhgFx/\n/fU577zzsnbt2mPHFixYkLfffjs//vGPmzjZ4GGF8QM6ePBgnn322cyePfu447Nnz86WLVuaNBUD\nad++fanX6xk9enSzR6Gf3XLLLZk/f36uvvrq+Bl76Fu/fn1mzJiRr3zlK7ngggsyZcqUrFy5stlj\n0Y/mzJmTDRs2ZOfOnUmSl156KRs3bswXvvCFJk82eLQ2e4APq71796avry8XXHDBccfHjBmTPXv2\nNGkqBlJnZ2emTJmSmTNnNnsU+tGaNWuye/fuPPbYY0nicvRZYPfu3Vm1alWWLFmSrq6ubN++/di+\n1YULFzZ5OvrDN77xjfzqV7/KZZddltbW1hw+fDhLly7Nrbfe2uzRBg3BCB/AkiVLsmXLlmzevFlA\nDGE7d+7Mt771rWzevDktLS1JkkajYZVxiKvX65kxY0buueeeJMmnPvWp7Nq1KytXrhSMQ9SDDz6Y\ntWvX5vvf/346Ojqyffv2dHZ2Zty4cfn617/e7PEGBcH4AZ133nlpaWnJm2++edzxN998MxdeeGGT\npmIgLF68OI8//ng2btyYcePGNXsc+tHWrVuzd+/edHR0HDvW19eXTZs2ZfXq1ent7c2wYcOaOCH9\n4aKLLsqECROOO3bppZfm1VdfbdJE9Ld77rknS5cuzY033pgk6ejoyCuvvJLu7m7B+P/Yw/gBDR8+\nPFOnTs1TTz113PGf/exnmTVrVpOmor91dnZm3bp12bBhQ9rb25s9Dv3sS1/6Ul544YU899xzee65\n57Jjx45MmzYtN910U3bs2CEWh6irrroqL7/88nHHfvnLX/oBcQhrNBqpVo9Pomq16mrCe1hhPA1L\nlizJ1772tcyYMSOzZs3Kww8/nD179tjzMEQtXLgwjz76aNavX59arXZsr+q5556bc845p8nT0R9q\ntVpqtdpxx0aNGpXRo0e/bwWKoWPx4sWZNWtWli9fnhtvvDHbt2/PihUrvMTKEDZv3rzce++9ufji\nizNhwoRs3749999/fxYsWNDs0QYNL6tzmh566KHcd999eeONNzJp0qTcf//9+fSnP93ssegH1Wo1\nlUrlfT9x3nXXXVm2bFmTpmKgXXPNNV5W5yzw5JNPpqurKzt37szYsWOzaNGiLFq0qNlj0U96e3tz\n55135oc//OGxrWU33XRTli1bluHDhzd7vEFBMAIAUGQPIwAARYIRAIAiwQgAQJFgBACgSDACAFAk\nGAEAKBKMAAAUCUYAAIoEIwAARf8X9EeGITMeOz0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d429d68>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I placed the sensors nearly orthogonal to the target's initial position so we get theese lovely 'x' shape intersections. I then computed the (x, y) coordinate corresponding to the two noisy bearing measurements and plotted them with red dots to show the distribution of the noisy measurements in x and y. We can see how the errors in x and y change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the y coordinate of sensor B the shape becomes strongly elliptical.\n",
      "\n",
      "Next I will alter the starting positions and rerun the simulation. Here the shape of the errors in x and y changes radically as the target position changes relative to the two sensors. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sa = [3, 4]\n",
      "sb = [3, 9]\n",
      "pos= [4, 4]\n",
      "\n",
      "plt.scatter(*sa, s=100)\n",
      "plt.scatter(*sb, s=100)\n",
      "plot_iscts(N=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uTbB0KfFMZqNp9WDpUoqHHkqwZAk0NbnuUYqgw2nrOXPm8MUvfpGTTjoJgH79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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d41f518>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Visualize Sigma Points"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Early in the chapter you were asked to pass points through a nonlinear function and to plot the mean. Use the UKF to generate sigma points and pass them through the nonlinear function, and plot the sigma points and their mean against the 5,000 points.\n",
      "\n",
      "Pass the points through the state transition function:\n",
      "\n",
      "$$\\mathbf{Fx} = \\begin{bmatrix}1 & 1 \\\\ .1x &y\\end{bmatrix}\\begin{bmatrix}x\\\\y\\end{bmatrix}$$ \n",
      "\n",
      "for the mean $$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}$$ and the covariance\n",
      "$$\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Your solution here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import unscented_transform\n",
      "\n",
      "def f(x,y):\n",
      "    return np.array([x+y, .1*x**2 +y*y])\n",
      "\n",
      "mean = (0, 0)\n",
      "p = np.array([[32., 15],\n",
      "              [15., 40.]])\n",
      "\n",
      "\n",
      "### compute mean via UKF\n",
      "kappa = 0.\n",
      "w = UKF.weights(2, kappa)\n",
      "sigmas = UKF.sigma_points(mean, p, kappa)\n",
      "sigmas_f = np.zeros((5,2))\n",
      "for i in range(5):\n",
      "        sigmas_f[i] = f(sigmas[i,0], sigmas[i,1])\n",
      "  \n",
      "\n",
      "ukf_mean, _ = unscented_transform(sigmas_f, w, w, np.zeros((2,2)))\n",
      "\n",
      "# generate 500000 points to compute accurate mean\n",
      "np.random.seed(73291)\n",
      "xs ,ys = multivariate_normal(mean=mean, cov=p, size=10000).T\n",
      "fxs, fys = [], []\n",
      "for x,y in zip(xs,ys):\n",
      "    fx, fy = f(x,y)\n",
      "    \n",
      "    fxs.append(fx)\n",
      "    fys.append(fy)\n",
      "\n",
      "computed_mean_x = np.average(fxs)\n",
      "computed_mean_y = np.average(fys)\n",
      "\n",
      "\n",
      "plt.subplot(121)\n",
      "plt.scatter (xs[0:10000], ys[0:10000], marker='.', alpha=0.1)\n",
      "plt.scatter(sigmas[:,0], sigmas[:,1], c='r',s=50)\n",
      "plt.axis('equal')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.scatter(fxs[0:10000], fys[0:10000], marker='.', alpha=0.1)\n",
      "plt.scatter(computed_mean_x, computed_mean_y, \n",
      "            marker='v',s=300,c='k', label='computed')\n",
      "plt.scatter(ukf_mean[0], ukf_mean[1], \n",
      "            marker='o', s=50, c='r', label='ukf')\n",
      "plt.ylim([-10,290])\n",
      "plt.xlim([-150,150])\n",
      "plt.legend(loc='best', scatterpoints=1)\n",
      "plt.show()\n",
      "print ('Difference in mean x={:.3f}, y={:.3f}'.format(\n",
      "       computed_mean_x-ukf_mean[0], computed_mean_y-ukf_mean[1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WM6AdLeA0r2uOgmUwSuPBYJWIiKiKZQaJxmgtrsolV71qJWSFqXIxWCUiIqoR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Fzm80JIDw+FaHY6xwlspQKJRJRGo0OrRb+iKfdLp+V32t4WaYDryqR8PC4uBclk8DNFJGI5d87Q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\nbsR1112HhQsX4itf+Qp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       "text": [
        "<matplotlib.figure.Figure at 0x7f07725400f0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Difference in mean x=0.083, y=-0.215\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Discussion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first exercise had an error of roughly 43 in the y axis, whereas with 10,000,000 points simulated the UKF has an error of around 0.03. It is very likely that a larger number is displayed above, but that is because I set the number of points to 10,000 so the cell will run quickly for you. I find this result very astonishing - using only 5 points the UKF generates a better estimate than using 5000 points with a naive algorithm. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementation (Optional)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implementing the UKF is quite straightforward. First, let's write the code to compute the mean and covariance given the sigma points. \n",
      "\n",
      "We will store the sigma points and weights in matrices, like so:\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "weights &= \n",
      "\\begin{bmatrix}\n",
      "w_1&w_2& \\dots & w_{2n+1}\n",
      "\\end{bmatrix} \n",
      "\\\\\n",
      "sigmas &= \n",
      "\\begin{bmatrix}\n",
      "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} &  \\mathcal{X}_{0,2} \\\\\n",
      "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} &  \\mathcal{X}_{1,2} \\\\\n",
      "\\vdots & \\vdots & \\vdots \\\\\n",
      "\\mathcal{X}_{2n+1,0} & \\mathcal{X}_{2n+1,1} & \\mathcal{X}_{2n+1,2}\n",
      "\\end{bmatrix} \\\\\n",
      "sigmas &= \n",
      "\\begin{bmatrix}\n",
      "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} &  \\mathcal{X}_{0,2n+1} \\\\\n",
      "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} &  \\mathcal{X}_{1,2n+1} \\\\\n",
      "\\vdots & \\vdots & \\vdots \\\\\n",
      "\\mathcal{X}_{D-1,0} & \\mathcal{X}_{D-1,1} & \\mathcal{X}_{D-1,2n+1}\n",
      "\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "In other words, each column contains the $2n+1$ sigma points for one dimension in our problem. The $0th$ sigma point is always the mean, so first row of sigma's contains the mean of each of our dimensions. The second through nth row contains the $\\mu+\\sqrt{(n+\\lambda)\\Sigma}$ terms, and the $n+1$ to $2n$ rows contains the $\\mu-\\sqrt{(n+\\lambda)\\Sigma}$ terms. the choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code a bit easier to code as I can refer to the ith sigma point for all dimensions as `sigmas[i]`."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Weights"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Computing the weights in numpy is extremely simple. Recall that for the Julier implementation\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "W_0 &= \\frac{\\kappa}{n+\\kappa} \\\\\n",
      "W_i &= \\frac{1}{2(n+\\kappa)}\\,\\,\\,\\text{for i=1,2..2n}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "These two lines of code implement these equations with the `np.full()` method, which creates and fills an array with the same value. Then the value for the mean($W_0$) is computed and overwrites the filled in value. \n",
      "\n",
      "    W = np.full((2*n+1,1), .5 / (n+kappa))\n",
      "    W[0] = kappa / (n+kappa)\n",
      "    \n",
      "Our final function will look something like this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def weights(n, kappa):\n",
      "    \"\"\" Computes the weights for an unscented Kalman filter. \"\"\"\n",
      "\n",
      "    k = .5 / (n+kappa)\n",
      "    W = np.full(2*n+1, k)\n",
      "    W[0] = kappa / (n+kappa)\n",
      "    return W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Sigma Points"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The equations for the sigma points are:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathcal{X}_0 &= \\mu \\\\\n",
      "\\mathcal{X}_i &= \\mu +  \\bigg[\\sqrt{(n+\\kappa)\\Sigma}  \\bigg]_i\\,\\,\\,\\, &\\text{for}\\text{ i=1 .. n} \\\\\n",
      "\\mathcal{X}_i &= \\mu - \\bigg[\\sqrt{(n+\\kappa)\\Sigma}\\bigg]_{i-n}\\,\\,\\,\\,\\, &\\text{for}\\text{ i=(n+1) .. 2n}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "\n",
      "The Python for this is not much more difficult once we wrap our heads around the $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ term.\n",
      "\n",
      "The term $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ has to be a matrix because $\\Sigma$ is a matrix. The subscript $i$ is choosing the column vector of the matrix. What is the 'square root of a matrix'? The usual definition is that the square root of a matrix $\\Sigma$ is just the matrix $S$ that, when multiplied by itself, yields $\\Sigma$.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\text{if }\\Sigma = SS \\\\\n",
      "\\\\\n",
      "\\text{then }S = \\sqrt{\\Sigma}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "However there is an alternative definition, and we will chose that because it has numerical properties that makes it much easier for us to compute its value. We can alternatively define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n",
      "\n",
      "$$\n",
      "\\Sigma = SS^\\mathsf{T} \\\\\n",
      "$$\n",
      "\n",
      "This latter method is typically chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition* [3]. \n",
      "Numpy provides this with the `numpy.linalg.cholesky()` method. If your language of choice is Fortran, C, C++, or the like standard libraries such as LAPACK also provide this routine. And, of course, matlab provides `chol()`, which does the same thing.\n",
      "\n",
      "This method returns a lower triangular matrix, so we will take the transpose of it so that in our for loop we can access it row-wise as `U[i]`, rather than the more cumbersome column-wise notation `U[i,:]`.\n",
      "\n",
      "    Sigmas = np.zeros((2*n+1, n))\n",
      "    U = linalg.cholesky((n+kappa)*P).T\n",
      "\n",
      "    for k in range (n):\n",
      "        Sigmas[k+1]   = X + U[k]\n",
      "        Sigmas[n+k+1] = X - U[k]\n",
      "\n",
      "    Sigmas[0] = X"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's implement the unscented transform. Recall the equations\n",
      "$$\\begin{aligned}\n",
      "\\mu &= \\sum_i w_i\\mathcal{X}_i\\;\\;\\;&(2) \\\\\n",
      "\\Sigma &= \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\\;\\;\\;&(3)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The scaled UKF uses different weights for the means and covariance, so we will use the variable `Wm` for the mean weights and `Wc` for the covariance weights.\n",
      "\n",
      "We implement the sum of the means with\n",
      "\n",
      "    X = np.dot (Wm, Sigmas)\n",
      "\n",
      "If you are not a heavy user of numpy this may look foreign to you. Numpy is not just a library that make linear algebra possible; under the hood it is written in C to achieve much faster speeds than Python can reach. A typical speedup is 100x. To get that speedup we must avoid using for loops, and instead use numpy's built in functions to perform calculations. So, instead of writing a for loop to compute the sum, we call the built in `numpy.dot(x,y)` method. If passed a 1D array and a 2D array it will compute sum of inner products:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([10, 100])\n",
      "b = np.array([[1, 2, 3],\n",
      "              [4, 5, 6]])\n",
      "\n",
      "np.dot(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "array([410, 520, 630])"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All that is left is to compute $\\mathbf{P} = \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}} + \\mathbf{Q}$\n",
      "\n",
      "    kmax, n = Sigmas.shape\n",
      "    P = zeros((n, n))\n",
      "    for k in range(kmax):\n",
      "        y = Sigmas[k] - x\n",
      "        P += Wc[k] * np.outer(y, y) \n",
      "    P += Q\n",
      "\n",
      "This introduces another feature of numpy. The state variable $X$ is one dimensional, as is $Xi[k]$, so the difference $Xi[k]-X$ is also one dimensional. numpy will not compute the transpose of a 1-D array; it considers the transpose of `[1,2,3]` to be `[1,2,3]`. So we call the function `np.outer(y,y)` which computes the value of $yy^\\mathsf{T}$ for a 1D array $y$.\n",
      "\n",
      "Our `sigma_points` function can be implemented as below"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sigma_points(x, P, kappa):\n",
      "    \"\"\" Computes the sigma pointsfor an unscented Kalman filter\n",
      "    given the mean (x) and covariance(P) of the filter.\n",
      "    kappa is an arbitrary constant. Returns tuple of the sigma points\n",
      "    and weights.\n",
      "\n",
      "    Works with both scalar and array inputs:\n",
      "    sigma_points (5, 9, 2) # mean 5, covariance 9\n",
      "    sigma_points ([5, 2], 9*eye(2), 2) # means 5 and 2, covariance 9I\n",
      "\n",
      "    **Parameters**\n",
      "\n",
      "    X An array-like object of the means of length n\n",
      "        Can be a scalar if 1D.\n",
      "        examples: 1, [1,2], np.array([1,2])\n",
      "\n",
      "    P : scalar, or np.array\n",
      "       Covariance of the filter. If scalar, is treated as eye(n)*P.\n",
      "\n",
      "    kappa : float\n",
      "        Scaling factor.\n",
      "\n",
      "    **Returns**\n",
      "\n",
      "    sigmas : np.array, of size (n, 2n+1)\n",
      "        2D array of sigma points. Each column contains all of\n",
      "        the sigmas for one dimension in the problem space. They\n",
      "        are ordered as:\n",
      "\n",
      "        .. math::\n",
      "            sigmas[0]    = x \\n\n",
      "            sigmas[1..n] = x + [\\sqrt{(n+\\kappa)P}]_k \\n\n",
      "            sigmas[n+1..2n] = x - [\\sqrt{(n+\\kappa)P}]_k\n",
      "    \"\"\"\n",
      "\n",
      "    if np.isscalar(x):\n",
      "        x = asarray([x])\n",
      "    n = np.size(x)  # dimension of problem\n",
      "\n",
      "    if  np.isscalar(P):\n",
      "        P = eye(n)*P\n",
      "\n",
      "    Sigmas = zeros((2*n+1, n))\n",
      "\n",
      "    # implements U'*U = (n+kappa)*P. Returns lower triangular matrix.\n",
      "    # Take transpose so we can access with U[i]\n",
      "    U = cholesky((n+kappa)*P).T\n",
      "    #U = sqrtm((n+kappa)*P).T\n",
      "\n",
      "    for k in range(n):\n",
      "        Sigmas[k+1]   = x + U[k]\n",
      "        Sigmas[n+k+1] = x - U[k]\n",
      "\n",
      "    # handle value for the mean separately as special case\n",
      "    Sigmas[0] = x\n",
      "\n",
      "    return Sigmas"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Predict Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For the predict step, we will generate the weights and sigma points as specified above. We pass each sigma point through the function f.\n",
      "\n",
      "$$\\mathcal{X_f} = f(\\mathcal{X})$$\n",
      "\n",
      "Then we compute the predicted mean and covariance using the unscented transform. In the code below you can see that I am assuming that this is a method in a class that stores the various matrices and vectors needed by the filter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def predict(self):\n",
      "    \"\"\" Performs the predict step of the UKF. On return, self.xp and\n",
      "    self.Pp contain the predicted state (xp) and covariance (Pp). 'p'\n",
      "    stands for prediction.\n",
      "\n",
      "    Important: this MUST be called before update() is called for the first\n",
      "    time.\n",
      "    \"\"\"\n",
      "\n",
      "    # calculate sigma points for given mean and covariance\n",
      "    sigmas = self.sigma_points(self.x, self.P, self.kappa)\n",
      "\n",
      "    for i in range(self._num_sigmas):\n",
      "        self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n",
      "\n",
      "    self.xp, self.Pp = unscented_transform(\n",
      "                       self.sigmas_f, self.W, self.W, self.Q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Update Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The update step converts the sigmas into measurement space via the `h(x)` function.\n",
      "\n",
      "\n",
      "$$\\mathcal{X_z} = h(\\mathcal{X_f})$$\n",
      "\n",
      "The mean an covariance of those points is computed with the  unscented transform. The residual and Kalman gain is then computed. The cross variance is computed as:\n",
      "\n",
      "\n",
      "$$\\mathbf{P}_{xz} =\\sum W(\\mathcal{X}-x)(\\mathcal{X_z}-\\mathbf{x}_z)^\\mathsf{T}$$\n",
      "\n",
      "\n",
      "Finally, we compute the new state estimate using the residual and Kalman gain:\n",
      "\n",
      "$$\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n",
      "\n",
      "and the new covariance is computed as:\n",
      "\n",
      "$$ \\mathbf{P} = \\mathbf{P}^- - \\mathbf{PKP}_z\\mathbf{K}^\\mathsf{T}$$\n",
      "\n",
      "This function can be implemented as follows, assuming it is a method of a class that stores the necessary matrices and data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def update(self, z):\n",
      "    \"\"\" Update the UKF with the given measurements. On return,\n",
      "    self.x and self.P contain the new mean and covariance of the filter.\n",
      "\n",
      "    **Parameters**\n",
      "\n",
      "    z : numpy.array of shape (dim_z)\n",
      "        measurement vector\n",
      "    \"\"\"\n",
      "\n",
      "    # rename for readability\n",
      "    sigmas_f = self.sigmas_f\n",
      "    sigmas_h = self.sigmas_h\n",
      "\n",
      "    # transform sigma points into measurement space\n",
      "    for i in range(self._num_sigmas):\n",
      "        sigmas_h[i] = self.hx(sigmas_f[i])\n",
      "\n",
      "    # mean and covariance of prediction passed through inscented transform\n",
      "    zp, Pz = unscented_transform(sigmas_h, self.W, self.W, self.R)\n",
      "\n",
      "    # compute cross variance of the state and the measurements\n",
      "    Pxz = zeros((self._dim_x, self._dim_z))\n",
      "    for i in range(self._num_sigmas):\n",
      "        Pxz += self.W[i] * np.outer(sigmas_f[i] - self.xp,\n",
      "                                    sigmas_h[i] - zp)\n",
      "\n",
      "    K = dot(Pxz, inv(Pz)) # Kalman gain\n",
      "\n",
      "    self.x = self.xp + dot(K, z-zp)\n",
      "    self.P = self.Pp - dot3(K, Pz, K.T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Full Source from FilterPy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Without further explanation, here is the full source from FilterPy.\n",
      "\n",
      "** author's note ** this is somewhat dated, but I am not going to update this section every time I make a minor change to the filterpy code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import (absolute_import, division, print_function,\n",
      "                        unicode_literals)\n",
      "\n",
      "from numpy.linalg import inv, cholesky\n",
      "import numpy as np\n",
      "from numpy import asarray, eye, zeros, dot\n",
      "from filterpy.common import dot3\n",
      "\n",
      "\n",
      "class UnscentedKalmanFilter(object):\n",
      "    \"\"\" Implements the Unscented Kalman filter (UKF) as defined by Simon J.\n",
      "    Julier and Jeffery K. Uhlmann [1]. Succintly, the UKF selects a set of\n",
      "    sigma points and weights inside the covariance matrix of the filter's\n",
      "    state. These points are transformed through the nonlinear process being\n",
      "    filtered, and are rebuilt into a mean and covariance by computed the\n",
      "    weighted mean and expected value of the transformed points. Read the paper;\n",
      "    it is excellent. My book \"Kalman and Bayesian Filters in Python\" [2]\n",
      "    explains the algorithm, develops this code, and provides examples of the\n",
      "    filter in use.\n",
      "\n",
      "\n",
      "    You will have to set the following attributes after constructing this\n",
      "    object for the filter to perform properly.\n",
      "\n",
      "    **Attributes**\n",
      "\n",
      "    x : numpy.array(dim_x)\n",
      "        state estimate vector\n",
      "\n",
      "    P : numpy.array(dim_x, dim_x)\n",
      "        covariance estimate matrix\n",
      "\n",
      "    R : numpy.array(dim_z, dim_z)\n",
      "        measurement noise matrix\n",
      "\n",
      "    Q : numpy.array(dim_x, dim_x)\n",
      "        process noise matrix\n",
      "\n",
      "\n",
      "    You may read the following attributes.\n",
      "\n",
      "    **Readable Attributes**\n",
      "\n",
      "    xp : numpy.array(dim_x)\n",
      "        predicted state (result of predict())\n",
      "\n",
      "    Pp : numpy.array(dim_x, dim_x)\n",
      "        predicted covariance matrix (result of predict())\n",
      "\n",
      "\n",
      "    **References**\n",
      "\n",
      "    .. [1] Julier, Simon J. \"A New Extension of the Kalman Filter to Nonlinear\n",
      "        Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and\n",
      "        Target Recognition VI, 182 (July 28, 1997)\n",
      "\n",
      "    .. [2] Labbe, Roger R. \"Kalman and Bayesian Filters in Python\"\n",
      "\n",
      "        https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python\n",
      "    \"\"\"\n",
      "\n",
      "    def __init__(self, dim_x, dim_z, dt, hx, fx, kappa=0.):\n",
      "        \"\"\" Create a Kalman filter. You are responsible for setting the\n",
      "        various state variables to reasonable values; the defaults below will\n",
      "        not give you a functional filter.\n",
      "\n",
      "        **Parameters**\n",
      "\n",
      "        dim_x : int\n",
      "            Number of state variables for the filter. For example, if\n",
      "            you are tracking the position and velocity of an object in two\n",
      "            dimensions, dim_x would be 4.\n",
      "\n",
      "\n",
      "        dim_z : int\n",
      "            Number of of measurement inputs. For example, if the sensor\n",
      "            provides you with position in (x,y), dim_z would be 2.\n",
      "\n",
      "        dt : float\n",
      "            Time between steps in seconds.\n",
      "\n",
      "        hx : function(x)\n",
      "            Measurement function. Converts state vector x into a measurement\n",
      "            vector of shape (dim_z).\n",
      "\n",
      "        fx : function(x,dt)\n",
      "            function that returns the state x transformed by the\n",
      "            state transistion function. dt is the time step in seconds.\n",
      "\n",
      "        kappa : float, default=0.\n",
      "            Scaling factor that can reduce high order errors. kappa=0 gives\n",
      "            the standard unscented filter. According to [1], if you set\n",
      "            kappa to 3-dim_x for a Gaussian x you will minimize the fourth\n",
      "            order errors in x and P.\n",
      "\n",
      "        **References**\n",
      "\n",
      "        [1] S. Julier, J. Uhlmann, and H. Durrant-Whyte. \"A new method for\n",
      "            the nonlinear transformation of means and covariances in filters\n",
      "            and estimators,\" IEEE Transactions on Automatic Control, 45(3),\n",
      "            pp. 477-482 (March 2000).\n",
      "        \"\"\"\n",
      "\n",
      "        self.Q = eye(dim_x)\n",
      "        self.R = eye(dim_z)\n",
      "        self.x = zeros(dim_x)\n",
      "        self.P = eye(dim_x)\n",
      "        self.xp = None\n",
      "        self.Pp = None\n",
      "        self._dim_x = dim_x\n",
      "        self._dim_z = dim_z\n",
      "        self._dt = dt\n",
      "        self._num_sigmas = 2*dim_x + 1\n",
      "        self.kappa = kappa\n",
      "        self.hx = hx\n",
      "        self.fx = fx\n",
      "\n",
      "        # weights for the sigma points\n",
      "        self.W = self.weights(dim_x, kappa)\n",
      "\n",
      "        # sigma points transformed through f(x) and h(x)\n",
      "        # variables for efficiency so we don't recreate every update\n",
      "        self.sigmas_f = zeros((2*self._dim_x+1, self._dim_x))\n",
      "        self.sigmas_h = zeros((self._num_sigmas, self._dim_z))\n",
      "\n",
      "\n",
      "    def update(self, z, residual=np.subtract, UT=None):\n",
      "        \"\"\" Update the UKF with the given measurements. On return,\n",
      "        self.x and self.P contain the new mean and covariance of the filter.\n",
      "\n",
      "        **Parameters**\n",
      "\n",
      "        z : numpy.array of shape (dim_z)\n",
      "            measurement vector\n",
      "\n",
      "        residual : function (z, z2), optional\n",
      "            Optional function that computes the residual (difference) between\n",
      "            the two measurement vectors. If you do not provide this, then the\n",
      "            built in minus operator will be used. You will normally want to use\n",
      "            the built in unless your residual computation is nonlinear (for\n",
      "            example, if they are angles)\n",
      "\n",
      "        UT : function(sigmas, Wm, Wc, noise_cov), optional\n",
      "            Optional function to compute the unscented transform for the sigma\n",
      "            points passed through hx. Typically the default function will\n",
      "            work, but if for example you are using angles the default method\n",
      "            of computing means and residuals will not work, and you will have\n",
      "            to define how to compute it.\n",
      "        \"\"\"\n",
      "\n",
      "        # rename for readability\n",
      "        sigmas_f = self.sigmas_f\n",
      "        sigmas_h = self.sigmas_h\n",
      "        W = self.W\n",
      "\n",
      "        if UT is None:\n",
      "            UT = unscented_transform\n",
      "\n",
      "        # transform sigma points into measurement space\n",
      "        for i in range(self._num_sigmas):\n",
      "            sigmas_h[i] = self.hx(sigmas_f[i])\n",
      "\n",
      "        # mean and covariance of prediction passed through inscented transform\n",
      "        zp, Pz = UT(sigmas_h, self.W, self.W, self.R)\n",
      "\n",
      "        # compute cross variance of the state and the measurements\n",
      "        Pxz = zeros((self._dim_x, self._dim_z))\n",
      "        for i in range(self._num_sigmas):\n",
      "            Pxz += self.W[i] * np.outer(sigmas_f[i] - self.xp,\n",
      "                                        residual(sigmas_h[i], zp))\n",
      "\n",
      "        K = dot(Pxz, inv(Pz)) # Kalman gain\n",
      "\n",
      "        y = residual(z, zp)\n",
      "\n",
      "        self.x = self.xp + dot(K, y)\n",
      "        self.P = self.Pp - dot3(K, Pz, K.T)\n",
      "\n",
      "\n",
      "    def predict(self):\n",
      "        \"\"\" Performs the predict step of the UKF. On return, self.xp and\n",
      "        self.Pp contain the predicted state (xp) and covariance (Pp). 'p'\n",
      "        stands for prediction.\n",
      "\n",
      "        Important: this MUST be called before update() is called for the first\n",
      "        time.\n",
      "        \"\"\"\n",
      "\n",
      "        # calculate sigma points for given mean and covariance\n",
      "        sigmas = self.sigma_points(self.x, self.P, self.kappa)\n",
      "\n",
      "        for i in range(self._num_sigmas):\n",
      "            self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n",
      "\n",
      "        self.xp, self.Pp = unscented_transform(\n",
      "                           self.sigmas_f, self.W, self.W, self.Q)\n",
      "\n",
      "\n",
      "\n",
      "    @staticmethod\n",
      "    def weights(n, kappa):\n",
      "        \"\"\" Computes the weights for an unscented Kalman filter.  See\n",
      "        __init__() for meaning of parameters.\n",
      "        \"\"\"\n",
      "\n",
      "        k = .5 / (n+kappa)\n",
      "        W = np.full(2*n+1, k)\n",
      "        W[0] = kappa / (n+kappa)\n",
      "        return W\n",
      "\n",
      "\n",
      "    @staticmethod\n",
      "    def sigma_points(x, P, kappa):\n",
      "        \"\"\" Computes the sigma pointsfor an unscented Kalman filter\n",
      "        given the mean (x) and covariance(P) of the filter.\n",
      "        kappa is an arbitrary constant. Returns tuple of the sigma points\n",
      "        and weights.\n",
      "\n",
      "        Works with both scalar and array inputs:\n",
      "        sigma_points (5, 9, 2) # mean 5, covariance 9\n",
      "        sigma_points ([5, 2], 9*eye(2), 2) # means 5 and 2, covariance 9I\n",
      "\n",
      "        **Parameters**\n",
      "\n",
      "        X An array-like object of the means of length n\n",
      "            Can be a scalar if 1D.\n",
      "            examples: 1, [1,2], np.array([1,2])\n",
      "\n",
      "        P : scalar, or np.array\n",
      "           Covariance of the filter. If scalar, is treated as eye(n)*P.\n",
      "\n",
      "        kappa : float\n",
      "            Scaling factor.\n",
      "\n",
      "        **Returns**\n",
      "\n",
      "        sigmas : np.array, of size (n, 2n+1)\n",
      "            2D array of sigma points. Each column contains all of\n",
      "            the sigmas for one dimension in the problem space. They\n",
      "            are ordered as:\n",
      "\n",
      "            .. math::\n",
      "                sigmas[0]    = x \\n\n",
      "                sigmas[1..n] = x + [\\sqrt{(n+\\kappa)P}]_k \\n\n",
      "                sigmas[n+1..2n] = x - [\\sqrt{(n+\\kappa)P}]_k\n",
      "        \"\"\"\n",
      "\n",
      "        if np.isscalar(x):\n",
      "            x = asarray([x])\n",
      "        n = np.size(x)  # dimension of problem\n",
      "\n",
      "        if  np.isscalar(P):\n",
      "            P = eye(n)*P\n",
      "\n",
      "        Sigmas = zeros((2*n+1, n))\n",
      "\n",
      "        # implements U'*U = (n+kappa)*P. Returns lower triangular matrix.\n",
      "        # Take transpose so we can access with U[i]\n",
      "        U = cholesky((n+kappa)*P).T\n",
      "\n",
      "        for k in range(n):\n",
      "            Sigmas[k+1]   = x + U[k]\n",
      "            Sigmas[n+k+1] = x - U[k]\n",
      "\n",
      "        # handle value for the mean separately as special case\n",
      "        Sigmas[0] = x\n",
      "\n",
      "        return Sigmas\n",
      "\n",
      "\n",
      "def unscented_transform(Sigmas, Wm, Wc, noise_cov):\n",
      "    \"\"\" Computes unscented transform of a set of sigma points and weights.\n",
      "    returns the mean and covariance in a tuple.\n",
      "    \"\"\"\n",
      "\n",
      "    kmax, n = Sigmas.shape\n",
      "\n",
      "    # new mean is just the sum of the sigmas * weight\n",
      "    x = dot(Wm, Sigmas)    # \\Sigma^n_1 (W[k]*Xi[k])\n",
      "\n",
      "    # new covariance is the sum of the outer product of the residuals\n",
      "    # times the weights\n",
      "    P = zeros((n, n))\n",
      "    for k in range(kmax):\n",
      "        y = Sigmas[k] - x\n",
      "        P += Wc[k] * np.outer(y, y)\n",
      "\n",
      "    return (x, P + noise_cov)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Radar Tracking"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far the performance of the filter hasn't looked very good. However, that is not the fault of the filter, but because I chose problems that were very easy to formulate due to a paucity of sensor information. Let's now solve a more realistic problem.\n",
      "\n",
      "We will use the radar tracking problem that we developed in the EKF chapter. We simulated tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
      "\n",
      "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ekf_internal\n",
      "ekf_internal.show_radar_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgA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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0776b2a0b8>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As in the EKF chapter  we need 3 state variables - horizontal distance, velocity, and altitude.\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude\\end{bmatrix}=  \\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our state transtion function is linear \n",
      "\n",
      "$$\\dot{\\mathbf{x}} = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n",
      "\\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix} \n",
      "$$\n",
      "\n",
      "but as discussed earlier we will need to provide a Python function to compute the transition. We could code this as\n",
      "\n",
      "    def fx(x, dt):\n",
      "        A = np.eye(3) + dt * np.array ([[0, 1, 0],\n",
      "                                        [0, 0, 0],\n",
      "                                        [0, 0, 0]])\n",
      "        return A.dot(x)\n",
      "        \n",
      "The measurement function is nonlinear. For the EKF we had to compute the Jacobian so that the EKF could linearize the nonlinear function. Here we merely provide the nonlinear function and the UKF passes the sigma points through the function and uses the unscented transform to compute the new mean and covariance. We can write this function as\n",
      "\n",
      "    def hx(x):\n",
      "        return np.sqrt(x[0]**2 + x[2]**2)\n",
      "        \n",
      "And that is the majority of the work. As with any Kalman filter we need to design R, Q, and P, but we have discussed this topic in detail in the *Multivariate Kalman Filter* chaper, so I will not spend a lot of time on it here. I will assume 'reasonable' values for each of these matrices, and just present the result.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "\n",
      "class RadarSim(object):\n",
      "    def __init__(self, dt):\n",
      "        self.x = 0\n",
      "        self.dt = dt\n",
      "\n",
      "    def get_range(self):\n",
      "        vel = 100  + 5*randn()\n",
      "        alt = 1000 + 10*randn()\n",
      "        self.x += vel*self.dt\n",
      "\n",
      "        v = self.x * 0.05*randn()\n",
      "        rng = (self.x**2 + alt**2)**.5 + v\n",
      "        return rng\n",
      "    \n",
      "def fx(x, dt):\n",
      "    A = np.eye(3) + dt * np.array ([[0, 1, 0],\n",
      "                                    [0, 0, 0],\n",
      "                                    [0, 0, 0]])\n",
      "    return A.dot(x)\n",
      "\n",
      "def hx(x):\n",
      "    return np.sqrt (x[0]**2 + x[2]**2)\n",
      "\n",
      "dt = 0.05\n",
      "\n",
      "kf = UKF(3, 1, dt, fx=fx, hx=hx, kappa=0.)\n",
      "\n",
      "kf.Q *= 0.01\n",
      "kf.R = 10\n",
      "kf.x = np.array([0., 90., 1100.])\n",
      "kf.P *= 100.\n",
      "radar = RadarSim(dt)\n",
      "random.seed(200)\n",
      "\n",
      "t = np.arange(0,20+dt, dt)\n",
      "n = len(t)\n",
      "\n",
      "xs = []\n",
      "for i in range(len(t)):\n",
      "    r = radar.get_range()\n",
      "    kf.predict()\n",
      "    kf.update([r])\n",
      "    \n",
      "    xs.append(kf.x)\n",
      "\n",
      "xs = np.asarray(xs)\n",
      "plt.figure()\n",
      "plt.subplot(311)\n",
      "plt.plot(t, xs[:,0])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('position')\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.plot(t, xs[:,1])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('velocity')\n",
      "\n",
      "plt.subplot(313)\n",
      "plt.plot(t, xs[:,2])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('altitude')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hD/uzJhEREZFe6+hsp72jleCgMNra3Thd5bgaqygs3sm+kl00uetP2cfd1tytvr9eAS4x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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f076d419908>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The estimates are not perfect, but this is still a very difficult filtering problem. As the aircraft goes further downrange a very small measurement error can translate into a very large error in velocity and altitude. We are simulating a velocity of 100 and an altitude of 1000. The filter does not produce exactly these numbers, but it does quite well considering that the only measurement we are receiving is range to the aircraft. This is a classical problem that is presented while learning Kalman filters, and so I have presented it here. However, recognize that this is a very difficult problem for the filter because it is easy for us. If we ran this simulation for 50-100 seconds the filter would begin to diverge because the information in the measurement would be swamped by the noise in the signal."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking a Circle"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's see how easy it is to deal with state equations which differ markedly, and nonlinearly, from the measurements. Let's assume that we are tracking an object travelling in a circle; perhaps a race car on a track. Our measurements give us coordinates in x,y, and we want to filter the car's position, heading, and speed on the race course. \n",
      "\n",
      "With a linear Kalman filter we don't have a lot of choice but to implement it as a constant acceleration model. $\\mathbf{H}$, the measurement matrix, must "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Batch Processing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in `KalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays. It may seem a bit trivial, but you will almost always want to do this if you can for several reasons. First, it will execute a bit quicker than if you implement the loop yourself. Second, the logic in your code will be a bit cleaner, and you will have a reduced chance of bugs. Third, and most importantly, it you batch process your data you can then use an extremely powerful techique to generate far smoother results than you have seen so far. We will present that technique in the next section; here I will show you how to use `KalmanFilter.batch_filter()`.\n",
      "\n",
      "All you have to do is collect your measurements into an array or list. Maybe it is in a CSV file, for example.\n",
      "\n",
      "    zs = read_altitude_from_csv()\n",
      "\n",
      "Or maybe you will generate it using a generator:\n",
      "\n",
      "    zs = [some_func(i) for i in range(1000)]\n",
      "    \n",
      "Just do whatever it takes to get your measurements in an array.\n",
      "\n",
      "Now we will just call the `batch_filter()` method.\n",
      "\n",
      "    Xs, Ps, Xs_pred, Ps_pred = kfilter.batch_filter(zs)\n",
      "    \n",
      "The funtion takes the list/array of measurements, filters it, and returns a list of state estimates (Xs), covariance matrices (Ps), and the predictions for the same (Xs_pred, Ps_pred).\n",
      "\n",
      "Here is a complete example drawing from the radar tracking problem above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "\n",
      "dt = 0.05\n",
      "kf = UKF(3, 1, dt, fx=fx, hx=hx, kappa=0.)\n",
      "\n",
      "kf.Q *= 0.01\n",
      "kf.R = 10\n",
      "kf.x = np.array([0., 90., 1100.])\n",
      "kf.P *= 100.\n",
      "radar = RadarSim(dt)\n",
      "\n",
      "t = np.arange(0,20+dt, dt)\n",
      "n = len(t)\n",
      "\n",
      "random.seed(200)\n",
      "rs = [radar.get_range() for i in range(n)]\n",
      "xs, covs = kf.batch_filter(rs)\n",
      "\n",
      "plt.figure()\n",
      "plt.subplot(311)\n",
      "plt.plot(t, xs[:,0])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('position')\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.plot(t, xs[:,1])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('velocity')\n",
      "\n",
      "plt.subplot(313)\n",
      "plt.plot(t, xs[:,2])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('altitude')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ee3jnnXcAWLhwIf/1X/+FzWbrUb0iIsNVe2cbpY7DHC7bS6Wrguq6ExyvOtrr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       "text": [
        "<matplotlib.figure.Figure at 0x7f076d2e1978>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Smoothing the Results"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have an entire chapter on using the Kalman filter to smooth data; I will not repeat the chapter's information here. However, it is so easy to use, and offers such a profoundly improved output that I will tease you will a few examples. The smoothing chapter is not especially difficult; you are sufficiently prepared to read it now.\n",
      "\n",
      "Briefly, the recursive form of Kalman filtering that we have been using up to now use information from the past to generate the current estimate. Recall the last section, where we used batch processing to filter a collection of measurements. This implies that we know now only the past, but the future! This is a key insight.\n",
      "\n",
      "Let's assume that  we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n",
      "\n",
      "However, if we have measurements from the future we can often figure out if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a true indication that a turn was initiated. On the other hand, if the subsequent measurements continued on in a straight line we would know that the measurement was noisy and should be mostly ignored.\n",
      "\n",
      "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `filterpy`. The algorithm that we have implemented is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n",
      "\n",
      "The routine is `UnscentedKalmanFilter.rts_smoother()`. Using it is trivial; we pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ms,_,_ = kf.rts_smoother(xs, covs)\n",
      "plt.figure()\n",
      "plt.subplot(311)\n",
      "plt.plot(t[0:100], xs[0:100,0], label='KF')\n",
      "plt.plot(t[0:100], Ms[0:100,0], c='k', label='RTS')\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('position')\n",
      "plt.legend(loc=4)\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.plot(t[0:100], xs[0:100,1], label='KF')\n",
      "plt.plot(t[0:100], Ms[0:100,1], c='k', label='RTS')\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('velocity')\n",
      "plt.legend(loc=4)\n",
      "\n",
      "plt.subplot(313)\n",
      "plt.plot(t[0:100], xs[0:100,2], label='KF')\n",
      "plt.plot(t[0:100], Ms[0:100,2], c='k', label='RTS')\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('altitude')\n",
      "plt.legend(loc=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DF3ZiMjUthLrgjaXEnasXMvhsyb9RXt601dBaS6lSMiBqACNHjmTkyJGMGDEC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\nFQVgEREREXGVfwA+++H4HKl49QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f07725ff940>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It was difficult to see the improvement in the position if I plotted all the data, so I have only displayed the first 5 seconds of output. From these charts we can see that the improvement in the position is decent, but the improvement in the velocity and altitude is truly spectacular."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Scaled Unscented Transform"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "todo"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Nonlinear State Variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "todo"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [1] Simon, Dan. *Optimal State Estimation*, John Wiley & Sons, 2006.\n",
      "\n",
      "- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman  Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
      "\n",
      "- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}