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      "Nonlinear Filtering"
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     "source": [
      "Introduction"
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     "source": [
      "The Kalman filter that we have developed to this point is extremely good, but it is also limited. All of the equations are linear, and so the filter can only handle linear problems. But the world is nonlinear, and so the classic filter that we have been studying to this point can have very limited utility.For example, the state transition function is $\\mathbf{x} = \\mathbf{FX}$. Suppose we wanted to track the motion of a weight on a spring. We might be tracking an automobile's active suspension, for example. The equation for the motion with $m$ being the mass, $k$ the spring constant, and $c$ the damping force is \n",
      "\n",
      "$$m\\frac{d^2x}{dt^2} + c\\frac{dx}{dt} +kx = 0$$,\n",
      "\n",
      "which is a second order differential equation. It is not possible to write a linear equation for this equation, and therefore we cannot even formulate a design for the Kalman filter. \n",
      "\n",
      "The early adopters of Kalman filters needed to apply the filters to nonlinear problems and this fact was not lost on them. For example, radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n",
      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
      "\n",
      "And then, of course, the behavior of the objects being tracked is also nonlinear. So shortly after the idea of the Kalman filter was published by Kalman people began working on how to extend the Kalman filter into nonlinear problems. \n",
      "\n",
      "\n",
      "It is almost true to state that the only equation you know how to solve is $\\mathbf{Ax}=\\mathbf{b}$. I don't mean you the reader, but the entire mathematical community. We only really know how to do linear algebra. I can give you a linear equation and you can solve it. If I told you your job depended on knowing how to solve the equation $2x+3=4$ you would trivially solve it. If I then told you I needed to know the answer to $2x-3=8$ you would not break out into a sweat because we know all the rules for solving linear equations. I could write a program to randomly generate linear equations and you would be able to solve every one.\n",
      "\n",
      "Any of us with a formal mathematical education spent years learning various analytic ways to solve integrals, differential equations and so on. It was all a lie, nearly. Even trivial physical systems produce equations that no one in the world know how to solve analytically. I can give you an equation that you are able to integrate, multiply or add in an $ln$ term, and render it insolvable. \n",
      "\n",
      "Instead of embracing that fact we spent our days studying ridiculous simplifications of problems. It is stuff like this that leads to jokes about physicists stating things like \"I have the solution! Assume a spherical cow on a frictionless surface in a vacuum...\"\n",
      "\n",
      "So how do we do things like model airflow over an aircraft in a computer, or predict weather, or track missles with a Kalman filter?  We retreat to what we know: $\\mathbf{Ax}=\\mathbf{b}$. We find some way to linearize the problem, turning it into a set of linear equations, and then use our linear algebra software packages to grind out a solution. It's an approximation, so the answers are approximate. Linearizing a nonlinear problem gives us inexact answers, and in a recursive algorithm like a Kalman filter or weather tracking system these small errors can sometimes reinforce each other at each step, quickly causing the algorithm to spit out nonsense. \n",
      "\n",
      "So what we are about to embark upon is a difficult problem. There is not one obvious, correct, mathematically optimal solution anymore. We will be using approximations, we will be introducing errors into our computations, and we will forever be battling filters that *diverge*, that is, filters whose numerical errors overwhelm the solution. \n",
      "\n",
      "In the remainder of this short chapter I will illustrate the specific problems the nonlinear Kalman filter faces. You can only design a filter after understanding the particular problems the nonlinearity in your problem causes. Subsequent chapters will then delve into designing and implementing different kinds of nonlinear filters."
     ]
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     "source": [
      "The Problem with Nonlinearity"
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     "source": [
      "As asserted in the introduction the only math you really know how to do is linear math. Equations of the form \n",
      "$$ A\\mathbf{x}=\\mathbf{b}$$.\n",
      "\n",
      "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n",
      " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n",
      "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n",
      "\n",
      "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n",
      "\n",
      "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n",
      "\n",
      "> If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if I sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n",
      "\n",
      "> $$\n",
      "\\begin{aligned}\n",
      "amp(roger) &= amp(roger + 0) \\\\\n",
      "&= amp(roger) + amp(0) \\\\\n",
      "&= amp(roger) + non\\_zero\\_value\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      ">which is clearly nonsense. Hence, an apparently linear equation such as\n",
      "$$L(f(t)) = f(t) + 1$$\n",
      "\n",
      ">is not linear because $L(0) = 1$! Be careful!"
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     "source": [
      "An Intuitive Look at the Problem"
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     "source": [
      "I particularly like the following way of looking at the problem, which I am borrowing from Dan Simon's *Optimal State Estimation* [1]. Consider a tracking problem where we get the range and bearing to a target, and we want to track its position. Suppose the distance is 50km, and the reported angle is 90$^\\circ$. Now, given that sensors are imperfect, assume that the errors in both range and angle are distributed in a Gaussian manner. That is, each time we take a reading the range will be $50\\pm\\sigma^2_{range}$ and the angle will be $90\\pm\\sigma^2_{angle}$. Given an infinite number of measurements what is the expected value of the position?\n",
      "\n",
      "I have been recommending using intuition to solve problems in this book, so let's see how it fares for this problem (hint: nonlinear problems are *not* intuitive). We might reason that since the mean of the range will be 50km, and the mean of the angle will be 90$^\\circ$, that clearly the answer will be x=0 km, y=90 km.\n",
      "\n",
      "Well, let's plot that and find out. Here are 300 points plotted with a normal distribution of the distance of 0.4 km, and the angle having a normal distribution of 0.35 radians. We compute the average of the all of the positions, and display it as a star. Our intutition is displayed with a triangle."
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      "from numpy.random import randn\n",
      "import matplotlib.pyplot as plt\n",
      "import math\n",
      "\n",
      "xs, ys = [], []\n",
      "N = 300\n",
      "for i in range (N):\n",
      "    a = math.pi / 2. + (randn() * 0.35)\n",
      "    r = 50.0         + (randn() * 0.4)\n",
      "    xs.append(r*math.cos(a))\n",
      "    ys.append(r*math.sin(a))\n",
      "\n",
      "plt.scatter(xs, ys, label='Measurements')\n",
      "plt.scatter(sum(xs)/N, sum(ys)/N, c='r', marker='*', s=200, label='Mean')\n",
      "plt.scatter(0, 50, c='k', marker='v', s=400, label='Intuition')\n",
      "plt.axis('equal')\n",
      "plt.legend(scatterpoints=1)\n",
      "plt.show()"
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AEBgYiPXr18PHxwdjx47FypUrkZaWhl69enlcR8KZRqPBypUrodfr8c9//hMD\nBgzAunXrCt1/woQJWLx4MX777TeMGTMGGRkZSEhIwBdffAGNRnNb74u8JBdj8uTJcrNmzTw+JkmS\nHBISIs+cOVPZZjQaZV9fX/k///mPy745OTnKPyrawYMH5YMHD1Z2N+gOxGOr7NhsNnnz5ltySIhN\nDgmxyR99dEOOjrbIISH27Tabzas2zp41yVlZRjkz0yifPWtye55jn8OHb8rR0RYZkGVAlqOjLfKn\nn95QXn/ePPvja9bckMePvyUHBtpkQJZDQmzy0KEm5TmbNl2XR40yyqNGGeXt22/KNptNNpvN8vr1\n9v7Pm3dTaXPZshty27ZmedOm6/I331yTly37UQ4MDJQBePUvKChI/uabH+WQEJvS75AQm5yaeks+\ne9bk1efq/Fk6PgvH53T2rMmt7S++uFHoY4W9JlVdVe2cZTQay7zNPXv2yIIgKH83aWlpXp0/iMpK\nUcd1cdfvXg13z5w5g9DQUDRs2BDx8fHIzMwEAGRmZuLSpUuIi4tT9tXr9ejYsSP27t1bdqMdIqJy\nUtjd7+LuihcMKSp457+4pGLHHfPu3VVYv15C+/ZatzvnznfVu3XTIykpf+ahRw8rhg0zuIQhzZ1r\nxLRpOixdqsOkSSZER1vx5ptG7NmjQkiIhCVLTDh5UkRGhhYZGVocOwZkZ+dhzx4zhg834MQJNebP\n1+Ltt28hPt6MWbN0GD8+D5mZAp58shZefz0aL73k/azE1KlT/5rJMCEkREJIiITUVBO6d7chPFzj\nVahWQoIOR4/a8z4+/9zoMsNgv/Zy9dlnKmRnWzyGKciyzHAnqnKcZyWqQm4EUUkUu45Eu3btsGLF\nCkRHR+PSpUt49dVX8dBDD+HYsWO4ePEiALjVGQ4ODsaFCxcKbfPQoUOl7HbNwM+JyguPLTtRFJGV\nFYkRI/wBAIsW5SAi4iwA4MKFSOzcaU8k7Nw5B/XqnXW58LRa6wCo77Fdf38J58/n4rffbkGrvep2\nwSqKIkymMCQk1EGvXvl5CQCQkKDD+vXnoFZfhtVaBwkJ9ZXH0tL0eOEFMzIytHj8cRMyMrQu7W7b\npsGJE2pl32nTjJg0SYcnn7Sid+9bEAQr0tLquLTXunUOvvjCgPh4M27cEODjI+PFF32Ufb78Uo2M\nDK1yYW8ydUZgYGCxSZBBQUFo3rw5srOvY8mSQPTqZR9YLVmixbJlV/Htt1dw/rwvhg93/ezN5kC3\nzzUjQ0CQRxFPAAAgAElEQVTLljaXfo0apcF7713H0qUWjB5tQE6OiDfeMGLBAi369DkPlUpAaurd\nSEvTA7DnZ1y5chnff1/b7fctSRJEUYTFEgSbzQCNxgiV6kqRAw1RFP/qKzz+jqlsVZVzVkREBPR6\nfZm26byuRFXIjaCa5/r16zh69KjHxxo3blzkc4sdSDgvF96sWTO0b98eDRo0wIoVK9C2bdtCn8dY\nMyKq6szmQIwY4a9cnI4Y4Y8NG4IgisAvv+iVC/WICAl16wZBEP5QnqvVXsU779ylDDY6dDBj/Hgf\nREdbMXWqEb171wEALFwYgIYNM5XYfcfg5dAh+8V7o0YSNm7UwFvPPnsNffrcglotIjVVq1wov/aa\nEbNm6Vz2/eknFW7eFBERIUGrvQ5P17pqtRX33CNjxgz7c9988xYMBhlXrohYt869Xx9//De8/PIU\njBv3YpH9TE2djGvXmmLMmLuQnGzGjBn5F/Q//FAL2dm+WLpU5/LZr18fCK32KhYtuku52E9NNSEz\nU8S+fflfV4GBEpKSzOjd2w8AMGOGEUeOqDBjhg6LFt2EXp8Dk8kfS5ZoXQYwbdroPf6+NZorOHcu\nUhnUpKaaEBXl6zZ4dHAfgN6lDEiIbkeLFi0wfPhwzkZQ9XM7sVSxsbHyiBEj5DNnzsiCIMiHDh1y\nebxnz57y4MGDSxRjRfmqWkwo3Tl4bLkqLMb+8OEbbtsPH77p8lybzSZv2pSfT7Bp0w35xx9vyN98\nc73QuH3Ha0ZHW+S5c+3PjY62yKtW3XDJCbBYLEruhPNrOOcLZGUZ5fHjb8kLF96UX3zRKLdta89z\ncM7ZGD/+lksuhHufb8pnz95S+hsYaHPJkZg376b8+efX5Pnzb7q0u3Jl0bkSQUFB8po1R5R2R460\n52QMHWqSAwPt7SxceLPQHIaCeSFDh9o/s9mz7X0dNcro9tyhQ03KY9u335TPnLklf/GFa95KZqb7\n87744oacmWlUXsfxWqNGGQvNqSgs/6JgDgeVXlU7Z5VHjoTDL7/8wuOGKkVpciSKnZEoyGQy4aef\nfkLnzp3RoEEDhISEYNu2bWjVqpXy+Ndff43Zs2eX4XCHiGo6SZKUvIPwcE2Z3LULD9cgPd2IYcMM\nAIAxY/KQnKzDhx/mue17112ur5edbcGQIfkhSUOG2GcYPPnsMxWioiyIiNBBEGSMG2eC2SygTx8z\nVq3S4tVXddiyxQh/fzVCQzX48kszNm2yt/vkkzL27TNDEASEh+sgiiIkScKxYxKWLs2/y9+rl4RO\nnXR44AH7ZxQaqkObNra/3qde+by6ddNj3z4zrl2T4O8vusxSOJd/BeyhT3v35qFZMwEdO5oAyOjb\nVwer1Z4rMWFCisf3+/LLU1C3bn540q1bAjZu1CjthoRI+PlnEZMnG5GVJSIqSkLjxjJCQ+3vRxRF\nREToIEkS5s7Nw6hRGiQlmbFkiRbx8WbExVncwrpq15YxZkweFi/WICLCjEGD7DMs6elG3H+/CmFh\n9vYWLDDin/90/X1/9FEekpIklzCo338XABQ2sy4poWCOWRtBkLFtWx4SEuyvu2xZHuLidCU6Tsvj\nGKfqo2HDhpXdBaISK/YsNWbMGOzevRuZmZk4cOAAnn32WRiNRrzwwgsAgH/961+YNWsW1q9fj6NH\nj2Lw4MHw9fVF//79y73zRFQzlFcpT1EUcf/9KsTHm9GnjxnZ2QJ69LAiIEDE0qX2BOHoaCtWrryJ\na9dssFgsyMrKw9mzJly/7p5MfeOGgBUrtC7JxWPG5GHzZrXyPn7+2YY//xQxcaIBa9dqMXGiCQBw\n5YqM8HANLlyw4tgxKAnRhw8LEEUgIiL/otR5EONItA4OlnH+vD2JOSJCB7VajYgIncvzHE6ckNGt\nmx5t22px+rSkvNfatd0TlEVRRP36ejRv7gM/PzVyckTExtqUXImCgoKCcONGZ1itIt5/34iQEAl7\n9qgwf77RJeH6wAEV7r4bWL5ch4kTDfjhBxFffml2+b2Kooi4OB22bLHh6acFLF5sgk4n48IFARMm\n5H/Gc+YYYTDImDlTh86dbS5rYQwbZoAsCxBFEefP2/DddyLi483o1cuCmTN1yMmxD6YKrp/Rtav9\ns3T83hwJ2haLBQcPSti8WY3atWUsWXILa9bcgiTBLUn83DlzkYndBcsHs1wtEVU7xU139OvXT65X\nr56s1Wrl0NBQ+dlnn5V/+uknl32mTJki33PPPbJer5c7deokHzt2rMRTI5Svqk3l0p2juh5bZV3K\n0zkExWKxyNu333QJ6dm06aZsNpvlH3+8Ln/00XVl+4cf5ofKzJ9/U1682LX8qqPkanS0Rf7yy2vy\nqFFGpUyro8Srp7AcR7uOcJ7iwqo8fR6OdosrPevpuVlZxmJDqRyf2+bN9nCpe++1yC+9tMAtrGnM\nmAVKaJCjpK3jcz571iRnZhrlrCyjx/dZVDiR8+/N3t9b8uHD9jC0c+duKf329Pk62nSElTlCpEJC\nbPKnn97wGPKUmWl0ec+O/b/88ppbG+vX23+/nsKmivssHY879mW4lKuqds4qz9AmospSrqFNGRkZ\nxQ5GJk+ejMmTJ5d6UENE5C1ZlpGVZQ9BKkkYiGN2wzkEpUkTICUlPzF39GgtFi82IjcXSEmppYTk\njBxpwMSJJkycqMeMGXr06WNGfLwZzZvboNXK0GrtYTtJSWbIsoiUFBlPPWXCli0q7NoFPPmkFZ5q\nXPzvfyrk5IgAbG4hVIB7WJVjETnHe0hNNWHaND2uXrXfCd+/3x5G5S1ZFpT9w8Ik7N/vCK9xnc1w\nzBDce28eHn44D4cPx7pUcHKsYp2YaMG772owcqTNpR8REWqn13QPHyuOI+TJk9BQe78FAeja1YQh\nQ+xhSsuW5SE8XPfX+9EooVLx8WY88YQNHTva36Pz57lsWR7q17f/7FyOFgAyM0X06GHF7Nn524YP\nN2DrVqNLmNzixUYkJ+tcqnE5/15+/dWMbdsE9Oplwbp1Gnz2mcrtPcly6cOlqOzJssyCMnTHkEu5\noneJcySIiCpawQvnpUtNOH0aGDQo/2KxuAssR/x5bq4No0ZpXcqILl58C0lJcImR375d7bHK0enT\nIsaPz8O772rguJawWgG9Xlbi5qdN00OrBbZvN+KHH0QsX27v99/+ZkPXrlZEROTH40+YYMLChVos\nXWpCeLheeX+OC+GlS02oX9+13KTjgn7/fvv76dtXi6tXvbu4LPhZOl9oO9ouahBif9yA0FArmjSJ\nQEDAVIwebc+VGDduCq5ebYB339Vg7lyLS7ue+uH8PlNTTWjaFMpnUFLO/a5Xz4qtW+0hYzExWuW4\nyA+VsgAQEB5uUB5zfJ72vuUfS85fsoGBEiRJxmOPuedoLF+uwubNaqxefQuiCGzf7hgcurNarfju\nOxsyMuyDjvHj8/DRR2qXgciyZXkQRcFlEDNqlAYffmiCn5+KORSVRKvVwmQyQavVQqVyH/wRVSc2\nmw1msxk6nfc3ngoS5NIORbyUm5ur/Ozn51cRL1ltOeplt27dupJ7Qnea6nxsOSeiCoKMtm21Lsm7\nRd2FLzgL4XwHf9Qoe9z98uU6l/b69DFDEIAGDfIv+seMycPMmTpotcDixTfx668qpazp3LlGTJ2q\nU9ZxCAmR8Omnt/Dkkz4u7X722U188okaoaEysrIEqNVA374SmjXLv6gtSdKtpxkWbwdV3rRfnJ9+\n+gmPPPIIBEHA7t27UatWlNftSpKEc+fyE7/DwrSlvji+nc+jKOfOmbB+vf0YiI+3r+ERGmrD6NFm\nvPSS/aLf+XgKCbEnYq9YocX48XmYPVsHf38JCxeaUKeOgIAAEadO2TBggOtxsXq1ER076nD+vCNB\nXoPsbAvatbMnqQcGSpg0yaQcizVldqIqnrNkWYbZbC71nVyqPNevXwdgXwCwJhMEAVqttsgZtuKu\n3zkjQURVSmEXuc53nM+eNZWozYJhJGlpeiQl5cFoFPDUUxZs2eJ+KjQa7SfWJUvsCdGnT4uYOVOn\nXCyq1cCMGXqnu8UGrF59CwMG2NeVWLYsD3XquN+x1GhEl/UTQkIkDBtmcQsh8jY0yXl2AnAPRyrs\nOSUJfSpKkyZNMGHCBAiCgOjo6BJd2IqiiMjIsl3cq2Ao0u2EejmTZUFZj6JRI/sU1bffapCSosIL\nL5jRp48FCQkGtxmhq1ftx0tSUh7atJGU4+K114w4dcr9uGjYUPVXgnz+seg8exQfb3ZbuLC498Uq\nUOVDEIRS3cGlyudYfK0qDVCrK55ViKjKKFidaedOE86eNblUvZEkCadPSy6Vkd5/36jkTEiS5FYN\n5/BhGzIytNi4UYPx4/MQEWFDmzYSMjK06NevFtq1s2LixPyqQm+8YcSePSrs2aPC1Kl5mD9f+9ei\nbvYL/6VLTahd2/0OTsOGauzfb8H+/RbExdkrJjkqIjmeFxOjw7Jleco2e2iR9wvSeeIYGHiq0FTe\nRFFEmzZt0Lp16zvyQtWeV2HBxo0azJ+vxVtv2Y8TrRZ46CEbWrXSY+5ci8vvuEcPm7LPY4/ZMHy4\nQanmNG6cAZJkn91yPCc93Yj69bVur+08SBw8uGQVnMqr0hkRkTPOSBBRhXO+UxoaqlLCOQRBVu4m\nBwZKOHYMGDTIfoHlCOXIzrYgJUWLbt2smDjRhMuXAatVxttvA4CMHj2MEARByZ9Yvdoed+64kzt7\ntg4ffHAT/frlJ1EnJdXCqlU3kJ5+E7t2aTBlir2MaO3aMtq1E7Bliw2CIOKppxzrOehhs9mweLER\nw4fnx7TXr+9+Id+tm95ptkD/18WhWKIZhKrOx8ensrugKC4HpKQKzvjUq6dFdLQj/8JeZjcuTqU8\nHhqqxZdfmpU1RTz9alu2tGHSJD0GD85D9+5WREbmfxV7+tsQBBm+vgJWr7YncOfkiG7vq+DsQ1nP\nzBARecKBBBFVKOcYdn9/CdOn5yElxX4xnp5uhL+/hIsXRbfF0RwXQoIgIynJrMSKv/vuDVy6pFKS\nXyMi7IuJOZ7nqRpOQID71d3nn2vRooUVzZo5Zi9EpKcbERZmcLvQlyQJX3xhxbhxOrfqPwV5CiMq\ny9CiqqAqxYrfTqiXN206/76aN9cU+nhWVh4GDco/bjdvtrokUaemmnD33QK2bLHgyBEJ/frVAmAf\n8HTposGOHRZlEDR/vhGzZ2sRH29RjnfnBfYcixOeO2fGmTNWJCfrkZNjXwPl3ntF+PtLSiWyPXsK\nTwz2NgSKoVJEVBDPAkRUoRx3Ss1mICXFjL17VTCboSwetmSJEdHRVpfF0QID7Qmsubk2yLKsDDDM\nZkCSBIwbZ3BZTOzBB60YOjQPgYH2hcPS040uoUQxMTqXbY5F4374QY2XXzagVy8L4uPNuP9+lceL\nJcd7OHFCjblz9RgwwKDMqlDlq8xQr4JycuyLHu7bZ8bWrSY884yIjh0NAERlpsyxgN3x42aXRe1S\nUgx4/nmL2wJ7OTkSfv3VjKwsIz7/3Ij27bUYMMAHiYkWmM3AkCF6iKJ9kL5xowYbN2owbVoe6tVz\n/yy8DYFiqBQRecIZCSKqcP7+EhITLZg+3X6Xdfx4ezUkAPjvfzV4/fU8tGghomtXE0aP1iozEBkZ\n7rMWu3a55xf8+aeIPXtUmDTJXlK0Uyf3O9Q9etjDnj77TIV339VgzhwzNBogIwPYuNEeHhMWdufM\nGlDF8BRa5Zg9KCsffiggOFhCVpaIjAzXsL3eve35HJcuSUhJya8M9eKLBgQFGdGpk+vg2NsQKIZK\nEZEnHEgQUYUKD9dg4UIjBgxwvQB64QUzQkNlzJypQ0YGsG2bEU2bqvDhh3no1i1/32HDDFi92ogB\nA0TUri1j82Y1xoyxl9kE7FVxZs3SITHRgiVLtNi82epWDQcA1Go1OnUSERVlwciRNmX9Am9CYso6\nDr+6qkohTVWFt6FVno6hmBityzZHaFNqqslljZMzZ+yVvxxhS85q15aRmmqCTudeDOCzz1SIiuLF\nPxGVHQ4kiKhCiaKIhg3d47VjYmz4978NSnnVM2ckpKbqsGSJRanL7yix2bChymkVYzNGj9YiPt6M\n9u2tGDdOj19+UWP2bBHx8eYi62N7ylXw5iKrPOLwqyPz2bOV3YUqyZscmMKOIedE/NBQHdq0yU/0\nv3ZNQt++WnToYA+jW7dOo6xVAThKy4po2hRK+J4jN2PMmDxltXFnhQ2KC+ZDcPBMRJ5wIEFEFa5+\nfdc7r4sXG3HxIpTyqqmpJly7JiAx0aIko06aZMKSJVrMnWtxqY4UFiZhyxYLcnMl9O1rH0Q4PPGE\nDeHhhnJ5D3dawvTtkE+dsv8QGFi5HammvEnEd55JkyQJc+fmYdQojTJL8e67GqxebUSDBiJUKhVi\nYwUlEbpg+J6n1cbdq1Kpcfy4EadPw6UiWVyczuPA53YTsJm4TXRn4ECCiEqlsAuCoi4UPJXU3LQp\nTymZec89Er79VoX338+PyU5L02PrVhOaNdN7XLzNcZGVkGB/LD3dWGglJSo9SZIg7NkDCAJUzzwD\nm43J5uXN8XezZYulQDli98pigKfwvaIri1mtVmzYkIe9e+1V0JzzIbZuNcHPT6X8LdurRZlw+LBN\nmfXwdrXtsl59nIgqDwcSRHTbCrsgAFDshULBO6+PPy6gQQMzABlXrwqwWNxDkvz8PFdRcrTnesfU\n88UVlQ1LdjY0770HCAICevbEZTW/TipCSWfCSrL/8eNmpKQYPOZeLF8uIiND41Kmdts2wSXZ29sE\nbCZuE905eOYnottW2AWB4+eCdzQLziY4U6vVaN7cfkqSJAkNG5oRG2t0udtZXEw2w43Kh/nSJcg3\nb7pskzIzIf72GwDA948/IAQFIe/MGeVxoVYtaOvWrdB+UtkomHuRmmrCtGn2ZO9t2wQEBZkwapRe\nydVw5lhhXhBkSBL+mjFh6BLRnYp/2URUIZYvF72uPS+KIurX1+Pxxw3Yv9+C/fstDH2oRIJaDem7\n76Dp0AHali2hbdkS+scfVx4PfO451O/ZE9qWLaHp0AHS999D4AxFtRMTo8X8+UZotcC772qwfPlN\nbNtmxJIl9sUex4/PQ0aGFk8+6YOkJDN27lRhzJg8ZT2WpUtNOH1aQvfuKqxfL6F9e63HNSccidvO\na7uEh7uXcSaiqk+QK6h+X25urvKzn59fRbxktXXo0CEAQOvWrSu5J3SnKezYKk3CpDehTWPG2NeJ\n0GrBEIZqSpIk5B04AG1yMlTff+9xH9sDD8C8aBF0Dz7IQV81ZbVacfy4PVcpJkYLUbTfALCHMeXn\nTYSE2BeJ3LxZjYUL89CwoQqiCLRtq0WfPmasXeu6b8G/e2/POfw+pPLA48p7xV2/80xPVAM5EiWP\nHLmFzEwjdu403daKtc55Cc6zBpIkISxMwvr1NxEfb8bMmTqldCtVT6IoQt+uHawffwxzUpLb4zf/\n7/9gXbcO+rZtOYioxuwhhj5o3twHarVa+RsfPNj9nDB4sIQtW2zo1MmAyEg9ZFmAv7+Ehx9m4j1R\nTcGzPVENI4oidu40Yf16Cd266fHQQzocOwaYzcDFiyISEnTKnUJv24uI0CEiwj6IcFR+6drVgIQE\nA9q1syllXRnCUL0JggBNZCTkqCi3x2xRUdBGRha5bgdVT6IoolkzvVs4UrNmeuXvHrDPLMyfb8Sc\nOVrMmGFU9l282Kj83VutVhw5chM7d95E9+4qdO+uwpdfGnH2rMnrGxhEVHUwiJWohjGbA7Fpk+gS\nppCWpsfAgWa8/ba+RG15Ck9wVH65eFHExYsiJk8GPv30FoKDNTV24bY7ifX336FOT7f/3K0bIMtQ\nb9sGn+XLYUlIgDYkpJJ7SOXBm0UYRVFEo0YqxMdb8MYbOmWRyJYtRZebDCkp9gIK//63CWo1MGBA\nycrHElHVwb9WIgIAPPKIFdHRVq9nDRz5EcWFROXkiNDpRJc7l1R9SadOQczMhGnePEhLl0JatgzX\nZs2C6swZSI4F6uiOVHD2sZC9kJamx4kTasydq8eLL/pAkuz7FrzJMGuWHmfOiMr/Pc2G2gcgdZCV\n5X3IJRFVHM5IEN1hikti1GqvomfPYDRvbsS4cfY7gWPG5GHSJD0+/DAPzZrZt2Vl5RXaBlB46VdH\n5RfHXcf5842IiWFy9Z1AlmVIv/0G0/bt0D78MFQa+4Dzpy5dENq0KXwuXoQsywxvqsEK+91nZeUh\nL69kAwFJkpCVFYkRI/wBcMaCqCriQILoDuKpilKXLhqcP29PfnQkQnfqpMXhw0ZMn27Ejz+qlIpK\nly/b29ixw6K0sXSpCU2bipBl7+rBq9VqPP008Le/mQAAMTE6qFkK9I5gNRohtGwJfVSUywWjRZKQ\nFRKCmLvugtVohMbHpxJ7SZXJUdrV+fxx+jQwaJAe/v4qvPWWESNH2m8yLFhghI+PjIwMSdlXEERk\nZdlnRbOzLRgxwh9mM9C7t30BvJgYM+rXL1kIJhGVH367E1Ujxc02FJwlGDVKg9dfz1MWdVu0KBJR\nUb9i9+48fPaZBps3q5GUZEZwsITERAuSk3X48EMzEhL0ShtDhugRH29WVrV13BEseMHgvGCc8+Jy\ndOfQ+PhA06iRx8dkWYahceMK7hFVNQVzKQRBRNu2WrecKZ1OREyM/Vyyf78Fsizj9Gl7+VjAfj6J\nibFXgUpMtCiL48XGGhEWZh943E7JaiIqW/zLI6omvM1JcNajhxXDhuXHJI8Y4Y+LFyMxYIABGRla\n/OMfZvz+u4AZM0xYvFiDnBzPp4QbNwS3GObCSr8SUc3mnEshy66hTjk5IoKDNS7lZSMidBAEAYMG\n6V3yJSQJeOutG5g9W6dsHzbMgHPnzCU+FxJR+eC3PlE14TzbUFhiYsEVY594wr2e+5YtWpdkR6NR\nQHKyD1JSzFi50oSYGK1LG6mpJqxb5zn52rvkSyKqqUqzirUgCPDzy3Xbfu2ahIQEHcxmoFcve8jT\nr7+ay7rrROQFxh4Q3UGcZwlkWYZaLWDlypvYtMkexjRjxk1MmFDL5TmO2Ya0ND327TNDrVYjLs41\n3MB1HQgmThORd7wpG2vf7jlU8sqVK1i0yNcl4drfXyw05MmRB1Yw7MnblbSJqGQ4kCCqJorKSXDm\nyF/YudOEY8eAtDT7wCE93YiIiCzMnBmmfCmnppowbVp+4qIjgdYx0wAA9etLxV4EEBEVxvl8UtQ+\nngYckiShQYNz2LrVfp6KidFCFEUsXHgLAwb4KLlcw4YZsH+/BeHhGo8FJ5wLSLD6E1HZ4UCCqJJ5\ne6fM2zt7gD0MquCic8OGGbB+/V2IiDiL/fubej3b4M1FABFRaXk614iiiMzM+hgxwj6QcAwMChsD\neCpLvXWryaWAhKNUNc9rRKXHgQRRJfJUrrWoO2VlcVEvSRJnG4ioWjCbA/8qEuE6MBg+XI8xY/KU\n0Kb0dCPCww1ueWNEVL44kCCqRIUt6uY8WHDMWAiCDEmyhx85z1x4mtEID9egZ08TIiJMSEuz38lb\nutQErfYqnIubcLaBiKqjnBwRM2fq0Lu3BUFBEho0sJ9P69UTXRbEXLDAiOho78JCmUdBVHL8KyGq\nRIIgIz7ejKFD8xAY6F6+0DFj0b27CuvXS2jfXutS7rCwkrCiKKJzZz2eeUbE1q0m7NtnRrduepZI\nJKJqRau9ikWLclyqPjkqy2m1wJ49KrRqJaFrVwPatdNgyxYz0tM1eOstI+LjzXjlFR22brWgWTMZ\nn356C1u3Gv8KjXK9/Lmd8tpEBAiyLMsV8UK5ufkl3Pz8/CriJautQ4cOAQBat25dyT2h8iRJErZu\nNWHIEPuMQWqqCU2bAp06aZWVqGVZRvv2WvTqZcHGjRpl5iIkJD8kqV079+2FzTLw2KLywOOKysuh\nQ4cgiiKCgpoCcK/CdP26FUuXqnDjhoB16zTQaoHp042YONHgcl58++1bePFF+4rrS5ea0K2b3mUw\nce6cCfPmwaUd5lHcuXjO8l5x1++ckSCqJNnZFgwZkr8AU1qaHlFRAnbssCh3xc6ccV8HgoioJnHk\ndTmvV+MI4czMBDIytNi4UYPx4/Pg7y+hcWP3mYR9+9TKuXbIEL1LLoUkSTh82ObWDhEVjwMJokog\nSRJyc90HCdevyy6LziUn65CebsSePSqkpprcFnUqzWJPRETVjSRJyMrKQ1ZWHs6dM2PYMINyvpw9\nW4eFC/Pw0EN6pKcblfPia68ZsXmzusTt8FxKVDwmWxNVMEcs7qhRWqSm5idDOxZacpaTI+L++1XY\nssUGQRDx1FPmv5Kt8+/MeVsSloioOitY5W71aqPbPg0bqqDRaPD44yplUc2zZ4GkJDPS0uznxgkT\nTDh8WMK4cRrk5IhKO4GBEnr3tqB2bRlRUSLPpURe4ECCqII5V2qaNk3ECy+YMXiwhGbN8gcUztVF\nwsKKHhyw8hIR1QQFq9w5ZmyHDbNXaFq2LA/169vPhQUX1axTx4hatYz48UcVJk/WQ6sFevWy4J13\n1EhO1mHp0ls4eVJUbux07WpCeLjEwQRRMTiQICpHBcsJAkBurg3x8TJWrNDi6lX7onEvvmhW9uvS\nRcMZBiKiYjhmbIs7X4qiCF9fNSZOdC1M4dxOaKig5KwBwJAheuzbZ0ZkpJ5lYYmKwL8GonJSsJzg\n1q0m7NxprxaSkaHFpEkmREdbsXSpCadPS8p+O3ZYEB6ucUksJCKq6TzlhIWFad0Ssb157pw59tyz\nkBAJ6elG3HWXyu05Z87YYLVaWRaWqAickSAqJwWn4YcM0SM+3qz8Py1Nj61bTfD3F9G2rbbIRemI\niGo6URRvOyfM8dy9e/Nw8qQVkyfr0aOHFd26WdC5sx6CIGDBAiP++U97mNSYMXlITtbhww/NSEjQ\n8/xMVAgOJIgqkZ+fChWzkgsRUfVXmpwwUbQnUA8eXAsXL4o4cECDjAytMjD57jsR8fFm3LghYOZM\nHaC59GsAABsQSURBVLTasuw50Z2JcRNEZcS5nKAkSW5T6UuXmtCzp8QSrkREVdAnn2gQGipj40b7\ngnTp6UZlFe2C5+eC53uimoozEkRloGBZwmXL8hAXpyswDW+vBuJpWp4lXImIyp/jxo3zuTo83P7z\n3Ll5GDVKg/h4M554woaOHXVQq9WIixOVUrKiKODcOTNOn5YwaFB+pb24OJ63qWbiQIKoDBTMh3CO\noy04De9pWp4lXImIyl9ReRZxcTps2WIBICA83OC2irbzzaLUVBPMZuDqVVE534eHa1jdiWocHuVE\nJcDpbCKi6s1x46ZgpafCtgOuN4suXrSvN9G7t8XpuRK+/NKIt96S0b27Clu3mnDunInfFXTH40CC\nyEsFy7nu3GnC2bP2L4rQUBXzHIiIapDatWWEhEhYudKEH36QMGCAARkZWiQmWjB6tBbz5oElY+mO\nx9AmIi8535EKDJRw7BgwaJC9rMeyZXlcSI6I6A5VMLdi6VITmjYVMXKkBbIson37/BLes2frlOpP\nFy+KLBlLdzQOJIhuQ+/eFqSlsbY4EVFNUDC3IjRUi/PnbYXu3769FUlJPm7buUo23Wl4BBN5yblM\na+3aXPyBiKgmceRQhIdrsGOHRQlzPX3aXt7bEdqanm7E3XcL0GrhVjKWq2TTnYYzEkRecr4jJQhA\n164mDBmSX/7PUUKQiIjuXAWr9A0apMeBA2an0Fb76tgFQ13PnjUVWt2PqLriQIJqtJJOMzuXaQ0L\nk5gTQUREkGWhyFLfkiThzJnCQ6GIqite+VCN5e00M0u+EhGRg3OYq7dV+rKzLUhO1mHMmDyXEChW\n96PqjgMJqrEK1gVPSNApsxMOhQ02GOtKRFQzOYe57t9v8XpV65wcETNn6tCrlwXx8WbcdRdz7aj6\n40CCqAiFDTa8GYQQEdGdqajF6zwJD9cgPd0IrRbYuFGD0FAZSUl6fm9QtcccCaqxCtYFL0nCtCDI\nSp3wdes4NU1ERIUTRRH3369SvjdmztRBqwUA5k1Q9caBBNVYBeuCe0qY9jTYCA3VYPt2MzIy7BWb\nJk0yoWlTIDxcX7FvgIiIqo2wMC3i4vKQkKCFVstqf3Rn4ECCajTnKkyFPV5wsJGdbcGQIfmL0aWl\n6bFvn5lVm4iIqFDe3Lwiqm44kCAqRnGDDQAQBKGCekNERNWVN98nRNUJh8JUY5RVGdfbKf1HRERU\nHJYbp+qGAwm6YzmfkK1Wa5mVa73d0n9ERESFYVlxqo549UN3pIIn5N2788q0XGtJS/8REREVpaiy\n4pypoKqKV0B0Ryp4Qv7sM1Vld4mIiKjEOFNBVRkHElSteXuXZvNmNdLTjcxrICKiKkeSJMiyjNWr\njYiOtrp8T3EBVKrKWLWJqi3HXRrnNR4c+QoF13+YO9eCLl1Ydo+IiKqWgt9l6elG3H+/CmFh/J6i\nqo9HKFVbRd2l8ZQQrVarmddARERVSsHvsmHDDJBlQfmeKlgpcOVKE2RZZr4EVQklupp67bXXIIoi\nUlJSXLZPmTIFoaGh8PHxQWxsLI4fP16mnSS6HUyIJiKi6s75xtiBA2ZYLED79lrmS1CV4PXV1f79\n+/HOO++gefPmLotvzZo1C3PmzMGCBQtw8OBBBAcHo2vXrrhx40a5dJjIges5EBFRdefNd5njxpgs\nCxgyRM98CaoyvBpI5ObmYuDAgVi2bBkCAgKU7bIsY968eRg3bhyeeeYZNG3aFCtWrMD169exZs2a\ncus0EcD1HIiIqPrjdxlVZ14dqcOGDcNzzz2HRx99FLIsK9szMzNx6dIlxMXFKdv0ej06duyIvXv3\nln1vieBaqQkAw5eIiKha8zYUt7jZC6vViiNHbuHIkVuwWq0V0XWq4Yqt2vTOO+/gzJkzygyDc1jT\nxYsXAQB169Z1eU5wcDAuXLhQaJuHDh26rc7WNPycXImiCJstCNnZ/khO9gUALFqUg4iIs4wRLSEe\nW1QeeFxReeGxlS84WMT69YEAAK32Kr77zv79p1arcfJkFEaOrAUAeOutm/jb337hgKIIPK6K17hx\n4yIfL/IW7s8//4wJEyZg9erVUKnsC3rJsuwyK1EY5wEHUWmJooisrEhkZNRFcrKvEh86YoQ/zObA\nyu4eERFRhZAkCWr1ZajVl11uot26VQ8jR9ZSvh9HjqyFW7fqVWJPqSYockZi3759uHz5Mpo2baps\ns9ls2LNnD/7zn//g6NGjAIBLly4hLCxM2efSpUsICQkptN3WrVuXtt93NMcImZ9TvqysPDz+uAa9\nelng7y+hVy97ctmePSrcc889iIj4//buP7aq+u4D+OdeKIXW5krcaid0iFsZ4qPGiK42CxtTqjh/\nkUU3u2HS5QmaIRFMJHM6SjIG0SnxyXBO+YMZlU2NickMsruECmtaJ+jQKYlZNrORsNa51druKcxx\n7/MHT2+sCO0pLbeXvl6Jif2e08unN5/ce97nnO/3nF3cAkuE3mIs6CvGit4avjfe+N+jxk477bS4\n4ALv3cfpq+Hr6ek57vbjXpFYsmRJvPnmm/H666/H66+/Hnv37o358+fHzTffHHv37o26urqoqamJ\nbDZb+J2DBw9GW1tbNDQ0jM5fAB+xY8ekuOeeQ/GrX5XFr35VFj/84aGYMWNSscsCgKKaN29K/OQn\n/YX5Ez/5SX/Mmzel2GVxijvuFYlMJhOZTGbQWEVFRUyfPj3mzZsXERErV66M9evXx9y5c6Ouri7W\nrVsXVVVV0dTUNHZVc8rK5XKFpexqa8uOeiBPNpuKu+6aFp2dR8ZXrJgWl1zyYcya5SHtAExckydP\njhtuiJgz52BERMybV/7/twUfWZjko9+pMFoSH32lUqlB8x9Wr14d/f39sXz58uju7o76+vrIZrNR\nWVk5qoVy6svlcpHNHorm5vKIiNiy5VBhGbyB5fHOOutg/OIXRS4UAMahyZMnxwUXHDm0O953KoyW\nxEGitbX1qLGWlpZoaWkZlYKYuPbv/zCam8sLVxuam4+sqz1r1pEPwXQ6Hf/1X1Njy5bBH4y1teVF\nqxkAxqOhvlNhNLgfhJLy0Qf3RETU1jq7AgBQDI7AGDeGetDOgOE+uAcAJqrhfKd+9AGvnsfESLgi\nQdF80sRqVxsA4MQN9Z1qDgWjQbdQFAMfYPX1ZVFfXxbZ7JGzIa42AMDoON536kfnUHR2pqO5ubxw\ncg+Gy5EaReEDDACgtAkSAAATzMfnUDz2WH+kUnlzJUhEkKAohjuxGgAYfQNzKDo6/h1PPdUfq1eX\nxxe/OKVwqzEMh8nWFIWJ1QBQXOl0OlKpVHzrW9M8b4IRESQomoFJYAAAlB6ngAEAJii3GnMiXJEA\nAJig3GrMiRAkAAAmMLcaM1KCBKPqk55WDQDAqcdRHqPmWE+rBgDg1CNIMGo8rRoAYOIQJAAAgMQE\nCUaNJeQAACYOk60ZNZaQAwCYOAQJRpUl5AAAJgZBgkQs7woAQIQ5EiRgeVcAAAYIEgyb5V0BABgg\nSAAAAIkJEgyb5V0BABhgsjXDZnlXAAAGCBIM6eMrNVneFQAAp5M5rv/85z/x0kv98T//k4+rrppk\npSYAIJFcLhd/+cuh+MtfHEOcagQJjimXy8WLLx6Kb31rWvziF1Piv//7w1i1qsxKTQDAsFg6/tQm\nSHBM+/d/GMuWTSss9/rAA+WxePF/il0WAFAiLB1/ahMkSOSaaw5bqQkAAEGCY/v4cq+PPdYfCxZY\nqQkAGJ6hlo43f6K0WbWJYzp6uddpQgQAMGzHWzp+YP5Ec/OR1SC3bDkUjY1OWJYSQYLjSqfTlnsF\nAEbsWMcSH50/ERHR3HwkcDjuKB0iHwAAkJggAQDASTfU/AnGP7c2AQBw0h1v/gSlQZAAAKAozMUs\nbWIfAACQmCABAAAkJkgAAACJCRIAAEBiggQAAJCYIAEAACQmSAAAAIkJEgAAQGKCBAAAkJggAQAA\nJCZIAAAAiQkSAABAYpOLXQAnLpfLxf79H0ZERG1tWaTT8iEAAGPLEWeJy+Vykc0eivr6sqivL4ts\n9lDkcrlilwUAwClOkChx+/d/GM3N5dHZmY7OznQ0N5cXrk4AAMBYESQAAIDEBIkSV1tbFlu2HIqa\nmlzU1ORiy5ZDUVtbVuyyAAA4xZlsXeLS6XQ0NpbHyy8PTLYuN9kaAJgQLDhTXN7tU0A6nY5Zs8pj\n1iwhAgCYGCw4U3yOOgEAKDkWnCk+QQIAAEhMkAAAoORYcKb4TLYGAKDkWHCm+AQJAABK0sCCMxSH\n2AYAACQmSAAAAIkJEgAAQGJDBomHH344LrzwwshkMpHJZKKhoSG2bds2aJ+1a9fGjBkzoqKiIhYu\nXBj79u0bs4IBAIDiGzJI1NbWxv333x+///3v49VXX42vfvWrccMNN8Trr78eERH33XdfbNy4MTZt\n2hS7d++O6urqWLRoUfT19Y158QAAQHEMGSSuu+66uPLKK+Occ86Jz3/+87Fu3bqoqqqKV155JfL5\nfDz00ENx9913x5IlS+K8886Lxx9/PHp7e2Pr1q0no34AAKAIEs2ROHz4cPzyl7+MgwcPxoIFC+Kd\nd96Jrq6uaGxsLOwzderUWLBgQbS3t496sQAAwPgwrOdI/OEPf4jLLrssDh06FNOmTYtnnnkmvvCF\nLxTCwplnnjlo/+rq6jhw4MAxX2/Pnj0nUPLE4X1irOgtxoK+YqzoLcaCvhpaXV3dcbcPK0jMnTs3\n3njjjejp6Ylnn302vvnNb0Zra+txfyeVSg2/SgAAoKQMK0iUlZXFOeecExERF110UezevTsefvjh\nWLNmTUREdHV1xcyZMwv7d3V1RU1NzTFfb/78+SdS8ylvICF7nxhteouxoK8YK3qLsaCvhq+np+e4\n20f0HInDhw9HLpeL2bNnR01NTWSz2cK2gwcPRltbWzQ0NIzkpQEAgBIw5BWJ733ve3HNNdfEzJkz\nC6sx7dy5M7Zv3x4REStXroz169fH3Llzo66urrCqU1NT05gXDwAAFMeQQaKrqyu+/e1vR2dnZ2Qy\nmbjwwgtj+/btsWjRooiIWL16dfT398fy5cuju7s76uvrI5vNRmVl5ZgXDwAAFMeQQWLLli1DvkhL\nS0u0tLSMSkEAAMD4N6I5EgAAwMQmSAAAAIkJEgAAQGKCBAAAkJggAQAAJCZIAAAAiQkSAABAYoIE\nAACQmCABAAAkJkgAAACJCRIAAEBiggQAAJCYIAEAACQmSAAAAIkJEgAAQGKCBAAAkJggAQAAJCZI\nAAAAiQkSAABAYoIEAACQmCABAAAkJkgAAACJCRIAAEBik4tdQKnL5XKxf/+HERFRW1sW6bRsBgDA\nqc9R7wnI5XKRzR6K+vqyqK8vi2z2UORyuWKXBQAAY06QOAH7938Yzc3l0dmZjs7OdDQ3lxeuTgAA\nwKlMkAAAABITJE5AbW1ZbNlyKGpqclFTk4stWw5FbW1ZscsCAIAxZ7L1CUin09HYWB4vvzww2brc\nZGsAACYEQeIEpdPpmDWrvNhlAADASeX0OQAAkJggAQAAJCZIAAAAiQkSAABAYoIEAACQmCABAAAk\nJkgAAACJCRIAAEBiggQAAJCYIAEAACQmSAAAAIkJEgAAQGKCBAAAkJggAQAAJCZIAAAAiQkSAABA\nYoIEAACQmCABAAAkJkgAAACJCRIAAEBiggQAAJCYIAEAACQmSAAAAIkJEgAAQGKCBAAAkJggAQAA\nJCZIAAAAiQkSAABAYoIEAACQmCABAAAkJkgAAACJCRIAAEBiggQAAJCYIAEAACQ2ZJDYsGFDXHLJ\nJZHJZKK6ujquu+66eOutt47ab+3atTFjxoyoqKiIhQsXxr59+8akYAAAoPiGDBI7d+6M22+/PTo6\nOmLHjh0xefLkuOKKK6K7u7uwz3333RcbN26MTZs2xe7du6O6ujoWLVoUfX19Y1o8AABQHJOH2mH7\n9u2Dfn7iiScik8lEe3t7fO1rX4t8Ph8PPfRQ3H333bFkyZKIiHj88cejuro6tm7dGsuWLRubygEA\ngKJJPEfigw8+iFwuF9OnT4+IiHfeeSe6urqisbGxsM/UqVNjwYIF0d7ePnqVAgAA40Yqn8/nk/zC\nTTfdFH/6059iz549kUqlor29Pb70pS/FX//615g5c2Zhv+985ztx4MCBwhWNnp6ewrY//vGPo1Q+\nAAAwFurq6gr/n8lkjto+5K1NH3XnnXdGe3t7tLW1RSqVGnL/4ewDAACUnmEHiVWrVsUzzzwTra2t\ncfbZZxfGa2pqIiKiq6tr0BWJrq6uwraPmz9//gjLnRj27NkTEd4nRp/eYizoK8aK3mIs6Kvh++gd\nRZ9kWHMk7rjjjnj66adjx44dMWfOnEHbZs+eHTU1NZHNZgtjBw8ejLa2tmhoaBhByQAAwHg35BWJ\n5cuXx5NPPhnPP/98ZDKZ6OzsjIiIqqqqqKysjFQqFStXroz169fH3Llzo66uLtatWxdVVVXR1NQ0\n5n8AAABw8g0ZJB555JFIpVJx+eWXDxpfu3ZtrFmzJiIiVq9eHf39/bF8+fLo7u6O+vr6yGazUVlZ\nOTZVAwAARTVkkMjlcsN6oZaWlmhpaTnhggAAgPEv8XMkAAAABAkAACAxQQIAAEhMkAAAABITJAAA\ngMQECQAAIDFBAgAASEyQAAAAEhMkAACAxAQJAAAgMUECAABITJAAAAASEyQAAIDEBAkAACAxQQIA\nAEhMkAAAABITJAAAgMQECQAAIDFBAgAASEyQAAAAEhMkAACAxAQJAAAgMUECAABITJAAAAASEyQA\nAIDEBAkAACAxQQIAAEhMkAAAABITJAAAgMQECQAAIDFBAgAASEyQAAAAEhMkAACAxAQJAAAgMUEC\nAABITJAAAAASEyQAAIDEBAkAACAxQQIAAEhMkAAAABITJAAAgMRS+Xw+fzL+oZ6enpPxzwAAAKMs\nk8kcNeaKBAAAkJggAQAAJHbSbm0CAABOHa5IAAAAiQkSAABAYoIEAACQmCAxTuXz+Vi8eHGk0+l4\n7rnnBm3r7u6OpUuXxumnnx6nn3563HLLLZbX5Zi6u7tjxYoVce6550ZFRUV89rOfje9+97vxz3/+\n86j99BUj8dOf/jRmz54d06ZNi/nz50dbW1uxS6KEbNiwIS655JLIZDJRXV0d1113Xbz11ltH7bd2\n7dqYMWNGVFRUxMKFC2Pfvn1FqJZStWHDhkin07FixYpB4/rqxAgS49SDDz4YkyZNioiIVCo1aFtT\nU1Ps3bs3fv3rX8f27dvjtddei6VLlxajTErAgQMH4sCBA/HjH/843nzzzXjyySdj165dcfPNNw/a\nT18xEk8//XSsXLky7r333ti7d280NDTE4sWLY//+/cUujRKxc+fOuP3226OjoyN27NgRkydPjiuu\nuCK6u7sL+9x3332xcePG2LRpU+zevTuqq6tj0aJF0dfXV8TKKRUvv/xybN68OS644IJBx1T6ahTk\nGXdeeeWVfG1tbf7dd9/Np1Kp/HPPPVfYtm/fvnwqlcq3t7cXxtra2vKpVCr/9ttvF6NcStC2bdvy\n6XQ639vbm8/n9RUjd+mll+aXLVs2aKyuri5/9913F6kiSl1fX19+0qRJ+RdeeCGfz+fzuVwuX1NT\nk1+/fn1hn/7+/nxVVVX+0UcfLVaZlIj3338//7nPfS7/0ksv5b/yla/kV6xYkc/n9dVocUVinOnt\n7Y2mpqbYvHlzfPrTnz5qe0dHR5x22mlx2WWXFcYaGhqisrIyOjo6TmaplLCenp4oLy+PioqKiNBX\njMy///3veO2116KxsXHQeGNjY7S3txepKkrdBx98ELlcLqZPnx4REe+88050dXUN6rOpU6fGggUL\n9BlDWrZsWdx4443x5S9/OfIfeeKBvhodk4tdAIPddtttcfXVV8eVV175ids7OzuPChipVCqqq6uj\ns7PzZJRIiXv//ffjBz/4QSxbtizS6SPnEvQVI/Hee+/F4cOH48wzzxw0rm84EXfccUdcdNFFhRMb\nA730SX124MCBk14fpWPz5s3x5z//ObZu3RoRg28V11ejwxWJk+Dee++NdDp93P927twZTzzxRLzx\nxhtx//33R0QUknPeMwP5BMPpq127dg36nb6+vrj22mujtra20GcA48Wdd94Z7e3t8dxzzx01P/CT\nDGcfJqa333477rnnnnjqqacKc07z+fywjqn01fC5InESrFq1Km655Zbj7lNbWxs///nPY9++fXHa\naacN2vaNb3wjGhoaYteuXVFTUxN///vfB23P5/Px7rvvRk1NzajXzvg13L4a0NfXF1dffXWk0+l4\n4YUXYsqUKYVt+oqR+NSnPhWTJk2Krq6uQeNdXV3xmc98pkhVUapWrVoVzzzzTLS2tsbZZ59dGB/4\nDOrq6oqZM2cWxru6unw+cUwdHR3x3nvvxXnnnVcYO3z4cPz2t7+NRx99NN58882I0FcnSpA4Cc44\n44w444wzhtzvRz/6Udx1112Fn/P5fJx//vnx4IMPxvXXXx8REZdddln09fVFR0dH4bJvR0dH/Otf\n/4qGhoax+QMYl4bbVxFH5t4sXrw4UqlUvPjii4W5EQP0FSMxZcqUuPjiiyObzcbXv/71wvhvfvOb\nuPHGG4tYGaXmjjvuiGeffTZaW1tjzpw5g7bNnj07ampqIpvNxsUXXxwREQcPHoy2trZ44IEHilEu\nJWDJkiVx6aWXFn7O5/PR3Nwcc+bMie9///tRV1enr0aBIDGOnHXWWXHWWWcdNV5bW1s4O3PuuefG\nVVddFbfeems89thjkc/n49Zbb41rr7026urqTnLFlILe3t5obGyM3t7eeP7556O3tzd6e3sj4kgY\nKSsr01eM2J133hlLly6NSy+9NBoaGuJnP/tZdHZ2xm233Vbs0igRy5cvjyeffDKef/75yGQyhXvX\nq6qqorKyMlKpVKxcuTLWr18fc+fOjbq6uli3bl1UVVVFU1NTkatnvMpkMpHJZAaNVVRUxPTp02Pe\nvHkREfpqFAgSJWjr1q2xYsWKwoTs66+/PjZt2lTkqhivXn311fjd734XqVRq0Jm+VCoVra2tsWDB\ngojQV4zMTTfdFP/4xz9i3bp18be//S3OP//82LZt26Db6uB4HnnkkUilUnH55ZcPGl+7dm2sWbMm\nIiJWr14d/f39sXz58uju7o76+vrIZrNRWVlZjJIpUalUatD8B3114lJ5M3kBAICErNoEAAAkJkgA\nAACJCRIAAEBiggQAAJCYIAEAACQmSAAAAIkJEgAAQGKCBAAAkNj/ARyQEH1KJYxPAAAAAElFTkSu\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56cb073710>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that out intuition failed us because the nonlinearity of the problem forced all of the errors to be biased in one direction. This bias, over many iterations, can cause the Kalman filter to diverge. But this chart should now inform your intuition for the rest of the book - linear approximations applied to nonlinear problems yields inaccurate results."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Effect of Nonlinear Functions on Gaussians"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian.  Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from numpy.random import normal\n",
      "\n",
      "data = normal(loc=0.0, scale=1, size=500000)\n",
      "ys = 2*data + 1\n",
      "\n",
      "plt.hist(ys,1000)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uukvHjh2TJB0/flzpdLrgmPb2di1YsECdnZ2SpM7OTk2ZMkVLlizJH9PR0aHG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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56cb050860>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is an unsuprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from nonlinear_plots import plot_transfer_func\n",
      "\n",
      "def g(x):\n",
      "    return 2*x+1\n",
      "\n",
      "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mBRw4vRltvTtJVui6eP3PesWwJ/KnWrXbG/0dCksK4GinxojekwzqvTVtuOQf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\nSAAAAAAYQ0ECAAAAwJj/A1Mr7UfRPpxPAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56cb047eb8>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The plot labelled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. For the output I computed the mean by taking the average of all the points, and drew the results with the dotted blue line. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n",
      "\n",
      "Now let's look at a nonlinear function and see how it affects the probability distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from nonlinear_plots import plot_transfer_func\n",
      "\n",
      "def g(x):\n",
      "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
      "\n",
      "plot_transfer_func (data, g, lims=(-3,3), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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t+vp0xo+wtrCtZ0RERPVnatwCYwe+Al+3QBwJ34bT1w6jXF6m1OZRzgNsC/kF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\nXugQzCEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56c9477ac8>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result may be somewhat suprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian.  Recall the equations for multiplying two univariate Gaussians:\n",
      "$$\\begin{aligned}\n",
      "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
      "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
      "\\end{aligned}$$\n",
      "\n",
      "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n",
      "\n",
      "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y=g(data)\n",
      "plot_transfer_func (y, g, lims=(-3,3), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SATkFmSgszpc7DCJqhTjOkD4aO/ApvDBhIUyNzdXKb2dcx2d/vY2E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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56c95469b0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As you can see the probability function is futher distorted from the original Gaussian. However, the graph is still somewhat symmetric around x=0, let's see what the mean is."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print ('input  mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n",
      "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "input  mean, variance: 0.0013, 1.0023\n",
        "output mean, variance: -0.0296, 2.2464\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n",
      "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def h(x): return -1.5*x\n",
      "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n",
      "out = h(data)\n",
      "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MkiIlhPCF1wHGmjVrcODAAWRkZEBbWxteXl5Ys2YNXFxc+GyGvEQoEEJXW4+T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\nDx027/TpJt6PAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56c95cf710>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "output mean, variance: -0.0020, 2.2553\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "out = h(data)\n",
      "out2 = g(data)\n",
      "\n",
      "for i in range(10):\n",
      "    out = h(out)\n",
      "    out2 = g(out2)\n",
      "print ('linear    output mean, variance: %.4f, %.4f' % \n",
      "       (np.average(out), np.std(out)**2))\n",
      "print ('nonlinear output mean, variance: %.4f, %.4f' % \n",
      "       (np.average(out2), np.std(out2)**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "linear    output mean, variance: -0.1129, 7499.3714\n",
        "nonlinear output mean, variance: -2.0601, 26297.8576\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A 2D Example"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is somewhat hard for me to look at probability distributes like this and really reason about what will happen in a real world filter. So let's think about tracking an aircraft with radar. the aircraft may have a covariance that looks like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "import numpy as np\n",
      "P = np.array([[6, 2.5], [2.5, .6]])\n",
      "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GDiKaea4fYrtvo6Pb6HsD9Nwe8vkE9VoR1TJPDSciul1JmuLyjo3Qz2FD3cBK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\nxcgbllzTlZt31G25cjxHruXIs035riXPseQ7Fl0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       "text": [
        "<matplotlib.figure.Figure at 0x7f56c9548160>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So what happens when we try to linearize this problem? The radar gives us a range to the aircraft. Suppose the radar is directly under the aicraft (x=10) and the next measurement states that the aircraft is 3 miles away (y=3). The positions that could match that measurement form a circle with radius 3 miles, like so."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib.patches import Ellipse\n",
      "circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7)\n",
      "ax = plt.gca()\n",
      "ax.add_artist(circle1)\n",
      "plt.xlim(0,10)\n",
      "plt.ylim(0,3)\n",
      "\n",
      "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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efPBBbN68GS6XC48//ji++c1v4oEHHsC99947fr9s9u2pxaNHj17C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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56cad58320>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see by inspection that the probable position of the aircraft is somewhere near x=11.4, y=2.7 because that is where the covariance ellipse and range measurement overlap. But the range measurement is nonlinear so we have to linearize it. We haven't covered this material yet, but the EKF will linearize at the last position of the aircraft - (10,2). At x=2 the range measurement has y=3, and so we linearize at that point."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib.patches import Ellipse\n",
      "circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7)\n",
      "ax = plt.gca()\n",
      "ax.add_artist(circle1)\n",
      "plt.xlim(0,10)\n",
      "plt.ylim(0,3)\n",
      "plt.axhline(3, ls='--')\n",
      "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HMTB0EM1zp/oT+PkLh7B9/xkY5vSrUK1qr8ad13Rg/bJ6LgdKZUHXDSSyoyMa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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56c98ac128>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we have a linear representation of the problem (literally a straight line) which we can solve. Unfortunately you can see that the intersection of the line and the covariance ellipse is a long way from the actual aircraft position."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib.patches import Ellipse\n",
      "circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7)\n",
      "ax = plt.gca()\n",
      "ax.add_artist(circle1)\n",
      "plt.xlim(0,10)\n",
      "plt.ylim(0,3)\n",
      "plt.axhline(3, ls='--')\n",
      "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)\n",
      "plt.scatter([11.4], [2.65],s=200)\n",
      "plt.scatter([12],[3], c='r', s=200)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4rR6EvX6EfNzscjYxdBAtUgVNx6v7T+OZN47h4MmRGds2VQVw+9VLsWVtC7ys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p074Xa7UV9fb1cJZBEhBGQ59VdNlmUIIWyqiKzm8XhQXFyMvr4+NDQ04PHHH7e7JDJZZWUlSkpK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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f56cad76198>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That sort of error often leads to disastrous results. The error in this estimate is large. But in the next innovation of the filter that very bad estimate will be used to linearize the next radar measurement, so the next estimate is likely to be markedly worse than this one. After only a few iterations the Kalman filter will diverge, and start producing results that have no correspondence to reality.\n",
      "\n",
      "Of course that is a rather large covariance ellipse for an aircraft - it spans miles. I exaggerated the size to illustrate the difficulties of highly nonlinear systems. In real radar tracking problems the nonlinearity is usually not that bad, but the errors can still accumulate. And other systems you may be working with do have this amount of nonlinearity - this was not an exaggeration to make a point. You will always be battling divergence when working with nonlinear systems."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Algorithms"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You may be impatient to solve a specific problem, and wondering which filter to use. So let me quickly run through the options. The subsequent chapters are somewhat independent of each other, and you can fruitfully skip around, though I recommend reading linearly if you truly want to master all of the material. \n",
      "\n",
      "The workhorses of nonlinear filters are the *linearized Kalman filter* and *extended Kalman filter*. These two techniques were invented shortly after Kalman published his paper and they have been the main technique used since then. The flight software in airplanes, the GPS in your car or phone almost certainly use one of these techniques. \n",
      "\n",
      "However, these techniques are extremely demanding. The EKF linearizes the differential equations at one point, which requires you to find a solution to a matrix of partial derivatives (a Jacobian). This can be difficult or impossible to do analytically. If impossible, you have to use numerical techniques to find the Jacobian, but this is expensive computationally and introduces error into the system. Finally, if the problem is quite nonlinear the linearization leads to a lot of error being introduced in each step, and the filters frequently diverge. You can not throw some equations into some arbitrary solver and expect to to get good results. It's a difficult field for professionals. I note that most Kalman filtering textbooks merely gloss over the extended Kalman filter (EKF) despite it being the most frequently used technique in real world applications. \n",
      "\n",
      "Recently the field has been changing in exciting ways. First, computing power has grown to the point that we can use techniques that were once beyond the ability of a supercomputer. These use *monte carlo* techniques - the computer generates thousands to tens of thousands of random points and tests all of them against the measurements. It then probabistically kills or duplicates points based on how well they match the measurements. A point far away from the measurement is unlikely to be retained, whereas a point very close is quite likely to be retained. After a few iterations ther is a clump of particles closely tracking your object, and a sparse clould of points where there is no object.\n",
      "\n",
      "This has two benefits. First, there is no process model. You do not need to predict your system state in the next time step. This is of huge value if you do not have a good model for the behavior of the system. For example, it is hard to predict the behavior of a person in a crowd for very long. You don't know where they are going, and they are endlessly being diverted and jostled by the crowd. Second, the algorithm can track arbitrarily many objects at once - some particles will match the behavior on one object, and other particles will match other objects. So this technique is often used to track automobile traffic, people in crowds, and so on. \n",
      "\n",
      "The costs should be clear. It is computationally expensive to test tens of thousands of points for every step in the filter. But modern CPUs are very fast, and this is a perfect problem for GPUs because the algorithm is highly parallizable. If we do have the ability to use a process model that is important information that is just being ignored by the filter - you rarely get better results by ignoring information. Of course, there are hybrid filters that do use a process model. Then, the answer is not mathematical. With a Kalman filter my covariance matrix gives me important information about the amount of error in the estimate. The particle filter does not give me a rigorous way to compute this. Finally, the output of the filter is a cloud of points; I then have to figure out how to interpret it. Usually you will be doing something like taking the mean of the points, but this is a difficult problem. There are still many points that do not 'belong' to a tracked object, so you first have to run some sort of clustering algorithm to first find the points that seem to be tracking an object, and then you need another algorithm to produce an state estimate from those points. None of this is intractable, but it is all quite computationally expensive. \n",
      "\n",
      "\n",
      "Finally, we have a new algorithm called the *unscented Kalman filter* (UKF) that does not require you to find analytic solutions to nonlinear equations, and yet almost always performs better than the EKF. It does especially well with highly nonlinear problems - problems where the EKF has significant difficulties. Designing the filter is extremely easy. Some will say the jury is still out, but to my mind the UKF is superior in almost every way to the EKF, and should be the starting point for any implementation, especially if you are not a Kalman filter professional with a graduate degree in the relevant mathematical techniques. The main downside is that the UKF can be a few times slower than the EKF, but this really depends on whether the EKF solves the Jacobian analytically or numerically. If numerically the UKF is almost certainly faster. Finally, it has not been proven (and probably it cannot be proven) that the UKF always yields more accurate results than the EKF. In practice it almost always does, often significantly so. It is very easy to understand and implement, and I strongly suggest this technique as your starting point. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The world is nonlinear, but we only really know how to solve linear problems. This introduces signifcant difficulties for Kalman filters. We've looked at how nonlinearity affects filtering in 3 different but equivelent ways, and I've given you a brief summary of the major appoaches: the linearized Kalman filter, the extended Kalman filter, the Unscented Kalman filter, and the particle filter. \n",
      "\n",
      "Until recently the linearized Kalman filter and EKF have been the standard way to solve these problems. They are very difficult to understand and use, and they are also potentially very unstable. \n",
      "\n",
      "Recent developments have offered what are to my mind superior approaches. The UKF dispenses with the need to find solutions to partial differential equations, but it is usually more accurate than the EKF. It is easy to use and understand. I can get a basic UKF going in just a few minutes by using FilterPy. The particle filter dispenses with mathmatical modelling completely in favor of a monte carlo technique of generating a random cloud of thousands of points. It runs slowly, but it can solve otherwise intractable problems with relative ease.\n",
      "\n",
      "I get more email about the EKF than anything else; I suspect that this is because most treatments in books, papers, and on the internet use the EKF. If your interest is in mastering the field of course you will want to learn about the EKF. But if you are just trying to get good results I point you to the UKF and particle filter first. They are so much easier to implement, understand, and use, and they are typically far more stable than the EKF. \n",
      "\n",
      "Some will quibble with that advice. A lot of recent publications are devoted to a comparison of the EKF, UKF, and perhaps a few other choices for a given problem. Do you not need to perform a similar comparision for your problem? If you are sending a rocket to Mars, then of course you do. You will be balancing issues such as accuracy, round off errors, divergence, mathematical proof of correctness, and the computational effort required. I can't imagine not knowing the EKF intimately. \n",
      "\n",
      "On the other hand the UKF works spectacularly! I use it at work for real world applications. I mostly haven't even tried to implement an EKF for these applications because I can verify that the UKF is working fine. Is it possible that I might eke out another 0.2% of performance from the EKF in certain situations? Sure! Do I care? No! I completely understand the UKF implementation, it is easy to test and verify, I can pass the code to others and be confident that they can understand and modify it, and I am not a masochist that wants to battle difficult equations when I already have a working solution. If the UKF or particle filters starts to perform poorly for some problem then I will turn other techniques, but not before then. And realistically, the UKF usually provides substantially better performance than the EKF over a wide range of problems and conditions. If \"really good\" is good enough I'm going to spend my time working on other problems. \n",
      "\n",
      "I'm belaboring this point because in most textbooks the EKF is given center stage, and the UKF is either not mentioned at all or just given a 2 page gloss that leaves you completely unprepared to use the filter. This is not due to ignorance on the writer's part. The UKF is still relatively new, and it takes time to write new editions of books. At the time many books were written the UKF was either not discovered yet, or it was just an unproven but promising curiosity. But I am writing this now, the UKF has had enormous success, and it needs to be in your toolkit. That is what I will spend most of my effort trying to teach you. "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}