{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Unscented Kalman Filter" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "import book_format\n", "book_format.set_style()" ] }, { "cell_type": "markdown", "metadata": {}, "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", "$$x=\\sqrt{\\text{slant}^2 - \\text{altitude}^2}$$\n", "\n", "The nonlinearity can also occur in the process model - we may be tracking a ball traveling through the air, where the effects of air drag lead to 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." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4cAAAGGCAYAAADILvQaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAA9hAAAPYQGoP6dpAABz1UlEQVR4nO3dd3xT5f4H8M/JTroHXbSlBdkIskGGVKQKCMhVFAcKij9RULlVEdCrxUEdXMUFggsERLz3KuilCkUFRTYXBNll0wF0pivJSXJ+f6QNLW2hpU1P0nzer1deyTl5zsn3PKQk3zxLkCRJAhEREREREXk1hdwBEBERERERkfyYHBIRERERERGTQyIiIiIiImJySERERERERGBySERERERERGBySERERERERGBySERERERERGBySERERERERGBySERERERERGBySCSbbdu2Ydy4cYiMjIRGo0FERATuuusubN269ZrPOXfuXKxevbrxgryCzMxMJCcnY+/evU3yekRERETkWkwOiWTwwQcfYMCAATh37hzeeustbNiwAfPmzUNGRgYGDhyIDz/88JrO29TJ4Zw5c5gcEhERETUTKrkDIPI2f/zxB6ZPn44RI0bgu+++g0p16c9w/PjxGDt2LJ5++ml0794dAwYMkDFSIiIiIvImbDkkamIpKSkQBAELFy6skhgCgEqlwoIFCyAIAt544w0AwMSJExEXF1ftPMnJyRAEwbktCAJKSkqwdOlSCIIAQRAwZMgQAMCSJUsgCALS0tIwadIkBAcHw8fHB6NGjcKJEyeqnDcuLg4TJ06s9npDhgxxnm/jxo3o3bs3AGDSpEnO10tOTr62SiEiIiIi2TE5JGpCNpsNv/76K3r16oXo6Ogay8TExKBnz5745ZdfYLPZ6nzurVu3Qq/XY8SIEdi6dSu2bt2KBQsWVCnzyCOPQKFQ4KuvvsL8+fOxY8cODBkyBAUFBfW6jh49euCLL74AALz44ovO15s8eXK9zkNERERE7oPdSomaUE5ODkpLSxEfH3/FcvHx8dixYwdyc3PrfO5+/fpBoVCgRYsW6NevX41levXqhc8++8y53blzZwwYMAAfffQRXnjhhTq/lr+/P7p06QIAaNOmTa2vR0RERESegy2HRG5IkiQAqNJttDHcf//9VbZvvPFGtGrVCr/++mujvg4REREReR4mh0RNKDQ0FAaDASdPnrxiuVOnTsHHxwfBwcGN+voRERE17qtPCyURERERNU9MDomakFKpREJCAnbt2oVz587VWObcuXPYvXs3br75ZiiVSuh0OpjN5mrlcnJy6v362dnZNe4LCQlxbjfm6xERERGR52BySNTEZs2aBUmS8MQTT1SbcMZms+Hxxx+HJEmYOXMmAMfsoRcuXMD58+ed5SwWC9atW1ft3FqtFmVlZbW+9ooVK6psb9myBadPn3bOQlrxevv27atS7ujRozhy5Ei11wJwxdcjIiIiIs/B5JCoiQ0YMADz58/H2rVrMXDgQKxYsQK///47VqxYgUGDBiE1NRXz58/HjTfeCAC45557oFQqMX78eKSmpuLbb79FYmJijTOZXn/99di4cSN++OEH7Nq1q1pCt2vXLkyePBnr1q3Dp59+irFjx6Jly5Z44oknnGUmTJiAgwcP4oknnsDPP/+Mzz//HKNHj0aLFi2qnKtNmzbQ6/VYsWIFNm7ciF27diEzM9MFNUZERERETYHJIZEMnnzySfzxxx+Ijo7GM888g5tvvhlJSUmIjIzE5s2b8eSTTzrLxsfHY82aNSgoKMBdd92F5557DuPGjcODDz5Y7bzvvfce2rZti/Hjx6N379547LHHqjz/2WefwWKxYPz48XjqqafQq1cvbNy4scrYxvvuuw9vvfUW1q1bh9tvvx0LFy7EwoUL0a5duyrnMhgM+Pzzz5Gbm4vExET07t0bixcvbuSaIiIiIqKmIkgV0yISUbO1ZMkSTJo0CTt37kSvXr3kDoeIiIiI3BBbDomIiIiIiIjJIREREREREbFbKREREREREYEth0RERERERAQmh0RERERERAQmh0RERERERARAJXcAjc1utyMzMxN+fn4QBEHucIiISEaSJKGoqAhRUVFQKPh7KBER0ZU0u+QwMzMTMTExcodBRERu5OzZs4iOjpY7DCIiIrfW7JJDPz8/AI4vAv7+/jJHIy9RFLF+/XokJiZCrVbLHY7H87T6PJhZiLsXbcM3j/VDp6gA2eK4ed5GXCgyI8xPi1+eHQLA8+rS3bE+a2c0GhETE+P8bCAiIqLaNbvksKIrqb+/P5NDUYTBYIC/vz+/MDYCT6tP3yIJCq0Bvn7y/i3semV0tX2eVpfujvV5dRxmQEREdHUcgEFERERERERMDomIiIiIiIjJIZHb+M/uc5j4xQ5sOnpR7lCIiIiIyAs1uzGHRJ5qyZZTAIB5647gpnYt5A2mEc3fcBRFJiv8dCpMv6Wd3OEQERERUS2YHBKRS3294yyyjSZE+OuYHBIRERG5MXYrJSIiIiIiIiaHRO7AbpfkDoGIiIiIvByTQyI3YJeYHBIRERGRvJgcErkBG5NDIiIiIpIZk0MiN2C3V922sZspERERETUxJodEbuDylkOL1V5LSSIiIiIi12BySOQGLm8ptNiYHBIRERFR02JySOQGLp+tlC2HRERERNTUVHIHQEQ1dCttRi2HfVsHI6/EgmAfjdyhEBEREdEVMDkkcgOXtxyKzajl8L3x3eUOgYiIiIjqgN1KidzA5S2HYjNqOSQiIiIiz8DkkMgNXD4hjbkZtRwSERERkWdgckjkBi5f57A5jTkkIiIiIs/AMYdEbqBat9Jm1HJ47+JtyCk2I9RXi5X/10/ucIiIiIioFkwOidxAc17n8GROCbKNJhSZrHKHQkRERERXwG6lRG7AzglpiIiIiEhmTA6J3EC1lsNm1K2UiIiIiDwDk0MiN8DZSomIiIhIbkwOidxA9W6lUi0liYiIiIhcg8khkRtgt1IiIiIikhuTQyI3wAlpiIiIiEhuTA6J3IDVxuSQiIiIiOTF5JDIDVzWq5QT0hARERFRk1PJHQARVe9W2pzGHD41tC1KLVYYNPzvhoiIiMidefy3NbPZDLPZ7Nw2Go0AAFEUIYqiXGG5hYrr9/Z6aCyurE+zKEKqlCCaRWuDX8dqtTrv5XwPjOsR6Xx8eR3yvdk4WJ+1Y50QERHVnSBJkkfPmZ+cnIw5c+ZU2//VV1/BYDDIEBFR/R3IF/Dj2Uu9vNv4Sxgb17DWw7PFwLz9Kjx7vRUxvg2NkMgzlZaW4r777kNhYSH8/f3lDoeIiMiteXxyWFPLYUxMDHJycrz+i4AoikhLS8OwYcOgVqvlDsfjubI+fzlyER/8cty53T0mAC/d3rFB5zyQacQdC7dh9eP90DnKvf4W+N5sXKzP2hmNRoSGhjI5JCIiqgOP71aq1Wqh1Wqr7Ver1fySVI510bhcUZ+CoIAgCM5tq4QGv4ZKpXLey/nvf8Fogk2SoBQEhPnrqjzH92bjYn1Wx/ogIiKqO49PDomag8snpGlOs5WO/vAPZBtNiPDXYdvsoXKHQ0RERES14FIWRG7Aar98nUOP7u1NRERERB6IySGRG7h8nUOL1SZPIERERETktZgcErkBO1sOiYiIiEhmTA6J3IDtsuTQ0ozGHBIRERGRZ2BySOQGmBwSERERkdyYHBK5gctnK7XYmBwSERERUdNickjkBmyXJYc2u1RtHCIRERERkSsxOSRyAzUlgmw9JCIiIqKmxOSQyA1cvs4hwOSQiIiIiJqWSu4AiKj6OodA85mUZsWjfWGzS1AqBLlDISIiIqIrYHJI5AZq6lYqNpOWwzYtfOUOgYiIiIjqgN1KidzA5RPSAIBo5YQ0RERERNR0mBwSuYHL1zkEAIvNJkMkREREROSt2K2UyA3U1K3U3EzGHK7Zm4Eyiw16jRJjbmgpdzhEREREVAsmh0RuoMZupbbm0a00JfUwso0mRPjrmBwSERERuTF2KyVyAzWuc9hMWg6JiIiIyDMwOSRyAzWtc9hcZislIiIiIs/A5JDIDdTUrZQth0RERETUlJgcErmBGnLDZjMhDRERERF5BiaHRG6gpqUs2K2UiIiIiJoSk0MiN1DjOodsOSQiIiKiJsTkkMgNsOWQiIiIiOTG5JDIDdhrXOeQySERERERNR2V3AEQUc3JYXOZkKaFn7bKPRERERG5JyaHRG7AaqueHBabrTJE0vh+eHKg3CEQERERUR2wWymRG6hpncP8Eku9zrH7dD5W78lAmcXWWGERERERkRdhyyGRG6jIDRUCoFAIsNok5NYjOTxvNCH5+wMAHC2OD/Rr5YowiYiIiKgZY8shkRuomK1UqRAQbNAAAPJL654c7jyV53y8aufZxg2OiIiIiLwCWw6J3EDl5DDIR4MLRWYYy6wQbXaolVf/DafUjbuSzvp2PwrLLAjQa5Dyt+vlDoeIiIiIasHkkMgNVCSHCkFAsI/GuT+/1IIwP91VjzeJ7psc/nr4ArKNJkT4X/06iIiIiEg+7FZK5AYqlrJQKi5LDkvEOh1fueVQEBo3NiIiIiLyDkwOidxAleTQcCk5zC0x1+n4yi2HOrWycYMjIiIiIq/A5JDIDVgvG3NYoa4th5WXr9AzOSQiIiKia8DkkMgNVB1zqHbuz6vjjKVG06UkkskhEREREV0LJodEbuDSOocCgip1K80rrltyWFh2KTnkmEMiIiIiuhZMDoncwKWlLIAQH61zf13XOqycHIo2e+MGR0RERERegckhkRuoSA5VCgX8dCooFI7mv7ySqyeHdruEIpPVuW22MjkkIiIiovpjckjkBmzl/UoFAVAoBAQZHOMO69JyaDSJzm6pAGBhckhERERE10AldwBEVHUpCwAI9tEgt9iCwjIRVpsdKmXtv+MYy6xVti1u1q109A1RKCwVEWBQX70wEREREcmGySGRG7BXjDksn02mYq1DSQIKykSE+mprPbbyeEMAsNok5/ncwewRHeUOgYiIiIjqgN1KiWRmt0uoyOUqWg6rrnV45a6llyeHACDa3av1kIiIiIjcH5NDIpnZKw0YVJS3HIZUSg7PG81XPL6grHryyHGHRERERFRfHt+t1Gw2w2y+9OXZaDQCAERRhChWb1HxJhXX7+310FhcVZ8Wqx2SM0GUIIoiYoN0zn17z+Shb1xArcfnF5srHe9QYrLAanWMRbRarW73HuB7s3GxPmvHOiEiIqo7Qbr8W6WHSU5Oxpw5c6rt/+qrr2AwGGSIiKh+LDbg/QNKAECsr4S7W9thsQEfHlTCLgEBGgmT29trXdx+Q4aAvblVOwFMbm9DkQjM26/Cs9dbEePr6quo3et7lCgUgQA18EJ3m3yBkFcqLS3Ffffdh8LCQvj7+8sdDhERkVvz+JbDWbNmISkpybltNBoRExODxMREr/8iIIoi0tLSMGzYMKjVnCmyoVxVn8VmK5ae2wUAaB0biBEjOgAAdksH8VeGoyW8+4BuiArU13j8gfVHcdKaV2XfwJu6oshkxbz92zBw4EB0jpLvb2HugU0wm8wQfLQYMeImAHxvNjbWZ+0qepMQERHR1Xl8cqjVaqHVVp/JUa1W80tSOdZF42rs+lRYAaG8WVClVDjP3SsuBAcyiwAA+7OK0apFzQlekdnmPL6CHQqoVI4/b5VKJeu/vwDBeX95HHxvNi7WZ3WsDyIiorrjhDREMqu87ISyUpLXIzbQ+fh/pwtqPf7ydQ4B91vrkIiIiIjcH5NDIpnZKg37rVjKAgDiQnwQWL5w/P6MApRZqo/Xs9sl5NWw1IVo8+ihxEREREQkAyaHRDKr0nJYKTlUKAT0iQsGAJhEO1L3Z1U79lC2EcXm6i2HZpETvxARERFR/TA5JJKZrYZ1Divc0b2lc5bS1XszYLos6dt09KLzcesWPs7HbDkkIiIiovpickgkM1ullkOFompyGBNswMDrQgEABaUifvor2/mc1WbH5mM5AACNSoFBbVs4n7PY2HJIRERERPXD5JBIZvZKc8coa1jM8J7eMc7HX249hcPZjqn595wtQJHJ0aW0b3wwAvSXZmW0WDkhDRERERHVD5NDIplV7laqUlZPDluF+ODWzuEAHN1FX/3vQaQdPI9PfjvhLHNTuxbQqC79OVvYrZSIiIiI6snj1zkk8nSVu5XW0HAIAHjspjbILDRh/7lCGMuseP/nY87nIgN06NEqCDtP5Tn3uVPL4etju8Ak2qFT87coIiIiInfG5JBIZnap5nUOK1MrFZg9oiPmfH8Ah7OLnPtbhRjw0qhOUCsV0FZuOXSj5HBox3C5QyAiIiKiOmBySCQzWy1LWVzOV6vCW3d1xd6zBfjl8AX4aFV4sH8rGDSOP2ONUuksa7FyQhpyTxeLzMgvtaBtmC+E2prKiYiISBZMDolkVtfkEAAEQUD32CB0jw2q9lzlMYdcyoLcUWGZiKkr/ocy0YaZwztgQPlMvEREROQeOAiISGb2K6xzWB/qSpPZWGzu0610/7lC7D6dj/3nCuUOhWS27q9slJWv1fnWT4dljoaIiIgux5ZDIpldaZ3D+qjccmh2ozGHj365C9lGEyL8ddg2e6jc4ZCMis1W52M7G7eJiIjcDlsOiWRWlwlp6qJqt1L3SQ6JKlT+0aIBv4MQERGRizA5JJJZ5TxO1ZCWQ6V7zlZKVMFcaaIkrUp5hZJEREQkByaHRDJrrG6llb9sMzkkd2QSL70vtVz3koiIyO3w05lIZlUnpLn281SZkIbJIbmhwjLR+bjyupxERETkHvjpTCSz+ixlcSVKheBMLjnmkNxRYZnF+ZgT0hAREbkfJodEMrNJjZMcCoLgnJTGnWYrJaqQX3Kp5bDUYr1CSSIiIpIDk0MimdntjTNbKQCoyyelcad1DokAR1fnyktZlFlskCQ2HxIREbkTJodEMqvcrVRoYHJY0XLIbqXkbiqPNwQc3Ur5IwYREZF7YXJIJDN7I3UrBS4tZ2EW+aWb3EtBqaXavjKLrYaSREREJBeV3AEQebvGWucQANRu2HK44ZmbIElSg1tFybPll4rV9pVabAg0yBAMERER1YjJIZHMKk9I05B1DgFAW2nMobuM5/LV8r8ZqqXlUGTLIRERkTtht1IimVWekKaBuaFzzKEkVR3LSCS3ghpaDtmtlIiIyL0wOSSSma0RZyvVVFpYXLQxOST3kV9Dy2Epk0MiIiK3wv5eRDJrrHUOgUtLWQCA1e4e4w4//f0EikxW+OlUmDyotdzhkExqGnPIbqVERETuhckhkcyqrHPY0NlKq7QcuktyeBLZRhMi/HVMDr1YYVlNs5VaayhJREREcmG3UiKZVW45bPA6h5VaDi1Wdisl95FXwm6lRERE7o7JIZHMXNVy6C7dSolsdgn5JexWSkRE5O6YHBLJrPKENA1d51DLCWnIDf30V7YzEfTTXRrNwNlKiYiI3AuTQyKZVc7hFA3sVlplQho3GXNI3q3IJGLF9tPO7YdujHM+ZrdSIiIi98LkkEhmVdY5bOBfZOXk0F0mpCHvZbNLWLDxOIpMjolnbmrXAt1jAp3PMzkkIiJyL5ytlEhmVZayaGDLYeVupUu3Olprlm07hetbBiI22IA+8cHQqZUNeg2iujCaRLy/4Ri2n8wD4BgP+9CNcdCpL71HTRxzSERE5FaYHBLJzNaIE9JEB+mdj82io+Vw96kCHMwsAgAYNEr0iQ9GuL8OYX5atKh006qYNFLdmK02qBUKKGp4v543mrD+QDZ+2JflHFOoUgp47tb2aOGnrfJ+L+VSFkRERG6FySGRzBpzttI+8cF47tb22HoiFztO5lZ7vtRiw8YjF2s8NkCvRpifFlGBevjqVNCqFIgOMiAuxIAAgxr+OjV0aiUkSYLVLlXpwkreQZIkvJt2FL8euQhBAIJ9NGgf4QedSokLRWZcLDLhQpEZlRrDoVcrMXtkR9xQ3p1UqRCgVgoQbRK7lRIREbkZJodEMqvcrbShE9IIgoDB7VpgcLsW+CujELd/sBnPD+8Af50K207k4bdjF2Gx1jwWsbBMRGGZiGMXims9v1opwGaXYJeAiAAdWof6IMCghgABZaIN0UF69IgNRInZhsIyx9IF0UF6hPhqEOqrhdlqq7IWI3mW/RmF+LX8xwVJAnKLLdiSXv1HCABQCMCwTuG4p3csWvhpqzzno1WhoFRkt1IiIiI3w+SQSGZVJ6RpWHJYk8gAHbq0DEDf1iF47KbWyC404WKxGReMjpYe5+NiM/JKLFVafS5XeXmM7EITsgtN1cos23q62j6FICCvxIK7Fm6FIAB6tQK2IgX2/XQEPjoNDBoltCoFbHYJFpsdolWCTq1AbLABWrUCVpuElkF6RAboUVBqgV2SEKDXIECvdq7tKEmSM3GtIAhgC2cj+nrnWefj2GADLhaZq6xV6KtVITJAh36tQ3BzxzCE+mprOk35uFeRLYdERERuhskhkcwqtxw2dJ3Dq9GplYgL9UFcqE+Nz1usdlwoMqHMYkOR2YqTF0uQbTTBWCbCaBJRZLJCrVRAAHAqt+Sa1lKUJJS3LArYfjIfQgNbS3VqR1JptUs1JrahvhpEBOhgLY9Vr1E6klCrHWqVAiqFANFmh0qhQLi/Fj5aFVQKASqlwtkFUqlQQK0Qyrcd+yvKlFqsuFhkhl6jRGSADoLgaF0VbXZYbY6E1aBRItRPC61KAUEQUGaxQZIkaFVKZBWWIaOgDAaNCqG+GgT7aOCrVcFqdxxbcW12SYLVJkGCBKVCgFJwxKNUCLDbbMg3AwWlIkL9VZAkx4QwOrUj6bbY7Cg121Aq2lBqtqLE4rg3W+3QqBTw06kQGaCHQgCKTFbYJAmS5KhPs9UOY5mIjIIy7D9XCMDxg8P793aHAOBMXikkAOH+Whg0dftIMWgc41uZHBIREbkXJodEMqu84kRDu5U2lKZ8nGGFHrFBtZa12uzILbHAWN59VKkQsD+jEOkXihGgVyPUVwtBAIxlIrIKTSi12GC22mG22lBQYkFhYePEbBKvvGRHTrEFOcWWxnkxNyVJEgoLlfh39m7o1EqIdsnZIq0QUKU1tTGM6xXjHB9b2w8NV1KRHFYk6RoVW3eJiIjcAZNDIpnZq4w5lDGQelIpFQj31yHcX+fc17qFb52OFUUR3/83FQMSekC0CzCJNphEO1RKARqVAmqFAkaTiLN5pbBLgAQJJy+WILfEghAfDRQKAcYyEQWlIorNVigUAtQKASqlUGVSH4tVwrn8Uq9qoTJfNqa0sRPD2GADEtq3aNA5Ki+nUibamBwSERG5CSaHRE3EarOjyGRFQfnEL2UWGyRI2Hr80oQeDZ2t1B1NXrrTmdR9+lBv536VAgjx0UCtVtd6bJeWAQ1+fUmSHN0nlQrYJQkmqx1KQXB2t7TaJWiUCpisNlwwmmASHfustop7CaLdDptNgtVud3b3tJZva1QKtPDVocRixYUiMwQ4Ju5RKRRQKQUoBAFFJivySsyw2CRAkqDTKKEQHElxgF6NuFAfmEUbcootyC22wGS1QaVwHKtSCFAqBee2IAjOGWNt5S2EotWGI0cLEBYTiJxiC9RKBYJ9NDBb7SizWKHXKGHQqOCjUcKgVcGgUcJHo4JWrYBZtCO/1IKsQhMEAH46NdQqAQIE55hNf50K/no1AvRqXN8yAKoGjuOsaDkEgDKLow6IiIhIfkwOya1UjHOyld/bK91XjPOySyifeESCTZJgs5Xf2ysdA8dELxXbVfYBzrFcl4/nspd/6bbbK75822GzA1a7HaJoxa7zAnK3nYFod4zPs0mOCVAkydE9zmy1l7eCOVrCTFYbzOX31jqMz2uOyeFfGUZkG02IqNTC2JQEQXC2VCkgwLdSYqNTXEpSNCoF/HWemaSIoohU0xGMGNHhism2u6g8NpFrHRIREbkPr0gO/75qL4pMIlQKhaPLmlKBK/3wLaDqF/TKw8BqGhJW0StQKu/+Vnmfs0zlcqj6ZMUv9EKlsnbHyZxdDisfUdOkG5fvkiQJkl1CZpYC64r+hKBQ1HhARfIloSLJKY9Qqoj5UrSSVLULZMVxklT1MeAYO6dQVB1DZ5ck2O1VEz57peSqsbu/NTbHuC4F/jJlNngSlZq0C/eDr9Yr/iTJy1XuVvrPtKPwKW9JdfxZCVAIjv9rFYJwTeNwKx9iKq19aRYiIiKqyuO/iZrNZpjNZue20WgE4PglXRQdE2WcN5bBWOZ9v05LkgSjSYAlt9QlyYy3kSoS9Sut9VBOIQBatRI6lcI5Y6RW7WiZ8tepEGhQQ69WQhAAH40KEQE6dIr0g9XaeO/TinNZrVbn34IcnD+YQHLGcfk9NYyn1adBLTj/jk7nlLj0tUSTa89PRETUnHh8cpiSkoI5c+ZU279+/XoYDI5ZF0sLFBCtgE0SYLUD1zD7viwEXNZqebXyNRRQKYDSYmONx1bsEwSp0uNK+y87b01laoqzgl261GKqEC6Vq3Jf/lhRfqKK9s1q5QHYys+pqHTMpRaGS/svnVeq9pqVz1/ldvm+WsoogyWoFfnQKACVcOn1BQBKAY79CsfjGvNxCUBZ+a2cDUAGgIx9NZRvgLPFAKDC5s2bcbpu88S4hMmkBCDAZDIhNTW1ynNpaWnyBNVMeUp9ihZAZVIg1+z6H62splKXvwYREVFzIUh1aQZxYzW1HMbExCAnJwf+/v41HlMxrs25fdlzNR5T43lqSpwu75RaqcwVWu8qxyQIVy5bV6IoIi0tDcOGDfOIcUjuztPq80CmEXcs3IbVj/dD56ia/xaawsC3N+G80Yxwfy02P3cTAM+rS3fnqfUpSVW7sNsrd2d3dj0HHHvr+n9i1f+tjYVGxMdEorCwsNbPBCIiInLw+JZDrVYLrVZbbb9arfaoL0muxLpoXJ5SnyqVynkvZ7wVP5cIEKrF4Sl16SlYn9WpJO8bUkBERHStuLgUERERERERMTkkIiIiIiKiZtCt9HIVYwYrZi31ZqIoorS0FEajkV3NGoGn1WdxkRF2cymKi4wwGuWbrdZqKoHdbIbVZKsym7An1aW7Y33WruI95+HD64mIiJqEx09Ic7lz584hJiZG7jCIiMiNnD17FtHR0XKHQURE5NaaXXJot9uRmZkJPz8/r1/br2Lm1rNnz3KWvkbA+mw8rMvGxfqsnSRJKCoqQlRUFBQKjqQgIiK6kmbXrVShUPDX4cv4+/vzC2MjYn02HtZl42J91iwgIEDuEIiIiDwCf0YlIiIiIiIiJodERERERETE5LBZ02q1ePnll6HVauUOpVlgfTYe1mXjYn0SERFRY2h2E9IQERERERFR/bHlkIiIiIiIiJgcEhEREREREZNDIiIiIiIiApNDr2Q2m3HDDTdAEATs3btX7nA8zqlTp/DII48gPj4eer0ebdq0wcsvvwyLxSJ3aB5jwYIFiI+Ph06nQ8+ePfH777/LHZLHSUlJQe/eveHn54ewsDDccccdOHLkiNxhERERkQdjcuiFZsyYgaioKLnD8FiHDx+G3W7HokWLcODAAbz77rv4+OOPMXv2bLlD8wirVq3C9OnT8cILL2DPnj0YNGgQhg8fjjNnzsgdmkfZtGkTpk6dim3btiEtLQ1WqxWJiYkoKSmROzQiIiLyUJyt1Mv8+OOPSEpKwn/+8x907twZe/bswQ033CB3WB7v7bffxsKFC3HixAm5Q3F7ffv2RY8ePbBw4ULnvo4dO+KOO+5ASkqKjJF5tosXLyIsLAybNm3C4MGD5Q6HiIiIPBBbDr3I+fPn8eijj2LZsmUwGAxyh9OsFBYWIjg4WO4w3J7FYsHu3buRmJhYZX9iYiK2bNkiU1TNQ2FhIQDwfUhERETXjMmhl5AkCRMnTsSUKVPQq1cvucNpVo4fP44PPvgAU6ZMkTsUt5eTkwObzYbw8PAq+8PDw5GdnS1TVJ5PkiQkJSVh4MCB6NKli9zhEBERkYdicujhkpOTIQjCFW+7du3CBx98AKPRiFmzZskdstuqa11WlpmZidtuuw3jxo3D5MmTZYrc8wiCUGVbkqRq+6jupk2bhn379mHlypVyh0JEREQejGMOPVxOTg5ycnKuWCYuLg7jx4/HDz/8UOULuM1mg1KpxP3334+lS5e6OlS3V9e61Ol0AByJYUJCAvr27YslS5ZAoeBvLVdjsVhgMBjwr3/9C2PHjnXuf/rpp7F3715s2rRJxug805NPPonVq1fjt99+Q3x8vNzhEBERkQdjcuglzpw5A6PR6NzOzMzErbfein//+9/o27cvoqOjZYzO82RkZCAhIQE9e/bE8uXLoVQq5Q7JY/Tt2xc9e/bEggULnPs6deqEMWPGcEKaepAkCU8++SS+++47bNy4EW3btpU7JCIiIvJwKrkDoKYRGxtbZdvX1xcA0KZNGyaG9ZSZmYkhQ4YgNjYW8+bNw8WLF53PRUREyBiZZ0hKSsKECRPQq1cv9O/fH4sXL8aZM2c4ZrOepk6diq+++gpr1qyBn5+fc8xmQEAA9Hq9zNERERGRJ2JySFRP69evR3p6OtLT06sl1myIv7p77rkHubm5eOWVV5CVlYUuXbogNTUVrVq1kjs0j1KxFMiQIUOq7P/iiy8wceLEpg+IiIiIPB67lRIRERERERFnKyUiIiIiIiImh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0RERERERAQmh0QeZdWqVejcuTP0ej0EQcDevXsBAA8//DBuu+22ep/v559/hq+vLzIyMho5UiIiomuzZMkSCIKAXbt2yR0KAGDu3LlYvXq13GEQNQkmh0Qe4uLFi5gwYQLatGmDn376CVu3bkW7du2wZ88eLF26FK+99lq9zzl06FD06dMHs2fPdkHEREREno/JIXkTJodEHuLo0aMQRREPPPAAbrrpJvTr1w8GgwFvvPEG+vTpg169el3TeadOnYoVK1bg7NmzjRwxEREREXkSJodEHmDixIkYOHAgAOCee+6BIAgYMmQIzp8/j++++w4TJkyoUn7KlCnQ6XTYvXu3c5/dbsfQoUMRHh6OrKws5/5Ro0bB19cXn3zySdNcDBERUT1MnDgRvr6+SE9Px4gRI+Dr64uYmBg888wzMJvNznKnTp2CIAh466238PrrryM2NhY6nQ69evXCzz//XO2ccXFx1V4rOTkZgiA4twVBQElJCZYuXQpBEJyfv0TNFZNDIg/wj3/8Ax999BEAR/eWrVu3YsGCBVi/fj1EUURCQkKV8vPnz0fHjh1x9913o6CgAAAwZ84cbNy4EcuXL0dkZKSzrEajwY033oi1a9c22fUQERHVhyiKGD16NIYOHYo1a9bg4Ycfxrvvvos333yzWtkPP/wQP/30E+bPn4/ly5dDoVBg+PDh2Lp1a71fd+vWrdDr9RgxYgS2bt3q/Pwlaq5UcgdARFfXpk0bdOrUCQDQtm1b9OvXD4DjA1Cv16NDhw5Vyut0OvzrX/9Cz549MWnSJEybNg2vvfYaZs+ejWHDhlU7f48ePZCSkoKSkhL4+Pi4/oKIiIjqwWKxYM6cORg3bhwAx5j5Xbt24auvvsJLL71UpazNZkNaWhp0Oh0A4NZbb0VcXBxeeuklpKWl1et1+/XrB4VCgRYtWjg/e4maM7YcEnmwzMxMtGjRokoXmArXXXcdPvnkE6xevRq33347Bg0ahOTk5BrPExYWBrvdjuzsbBdHTEREVH+CIGDUqFFV9nXt2hWnT5+uVvZvf/ubMzEEAD8/P4waNQq//fYbbDaby2Ml8mRMDok8WFlZWZUPwMuNHDkS4eHhMJlMSEpKglKprLFcxTnKyspcEicREVFDGAyGap93Wq0WJpOpWtmIiIga91ksFhQXF7ssRqLmgMkhkQcLDQ1FXl5erc9PmTIFRUVF6Ny5M5566ink5+fXWK7iHKGhoS6Jk4iIqKnU1AsmOzsbGo0Gvr6+ABw/ilaezKZCTk6Oy+MjcmdMDok8WIcOHZCbm4vCwsJqz3366adYvnw5PvzwQ3z//fcoKCjApEmTajzPiRMnEBISgvDwcFeHTERE5FLffvttlRbFoqIi/PDDDxg0aJCzB01cXBwuXLiA8+fPO8tZLBasW7eu2vm0Wi171pDXYHJI5MGGDBkCSZKwffv2Kvv379+Pp556Cg899BAmTZqE1q1b47PPPsOaNWswf/78aufZtm0bbrrpphrHLhIREXkSpVKJYcOG4bvvvsN//vMfDB06FEajEXPmzHGWueeee6BUKjF+/Hikpqbi22+/RWJiYo1jEq+//nps3LgRP/zwA3bt2oUjR4405eUQNSkmh0QebMCAAYiLi8OaNWuc+0pKSnD33XcjPj6+ynTbd955J6ZOnYoZM2Zgx44dzv3Hjx/H/v37cf/99zdp7ERERK4wbdo0DBs2DE899RTuu+8+WK1WrF27FgMGDHCWiY+Px5o1a1BQUIC77roLzz33HMaNG4cHH3yw2vnee+89tG3bFuPHj0fv3r3x2GOPNeXlEDUpQZIkSe4giOja/fOf/8Trr7+OjIwM6PX6eh//j3/8A19++SWOHz8OlYqr2xARkWc6deoU4uPj8fbbb+PZZ5+VOxwij8SWQyIPN3XqVAQEBOCjjz6q97EFBQX46KOPMHfuXCaGRERERF6OySGRh9PpdFi2bBm0Wm29jz158iRmzZqF++67zwWREREREZEnYbdSIiIiIiIiYsshERERERERMTkkIiIiIiIiMDkkIiIiIiIiAM1uekK73Y7MzEz4+flxQW8iIi8nSRKKiooQFRUFhcK7fg/l5yEREQH1+yxsdslhZmYmYmJi5A6DiIjcyNmzZxEdHS13GE2Kn4dERFRZXT4Lm11y6OfnBwD49NNPcccdd0CtVsscUdMTRRHr169HYmKiV14/wDoAAHHXLqiHDoX4889Q9+oldzhNju8B1gEA5OXlIT4+3vnZ4CmSk5MxZ86cKvvCw8ORnZ1d53NUXPPZs2fh7+9/TXF42nuI8bqWJ8XrSbECjNfVPCleV8RqNBoRExNTp8/CZpccVnSdMRgM8Pf3d/s3gCuIoujV1w+wDgBA9PWFuuL+Gr8YejK+B1gHgKMOAHhkt8rOnTtjw4YNzm2lUlmv4yuu2d/fv0HJoSe9hxiva3lSvJ4UK8B4Xc2T4nVlrHX5LGx2ySEREVFzoFKpEBERIXcYRETkRZgcEhERuaFjx44hKioKWq0Wffv2xdy5c9G6detay5vNZpjNZue20WgE4PgVuqIFtT7sdgkf/pqO4+cEFO88g7t7x9b/IppYxXVey/XKgfG6jifFCjBeV/OkeF0Ra33OxeSQiIjIzfTt2xdffvkl2rVrh/Pnz+O1117DjTfeiAMHDiAkJKTGY1JSUqqNUwSA9evXw2Aw1DsGmwR8sE0FQIlDBYfge/Gvep9DLmlpaXKHUC+M13U8KVaA8bqaJ8XbmLGWlpbWuSyTQyIiIjczfPhw5+Prr78e/fv3R5s2bbB06VIkJSXVeMysWbOqPFcxAUFiYuI1jTm02uxI2uYY8xgUGIgRI/rW+xxNTRRFpKWlYdiwYW4/rghgvK7kSbECjNfVPCleV8Ra0ZOkLpgcEhERuTkfHx9cf/31OHbsWK1ltFottFpttf1qtfqavmAICvulx4Lg9l+oKrvWa5YL43UdT4oVYLyu5knxNmas9TkPk0MvIUkSCgsLkZmZifz8fBQUFKCwsLDKzWQyAbg0k5EgCBAEAQqFAgEBAQgJCalyCw0NRVhYmMf8kREReSqz2YxDhw5h0KBBcodCRETNGJPDZsJqteLs2bNIT0/H0aNH8csvv+Cbb75BVlYWzp07h4yMjHr1N64rpVKJNm3aoEOHDtVuQUFBjf56RETe4Nlnn8WoUaMQGxuLCxcu4LXXXoPRaMRDDz0kd2hERNSMNdvkcP369ejWrRs6duzoketb1cRut+PcuXM4cuSI85aeno7jx4/j5MmTsFqtVz1HUFAQQkJCEBAQUOUWGBgInU7nLCdJEiRJAgDYbDbk5+cjNzfXecvJyUFeXh5sNhuOHj2Ko0eP4vvvv6/yWh06dMDgwYOdt5iYmMatECKiZurcuXO49957kZOTgxYtWqBfv37Ytm0bWrVqJXdoRETUjDXb5HDJkiVYsmQJ4uLiMGzYMAwbNgxDhw5FcHCw3KFdldFodCZclRPBo0ePXrH1T6vVonXr1oiPj4cgCBgwYABatWqFli1bIjo6GlFRUdDr9Y0Wp91uR2ZmJg4fPlztlpGR4Xy8ePFiAEBcXBwGDx6MW265BaNGjUJgYGCjxUJE1Jx8/fXXcodAREReqNkmhx07dkR6ejpOnTqFTz75BJ988gkEQUCXLl3QrVu3KrewsLAmjU2SJOTk5ODEiRM4efIkTp48iRMnTuDYsWM4cuQIsrOzaz1WrVY7u3G2b98ebdu2RZs2bdCmTRu0bNkSCoUCoigiNTUVI0aMcOl4QIVCgejoaERHR+OWW26p8lxubi7++OMP/Pbbb9i0aRP+97//4dSpUzh16hS+/PJLqNVqJCYmYty4cRgzZgwTRSIiIiIimbk0OUxJScG3336Lw4cPQ6/X48Ybb8Sbb76J9u3b13rMxo0bkZCQUG3/oUOH0KFDhzq/9j/+8Q8MHz4cW7duxfr165GWloYDBw5g//792L9/P5YvX+4sGxERgeuvv97ZuhYZGVnlPiAgABqNBhqNBkqlstpr2Ww2lJWVoaSkxHnLycnB+fPnkZ2dXeWWkZGBkydPoqSk5Irxh4eHo3379mjXrh3at2+P9u3bo0OHDoiPj4dK5f45fUhICEaPHo3Ro0cDAIqKirBlyxZs3LgRa9aswaFDh7B27VqsXbsWarUaw4YNw7hx43DXXXfB19dX5uiJiIiIiLyPS7OMTZs2YerUqejduzesViteeOEFJCYm4uDBg/Dx8bnisUeOHKmyLlOLFi3q/fo+Pj4YPny4c72ozMxM7N69G3/++afzlp6e7kzc6kKpVDoTRYVCgbKyMucsn/UhCAKioqIQHx/v7Ap63XXXORPCgICAep/Tnfn5+eHWW2/FrbfeipSUFBw4cAD/+te/8O9//xsHDhxAamoqUlNT8fTTT2PixIl4/PHH6/VjABERNS5J7gCIiKjJuTQ5/Omnn6psf/HFFwgLC8Pu3bsxePDgKx4bFhbW6F0No6KiEBUVhVGjRjn3FRcX46+//sKhQ4eQmZmJzMxMZGVlOe+zsrIgiqKzfEUrYVlZWY2vYTAYYDAYEBISgoiIiGq3yMhIxMfHo1WrVjWuR+UtOnfujM6dOyM5ORmHDh3Cv//9b3z55ZdIT0/H+++/j/fffx9Dhw7F1KlTMWrUKI9oLSUiak4s1kvrHNolpopERN6gSb9xFxYWAkCdJoXp3r07TCYTOnXqhBdffLHGrqaAY+0ns9ns3DYajc7HlZO62mi1WvTs2RM9e/as8XlJkmCxWJw3s9nsfGy1WmEwGODj4wODwQC9Xg+FQnHV16xPfNei4ryuOn9ju+666zBz5kzMmDEDGzZswMcff4zU1FT8/PPP+PnnnxETE4PHH38cU6ZMqXOXU0+rA1ewiiLU5ffwwnrge4B1AHj3tTeUQXNpGEVOsUXGSIiIqKk0WXIoSRKSkpIwcOBAdOnSpdZykZGRWLx4MXr27Amz2Yxly5Zh6NCh2LhxY42tjSkpKZgzZ06N50pLS2u0+D2Rp17/5MmTMWrUKOdY0bNnz2L27NlISUnBHXfcgREjRtR51lVPrYPGEHD8OIYA2L59OwpzcuQORzbe/B6o4M114Ir1Xb2JWilAtElQKZrHklBERHRlTZYcTps2Dfv27cPmzZuvWK5i8pUK/fv3x9mzZzFv3rwak8NZs2YhKSnJuW00Gp3r6Q0bNsyls3W6K1EUkZaW5vHXP2nSJJhMJnzzzTd44403kJ6ejmXLliE1NRV///vf8fjjj8PPz6/GY5tLHTSEdccOAEDfvn2h6tNH5miaHt8DrAPAMXMyXRtBEKBRKSDabLjIlkMiIq/QJMnhk08+ie+//x6//fYboqOj6318v379qswuWplWq6117J5arfbaL0RA87h+tVqNRx55BA899BC+/vprvPLKKzh27BhefPFFvPPOO3j22Wfx1FNP1TrBUXOog2tWft0qb64DePl7oJw314G3XndjCffT4oS5FDa7/eqFiYjI49V9gNw1kCQJ06ZNw7fffotffvkF8fHx13SePXv2IDIyspGjI0+iUqnwwAMP4ODBg1i2bBnatWuHvLw8zJ49Gx06dMCKFSsgccIEIqJG5at1/IZcJtpht/P/WCKi5s6lyeHUqVOxfPlyfPXVV/Dz83MuGVF5ps9Zs2bhwQcfdG7Pnz8fq1evxrFjx3DgwAHMmjUL//nPfzBt2jRXhkoe4vIkMS4uDufOncMDDzyAG2+8Edu3b5c7RCKiZuNC0aUJ387mc/wmEVFz59LkcOHChSgsLMSQIUMQGRnpvK1atcpZJisrC2fOnHFuWywWPPvss+jatSsGDRqEzZs3Y+3atfjb3/7mylDJwyiVSjzwwAM4dOgQ5s6dCx8fH2zbtg39+vXDhAkTcO7cOblDJCLyeNnGS8nhugN1Ww+YiIg8l8u7ldZ0mzhxorPMkiVLsHHjRuf2jBkzkJ6ejrKyMuTl5eH333/HiBEjXBkmeTCdTodZs2bh2LFjmDRpEgRBwPLly9GlSxf861//gsXCSRSIiK7VlMGXhoNkFZpkjISIiJqCS5NDoqYSGRmJzz//HDt37sSAAQNQWlqKFStWoHfv3tiyZYvc4REReaR+rS+tS7xs62nkFpuvUJqIiDwdk0NqVnr27Inff/8dS5cuRUBAAA4dOoSBAwfiiSeeQGFhodzhERF5lJ6xgc7HVruEDYfOyxcMERG5HJNDanYEQcC9996LDz/8EBMnToQkSVi4cCE6deqE7777Tu7wiIg8hk6thF55aZbSt9cdlTEaIiJyNSaH1Gz5+flh8eLF+OWXX9C2bVtkZmbib3/7G8aOHYusrCy5wyMi8ggjYy+tcZhTbObENEREzRiTQ2r2EhISsG/fPrz44otQqVRYvXo1unTpUmXWXCIiqtn1QVXXN3xs2W7kl3CyLyKi5ojJIXkFnU6HV199FXv27EGPHj2Ql5eH8ePH45577kFOTo7c4RERua1ALbDikV5V9nV/NQ3nuO4hEVGzw+SQvEqXLl2wbds2vPzyy1Aqlfjmm2/QpUsX/PDDD3KHRkTktvrEBeP9e7tX2TfwzV+RVVgmU0REROQKTA7J66jVaiQnJ2P79u3o1KkTzp8/j9GjR+Phhx/mjKZERLUY3S0KA64LqbKvf8ovWLH9tEwRERFRY2NySF6rZ8+e2L17N5555hkIgoAvvvgC3bp1wx9//CF3aEREbmnJpD7oExdcZd8L3/2FKct2s5spEVEzwOSQvJpOp8O8efOwadMmxMfH4/Tp0xg8eDBefvllWK1WucMjInIraqUCqx7rh9fHdqmy/6cD2Rj45q+YvHQXVu08gwtGk0wREhFRQzA5JAIwaNAg7N27FxMmTIDdbscrr7yCwYMH48SJE3KHRkTkVgRBwP19W+GDe7sj0KCu8tyGQ+fx/H/2Y9Bbv+JCERNEIiJPw+SQqJy/vz++/PJLfPXVVwgICMDWrVtxww03YNmyZZAk6eonICLyIqO6RWH3i8OweuoATE1oA1+tyvmc2WpHn9d/xqC3fsHYBX/g1yMXZIyUiIjqiskh0WXuvfde/Pnnnxg4cCCKiorw4IMP4v777+dkNUREl1EqBNwQE4jnbu2A7bOHYmpCmyrPn80rw54zBZj0xU70nbsB93+6DS+v+Qvf/u8cRJtdpqiJiKg2TA6JatCqVSts3LgRr776KpRKJVauXInu3btj+/btcodGROSWfLQqPHdrByy8vwcGtQ2t0pIIAOeNZvyRnoulW08j6Zs/0faFH/HGj4fx6e8n8N2ec/jt6EXklVhkip6IiABAdfUiRN5JqVTixRdfxC233IJ7770XJ0+exMCBA/Haa6/hueeeg0LB31aIiC43/PpIDL8+EgDwR3oO/r37HE7lluBUTgnyS8UqZT/edLza8Td3CMOYG6LQpWUA4kN8oFAITRI3ERExOSS6qn79+mHv3r147LHHsGrVKsycORMbNmzAl19+icjISLnDIyJyWwOuC8WA60Kd2xeLzHj2X39iz5l8GE01zwj9y+EL+OWwY4yiWikg0KBBkEGNvBILcootGHhdKOaM6Yw2LXyb5BqIiLwJk0OiOggICMDKlSuRmJiIJ598Ehs2bEC3bt2wdOlSDB8+XO7wiIg8Qgs/LZY+3AcWqx0nc0qQW2xGTokFJy+W4N0NR6uVF20SLhaZcbHI7Ny3OT0HQ/+5Cf46FYJ8NAjx0eCWTuFI7BSO2EBtU14OEVGzw+SQqI4EQcDDDz+M/v37Y/z48di3bx9GjBiBpKQkzJ07F1otv5QQEdWFRqVA+wg/AH7OfU/f0hYXi8z4K7MQf50rxP6MQpzLL0NBqQWZhdWXxTCarDCarDidW4r/nSnAWz8dQZBBjWitAofVxxDip0Owj6bazaDhVx8iotrwf0iieurYsSO2b9+OGTNm4IMPPsA777yDjRs3YuXKlWjXrp3c4REReawWfloktA9DQvuwKvuLTCIW/3YCH/ySDo1KgU6R/igsE5FfakFBpXGM+aUi8ksV2P/byVpfQ6dWINigQZCPBlGBenSI8EO7cD/EhfggNtiAgMvWbiQi8iZMDomugU6nw/vvv49bbrkFkyZNwv/+9z/06NEDCxYswIQJEyAInECBiKix+OnUeCaxPZ5JbF/tudO5Jfjpr2zsPJWHnafyUFhW81jGCibRjsxCEzILTTiQaUTawfNVng/QqxEbbEBsiAHRgXr4alXw0aou3etU8NUq4aNVwU+nRrBBA71G2ajXS0QkFyaHRA0wevRo7Nu3Dw888AA2btyIhx56COvWrcPChQvh7+8vd3hERM1eqxAfPHZTGzx2UxuYzRYs+fZHtO/eF0azHXnFZuSVWJBXanHcO2+OVkebXap2vsIyEfszHN1a60qvVjq7rYb76zC0YxjiQnwQaFA7bnoNdGoFfzgkIrfH5JCogVq2bIkNGzbgjTfewMsvv4yvvvoK27Ztw8qVK9GnTx+5wyMi8hoKhYAIAzCgTQjU6it3D7XbJZzNL8Xh7CKkXyjG2bxSnM4txZm8UmQVlqGGvLFWZaINGQVlyCgow/6MQmw4dL5aGY1SgeggPcZ2b4n+bUIQG2KAQrLDYgNsdgnszEpE7oDJIVEjUCqVeOGFF5CQkID77rsPJ06cwIABA5CcnIyZM2dCqWSXIyIid6JQCGgV4oNWIT64tXPV5yxWOzIKypBVWIYSsw0lZiuKzVaUlN+Ky/cZTaKzNTK/vHWytqTSYrPjRE4J/pl2FEir/IwKz+1Ig1IhQKtSQKNSQKMsvy9/7NyvUkCvVqF3XBBu6RSO1qE+bI0kokbF5JCoEd14443ONRG/+eYbvPjii/jpp5+wbNkyxMXFyR0eERHVgUalQHyoD+JDfep1nN0u4X9n8rHjVB4KS0UUlIooLBNRUGZBbrEFxy4U13qszS6h1GJDqcV21dfZcOg8Un48DH+dCqG+Wug1SvhoVI57rRJ6tQoGjRIGrWN/Cz8twv21CPfXIdxfh0C9Giqlol7XRkTeweXJ4YIFC/D2228jKysLnTt3xvz58zFo0KBay2/atAlJSUk4cOAAoqKiMGPGDEyZMsXVYRI1msDAQHz99dcYOXIkpk2bhs2bN6Nbt2746KOPcP/99/NXXiKiZkqhENArLhi94oJrfP50bgm2HM/F3jMFyCu1wGSxIuvCRfgFBEG0S7BY7ZduNjvMlR5LNbRIVizncS18tSoE6NVVboEGx71/pe1AvWMsZaifBv4aJpREzZ1Lk8NVq1Zh+vTpWLBgAQYMGIBFixZh+PDhOHjwIGJjY6uVP3nyJEaMGIFHH30Uy5cvxx9//IEnnngCLVq0wJ133unKUIkalSAIePDBBzFo0CA88MAD2LJlCyZMmIC1a9di4cKFCAwMlDtEIiJqYhXdWO/t4/gOJIoiUlNTMWJE3yuOkZQkCaJNgsVmR1ZBGTYcuoBdp/JwKMuIYrMVpRYbrPUZJAmguLyrbEZBWZ2PEQTAR6nEe8c2w6BVQa9WQqdWQq9WQq+57F6tRJi/FkPahyHMT8sfRok8hEuTw3feeQePPPIIJk+eDACYP3++cybHlJSUauU//vhjxMbGYv78+QAc68nt2rUL8+bNY3JIHik+Ph6bNm1CSkoK5syZg6+//hp//PEHli5dioSEBLnDIyIiDyAIAjQqARqVAm3D/dA23A9AmyplLFY7Si3W8q6pjvsSsw3FZisuFpmRbTThgtGEC0VmFJRaUFgmorDMisIyC0Rb3RJLSQKKrQKKc0rrFb9CcLRU+unU8HUuB+K4D9CrEVTeQhloUCPIoEGQjxqBBg2CDBoE6NVQKphYEjUVlyWHFosFu3fvxsyZM6vsT0xMxJYtW2o8ZuvWrUhMTKyy79Zbb8Vnn30GURSvOvMYkTtSqVT4xz/+gcTERNx///04fvw4br75ZkydOhVvvPEGfH195Q6RiIg8nGPCGg0CDfU7TpIklIk2x9jI8jGShWUiCssf55c6xkvmFJtxsdiEcxcLIQpqmERbnZNKu3TtXWAFAfDXORJIH63K2VKpUyugq9RyqVMroFcroVUr4atVIaFdSL1fi4hcmBzm5OTAZrMhPDy8yv7w8HBkZ2fXeEx2dnaN5a1WK3JychAZGVntGLPZDLPZ7Nw2Go3Ox6IoNuQSPFbFdXvr9QPuWQc9evTAzp078fzzz+OTTz7BRx99hB9//BGffPLJFcfhXiurKEJdfg83qoem4o7vgabGOvDuayeqC0EQYNCoYNCoEBmgv2LZS91gb4VarYZos8Mk2lBmsaFMdNxKLTaYLDaUWGz482wB9pzNR5HJimKTFUVmx32ZePVJdypIEpwJa328DECjUCL5z18dyaNGCZ2qalJZ5XGl5yqSTa3zOQX0Gsdjf50akYE6+OvYYEHNk8snpLm8j7kkSVfsd15T+Zr2V6jorleTtLS0Gvd7C2+/fsA962DkyJFo2bIlPvzwQ5w4cQJDhw7F7bffjgceeAA6na7RXifg+HEMAbB9+3YU5uQ02nk9jTu+B5qaN9dBaWn9ur8RUd2plQqolQr41ZIoDesUXuN+q82OErMNRtOl1sn8UhGF5ff5pRYUlF7aX1BqQX6JBWX1aK0EAItdgKVURD4a/0ciX60KkQE6+OkcibVOrXTMEFueRBoqjcH00arQKsSADhH+CPbRNHosRI3JZclhaGgolEpltVbCCxcuVGsdrBAREVFjeZVKhZCQmrsHzJo1C0lJSc5to9GImJgYAMCwYcO8siuqKIpIS0vz2usH3L8ORowYgWnTpmHGjBn4/PPP8d///heHDx/GJ598ggEDBjTKa1h37AAA9O3bF6o+fRrlnJ7E3d8DTYF1AOTm5sodAhFdRqVUIMCgQIBBjZh6Hmu12WGyXmqxNFttKLPYYbI6tn8+dB4/H76AIIMaF/MKodIZYC4vbxYdM782hmKz9YpLk9TGsVblpcTR2YKpUsCYr8C6oj9h0Kph0DhaKQMNlWaP1asRUD4+M0Cvhk6t4EQ/1OhclhxqNBr07NkTaWlpGDt2rHN/WloaxowZU+Mx/fv3xw8//FBl3/r169GrV69av9hotVpotdoan1Or1V77hQjg9QPuXQchISH47LPPcPfdd2Py5MlIT0/HzTffjP/7v/9DSkoKgoKCGvYC5detcuM6aAru/B5oKt5cB9563UTNlUqpgK9SAV9tzV9hB7drgTljKneBHVTl/wGbXYJJtDlulyWZJtFe/pwdZRVlRJszuSyz2JBfKiKzoAxZhWXIKjTBbK1fslmxVEnN3WQVOJB/vs7n0qgUEABnDLNHdECnyIBK3WUV0KqU0FZsq5RQKwUmlHRFLu1WmpSUhAkTJqBXr17o378/Fi9ejDNnzjjXLZw1axYyMjLw5ZdfAgCmTJmCDz/8EElJSXj00UexdetWfPbZZ1i5cqUrwySS1a233oq//voLzzzzDD777DMsWrQI3377Ld555x2ui0hERNSIlAoBPloVfGpJLuuroiWz1GKFyWJHqWh1jMGsNA6zsEzEsfPFOHq+CAWloiPRrLhZbPVOMCtYLjtuburhOh/75M3XoU0LX0e3V42qvPtreQKpUkCtEBzdhlUKqJUC1AoFFJw11iu4NDm85557kJubi1deeQVZWVno0qULUlNT0apVKwBAVlYWzpw54ywfHx+P1NRU/P3vf8dHH32EqKgovP/++1zGgpq9gIAAfPrpp3jwwQcxZcoUHDp0CBMmTMDnn3+OhQsXon379nKHSERERJe5WktmXdjtEorKTPjvj+sx8KYEiJICJWYrjKbLZpAtn0W2oMzinF32cHbRNb3mB7+k1/sYpUJwJIpKR8JoE5V4+/Dv0JSPPVWrHM9plAqE+GpwX59W8NE6Zo+tSMh9tSouTeLmXD4hzRNPPIEnnniixueWLFlSbd9NN92E//3vfy6Oisg9DR48GHv37sU///lPvPLKK/j111/RtWtXzJw5EzNnzoRef+WZ5IiIiMizKBSOGWN91UBUoL5e3eELSi1Yf+A8TuaWwKBWOrvAmip1k/3t6MVrWkbkcja7VN4tt6LFUkChpazW8qn7a16dQKd2TGIUoFfDv3yty4pxlUEGDaICdYgM0CMqUIdgHy38dCqolYoGx0914/LkkIjqR6PRYNasWbjnnnswbdo0/Pjjj3jllVewZMkSzJ07F/feey8UCv4nSURE5O0CDRrc3fvq0/qcN5qw9Xgu/HQqx5IjZhtKLVaUOh87ts1WO0RbxU2CaHOMkay8XbGvqKQUSrXW+ZzVbq/TbLKOpNWMi0Xmq5atUDFBj79eBf/yxDLEV4MQXy1CfbUI9dUgJtiAduF+DWrFJSaHRG6rdevWWLt2Lb799ltMnz4dZ86cwQMPPIB33nkH8+bNQ0JCgtwhEhERkQcI99fhju4tG+18lyb8GVKlpVOSJKQdPI/0i8UoMVtRYrah2GxFidla5b7IZIWxTESJpW5rXjqSVxuyjVcvG+qrhUGjhFZ1aWIejVKBwjzHbLB6jRoXikw4nF0EAUDy6M4Y3iWCczyUY3JI5MYEQcCdd96JESNG4L333sPcuXPxv//9DzfffDNuv/12vPXWW+jYsaPcYRIRERFBEAQkdo5AYh3LizY7jGUijCYrCstE5BSZkVVYhsxCE7IKylBY/pyjjIgikxWlV0koc4pra5FU4K8aZoN9YoVjOJtaKTjGT6oUzrGTmooJeZyPL+3Xq5XOlkx/vdqRgJaJ6BDph+FdIj12bCWTQyIPoNfrMXPmTDz88MN45ZVX8PHHH+O///0vfvzxRzz88MOYNWsW4uPj5Q6TiIiIqM7USgVCfLUI8a15WbqaiDY7CkpF5JaYkVNkQU6xo4vq8YvFOJxdhAtGk3OZEpNog/3qPV3LzytBtNmAOrZmXskdN5zH/PHdG3weOTA5JPIgYWFh+PDDD/Hkk0/i+eefx5o1a/DJJ5/g888/x3333YeZM2eiU6dOcodJRERE5BJqpQIt/LRo4acFIq5cVpIkWO0SikrNWPuTYzbYv7KKMX3VXtjKs8aWgXq08NNWGU8p2iRYqoy3rNt4ygqr92biYrEZIT5atGnhi7bhvogO0iPYR4MQHy30GmVDqsClmBwSeaD27dtj9erV2Lx5M1599VWsX78ey5Ytw/LlyzF27FjMnj0bXeUOkogabMGCBXj77beRlZWFzp07Y/78+Rg0aJDcYREReQRBcCy/4adTwV8DRAfpER/mj1Hdoup9Lrtdglg+6Y7FakeJ2Yqh/9wEi63mdSr/SM+t9Vw6tQIhPlpEBugQG2xAdJAet3aJQOeogHrH1diYHBJ5sIEDB2LdunXYuXMnUlJS8N133+Hbb7/Ft99+i8f79sUCAHZbw7tHEFHTW7VqFaZPn44FCxZgwIABWLRoEYYPH46DBw8iNjZW7vCIiLyKQiFAq1BCqwKgBYJ9NNj78jB8vzcTO0/lI6uwDHklFuSXWpBfItaaNAKOGVszCsqQUVCGXafzAQDvV1l7UoWnt64HAAQa1FgyqQ9uiAl03cVVeWUi8ni9e/fGt99+iwMHDuCNN97AypUrsW37dgDAc7ffjs533YXRo0cjMjJS5kibkNWKgOPHgT17AFXj/lcnSRJEUYQoirBYLBAEAXq9HhqNxr1mO3NhHXiMggK5I7hm77zzDh555BFMnjwZADB//nysW7cOCxcuREpKiszRERGRQaPC+D6xGN+n6g92kiShxGJDdmEZjp0vxrELxbhQZMLybWfq/RoFpSL+vmovfn12SCNFfWVe+m2BqHnq3Lkzli1bhjlz5mBFcjKwbBnez8sDFi923LyIGsAQF51bAKApv/m46DUagyvrwFPUfSlp92KxWLB7927MnDmzyv7ExERs2bKlxmPMZjPM5kuz9BmNjjnfK37IuBYVx13r8U2N8bqWJ8XrSbECjNfV5IhXqwBaBenQKkiH66N8kfLT0Ws+V69WgQ2KvT7HMjkkaoZat26NmZ99hh979YKtoADff/89du3e7Xw+MCAAgwYNwk033YT+/ftDr9fLGK1riFYr/ti8GQMGDoRkt+PcuXM4ffo0zpw5g7NnzyIjIwNZWVnIzs6GRYYPN18fH3Ts2BGdOnVCp06d0LlzZ0RGRjZqy2PlOlB7acuhWFAADB0qdxj1lpOTA5vNhvDw8Cr7w8PDkZ2dXeMxKSkpmDNnTrX969evh8FgaFA8aWlpDTq+qTFe1/KkeD0pVoDxuppc8a5IV2DHRUW9jlEIEh5uZ0eARkKs5jRSU09f8+uXlpbWuax3flsg8hKWVq0w4vHHcftLL+HYsWP49NNPsWTJEuy5cAG//ve/wH//C61Wi1tuuQVjxozB7bff7rFdTyVJQkZGBg4fPowjR47g0KFD+OOPP1DwwQc4c+YM7Pba+/4LgoCWLVuiVatWiI6ORlhYGEJDQ9GiRQvnLSQkBAaDAVqtFhqNpspNkiSUlJRUuxmNRpw9exanT5+ucsvIyIC9pAS/79oF7NrljCM0NBR9+vTBLbfcgttvvx1t27ZtWKWIIgqzsoDu3QG1p7ahNVBu7RMCeILLfyyQJKnWHxBmzZqFpKQk57bRaERMTAwSExPh7+9/Ta8viiLS0tIwbNiwKgtduyvG61qeFK8nxQowXleTK16bXcJ/92djx9b99TouSCPhk4d6o1tscKPEUdGTpC6YHBJ5ibZt2+LNN9/Ea6+9hj/++ANr1qzBmjVrcPLkSaxduxZr164FALRr1w79+vVDv3790L9/f3Tp0gUqN2p1ys3NxbFjx3Ds2DGkp6fj2LFjOHLkCI4cOYKSkpJaj/Pz80O7du3Qtm1btG3bFq1bt0arVq0QFxeH6OjoBn9YBAQEICCgbrOMiaKIQ4cOYefOnc7bvn37kJOTg9TUVKSmpiIpKQlt27bFyJEjMXLkSAwePBgajaZBMZLnCA0NhVKprNZKeOHChWqtiRW0Wi202uprhanV6ga/vxvjHE2J8bqWJ8XrSbECjNfVXB3v1zvOYOa39UsEKyx7pA8GtW0BURSRmpqKbrHBjRZrfc7jPt/4iKhJqNVqDBkyBEOGDME777yDAwcOYM2aNfj++++xY8cOHD16FEePHsWXX34JADAYDOjduze6deuGNm3aoHXr1mjdujXi4+MbvTuqJEnIz8/HmTNnqt1OnjyJY8eOIT8/v9bjlUolrrvuOrRv3x5t27aFyWTCnXfeiU6dOiEsLMxtJotRq9Xo2rUrunbtikceeQQAYDKZsG/fPmzevBmpqan47bffcOzYMcyfPx/z58+Hn58fRo4ciYkTJ+KWW26BUum+ayRRw2k0GvTs2RNpaWkYO3asc39aWhrGjBkjY2RERM3Xr4cv4P+W7ap1TcMbYgIhAbBY7bBYbc61EM1WO4pNVljtdV8LscL9fWPx6pguUCjc4zsKk0MiLyYIArp06YIuXbrghRdeQG5uLnbs2IFt27Zh69at2L59O4xGIzZt2oRNmzZVOz4qKgqtWrVCUFAQ/P39q92USiWsVmuVm81mg8lkQl5eHnJzc5Gbm1vlsclkumrcLVu2RNu2bXHdddehbdu2aN++Pdq3b4/WrVs7W9cqfnkbOHCgR/yqqdPp0KdPH/Tp0wdJSUkwGo1IS0vD2rVrkZqaivPnz+Prr7/G119/jejoaEycOBETJ05EmzZt5A6dXCQpKQkTJkxAr1690L9/fyxevBhnzpzBlClT5A6NiMhj5JdYsDX9IraeF5C5+RRKLHYYTSIKy0QYy0SUWGwwiTYcyS6C2Vr7EBQA2Hu2oMHxvDyqE5QKAQKALi0D0D02qMHnbExMDonIKSQkBMOHD8fw4cMBAHa7HYcPH8a2bdtw+PBhnDhxAidOnMDx48dhNBqRmZmJzMzMRo8jLCwMsbGx1W5t27ZFmzZt4OPjznOENg5/f3/ceeeduPPOO2G327Fz504sX74cK1aswLlz5/Daa6/htddew5AhQ/Dwww/j7rvvrrFLIXmue+65B7m5uXjllVeQlZWFLl26IDU1Fa1atZI7NCKiJldstiKv2AKz1Qaz1e64F+2XHlvtl26iI+H7774sHLtQDJtdAqAETlz7jKGVaZQKaFUKaCrflAr4aFXQKBWw2u2w2SXYJAlWmwSbXcL9fWNxX99W0KjqNzFNU2NySES1UigUztk0K5MkCXl5eThx4gTOnDkDo9FY7VZYWAi73Q6VSlXtptFoEBwcjJCQEOd9xeOIiIhmOXtqQygUCvTt2xd9+/bF22+/jTVr1uCLL77A+vXrsXHjRmzcuBEzZszA9OnTMWXKlDqPfST398QTT+CJJ56QOwwiokZns0sotVhRZrGh1GJDmVh+b7Gh2GxFfqnFsah8iQUHs4zYctx1E4wpBECnVsJml67YevjiyI54eEC823QBdQUmh0RUb4IgOBO63r17yx2OV9HpdLjnnntwzz334OzZs1i6dCkWLVqEc+fOYebMmZg7dy4ef/xxPP300wgNDZU7XCIi8gJ2u4RS0YbCMhGZBWXILChDRkEZcosdCV7lW7HZijLRBstVunA2prt6tISy4AwG9O6OYF89/PUq+OvU8Ner4aNVQqNUuM28BHJjckhE5KFiYmLw4osvYsaMGVi5ciXeeustHDx4EG+++Sbeffdd53g1IiKimog2O4xlIopMVhhNIoxlFfdite1isxWlFhtKLDaUmkXkFiqR/OevKBNtMImuT/QUAtC6hS+6xwRCq1ZAq1JCqyq/VyucjzWqiscKaNVKtA71QYSfGqmppzG8S4RHzEMgJyaHREQeTqPR4KGHHsKECRPw3//+F2+++Sa2bNmCzz77DEuWLMGff/6J5OTkWpdAICIizyJJEowmK0SbHVabBNFmh6Uuj612zPj3PlhsjZHMCQDEOpdWCECQQQM/nQp6jQoGjRJ6tRJ6jRKG8pterYJeo4BBo0KwjwZBBg1CfB33Lfy0CNBfW2IninWP09sxOSQiaiYUCgVGjx6N0aNHY/PmzXjttdewbt06fPzxx1i+fDmeffZZPPPMM/D19ZU7VCIiqkS02VEiAhkFZTDbTCg2W1FSfnM+Lh+Ld77QhG/3ZMgar16tgBI2BPoa4KtVORM8X60KkQF6RAfpERmgR5i/FsE+GgQbNAjQq5v1WL3mgskhEVEzNHDgQPzwww948803sWbNGuzatQvJyclYuHAhXn75ZUyePJlda4iI6kGSJBSWicgptiC32IycYgvySswotTjGz1lsjpkyLdZLM2haKm1XlLGUP1daPhFLsdlaPv5OBez6Xbbrm9CvVZWxeP46Nfx0qvLHKvjqVPDRqKBXK2GzWZGamooRIwbxs6SZYXJIRNSMXX/99ZgxYwZWr16N2bNn4/jx43jiiScwf/58zJ8/37lsCRGRN5Ekx/ICFpsdolWC2WaDaJMgVkrgjCYR+88V4kCmEccvFuNkTglKLTa5Q6+iU6Q/4kINUCkUUCsVUCuF8vtLj1Xl95pKj1UKAUaTiItFZrSP8MeYG6KgVtZ9iQWbe1UDNSImh0REzZwgCLj77rtxxx134JNPPsGcOXNw9OhRjBgxAnfeeSfeffddxMTEyB0mEZGTvXxJAZNog8nqWN7AJNphsjrWrzOL9vKJUBxLIBSWiSgoFZFfYkFBmYj8EjMyLyrx3rHNEO0SRGtFImiH2WaHaLNDkuS5NqVCgEapgF6jhI9WCR+NCj4aJUqNeYhrGQk/vRo+WhV8tSr4lN98y8tV3hcdpIdOrZTnIqjZYnJIROQlNBoNpk6digcffBBz5szB/Pnz8Z///Ac//fQTkpOT8fTTT7N7EBG5hNlqw86T+VAqBJitl5K6MkulJK98rbuj54uw9XgurPaGZm8CUFraKPErBCAm2IDYYANCfbUI8dEg1M8xns63fOFzrdrROqepYdbMygulq2pooRNFsbybZjf+P0yyYnJIRORl/Pz8MG/ePDz00EN4/PHH8ccff+C5557DkiVLsHDhQgwaNEjuEInIQ5hEG4pMVhSZxPL7S4+N5ffnjSZ8vfNsk8emFiTotGpoVYoqXS01KiU0FV0tKz3nKHdpv1alRPsIX3SNDkTrFj7QqthKR82fy5LDU6dO4dVXX8Uvv/yC7OxsREVF4YEHHsALL7wAjUZT63ETJ07E0qVLq+zr27cvtm3b5qpQiYi80vXXX4/ffvsNS5cuxXPPPYcDBw5g8ODBmDRpEt555x0EBgbKHSIRuZjZakNmgQmFZWKlBK8iubNW2WcsE3HuvBLvHNmMYrMjEWycJRGqC/XV4rowH+jUjuUOdGoldGpF+b0SOpVjW69xPPbXqxFoUCPIoEGQQQ2DWsDP63/CiBG3siWOqB5clhwePnwYdrsdixYtwnXXXYe//voLjz76KEpKSjBv3rwrHnvbbbfhiy++cG5fKZkkIqJrp1AoMGnSJIwePRqzZ8/G4sWL8cUXX2DdunVYvHgxRo4cKXeIRHQVkiTBJNpRanEsUl4mls+E6Vy03IqCUhG5JY7ZNfNLRFwsNuNcXimyjKZ6jr0TgJKGd9Xs1SoIo7pFORI/jRI6lSPR06uV8NGq0DbMt8bul3XFde2Iro3LksPbbrsNt912m3O7devWOHLkCBYuXHjV5FCr1SIiIsJVoRER0WVCQkKwaNEiPPjgg5g0aRKOHTuG22+/HQ8++CDmz5+PoKAguUMk8iom0YacYjMuFpXfKj2+UHTpcUGpBaWirckmVxEgwV+vhp+u4qaCv07lfOxX5XFNz6vho1FCELjeHZE7atIxh4WFhQgODr5quY0bNyIsLAyBgYG46aab8PrrryMsLKwJIiQi8m4DBgzA3r178dJLL+Gdd97Bl19+ibS0NHz88ccYPXq03OEReaQDmYX46a9shPnrIFrt5S17VhSbRBw9rkDaN/tgskooNovOpM9osro8riCDGrEhPogJ0iPER1Mtqat4XJHc6ZQSNm5Yj5Ej2VWTqLlqsuTw+PHj+OCDD/DPf/7ziuWGDx+OcePGoVWrVjh58iT+8Y9/4Oabb8bu3buh1WqrlTebzTCbzc5to9HofOytXQoqrttbrx9gHQCsA2+/fuDa60CtViMlJQWjR4/Go48+iqNHj2LMmDG49957Pa4V0Zv//anpSZKE3BILftyfhdO5pSgoE/Hv3eeucpQCuJB9Ta8X4qNBsI8GBq0KBrUSBo3SsTyCRgW9xrHt2KdCkEGN4PLyFTeDpn5fA0VRBBv8iJq3eieHycnJmDNnzhXL7Ny5E7169XJuZ2Zm4rbbbsO4ceMwefLkKx57zz33OB936dIFvXr1QqtWrbB27Vr87W9/q1Y+JSWl1njS0tKu+FrNnbdfP8A6AFgH3n79QMPq4NVXX8XKlSvx/fffY+XKlVi/fj2efvppdO3atREjdJ3SRprGnryLSbRh37lC5JWYneP3yiyXllootTiWXii1OG55JZe6fZrEhk3QolcrEeavRZifFi38tGjhW37v3NYhzN+xhEJ9Fi0nIqqLeieH06ZNw/jx469YJi4uzvk4MzMTCQkJ6N+/PxYvXlzvACMjI9GqVSscO3asxudnzZqFpKQk57bRaHQu5jxs2DCv7PYgiiLS0tK89voB1gHAOvD26wcarw7Gjh2L7du3Y9KkSUhPT8dLL72Ev//973jllVdq7NHhTnJzc+UOgdxQbrEZZ/PLcC6/FJkFZbhgdCR3OcVm5BRZcDK3BBara2bh7BTpj+m3tIVBo4JGIWHX9i1IHDoE/gYtfLWqerfmERE1pnr/DxQaGorQ0NA6lc3IyEBCQgJ69uyJL774AgpF/X/hys3NxdmzZxEZGVnj81qtttYvJ2q12mu/FAK8foB1ALAOvP36gcapg4EDB2LPnj145plnsHjxYrz77rvYsGEDVqxYgeuvv76RIm183v5v763KLDZkF4mOZK/YgtyKxK/Ygr1nC7D3bEGjv2aQQe1s3buuhS8SO0cg3F+LAL0GAXo1NKqaFz7P+gtoFWzge5WI3ILLfp7KzMzEkCFDEBsbi3nz5uHixYvO5yrPRNqhQwekpKRg7NixKC4uRnJyMu68805ERkbi1KlTmD17NkJDQzF27FhXhUpERHXg6+uLRYsWYeTIkZg8eTL279+P3r17IyUlBU8//fQ1/QBIdC0kSUJBqWM5hpzymTwPZBqx4WA2MvKUMG/9+ZrPrVUpEBWoR++4ILRu4Qu9WulcYsFQfq/TXHqs1ygRqNfUmPwREXkalyWH69evR3p6OtLT0xEdHV3lOanSfMtHjhxBYWEhAECpVGL//v348ssvUVBQgMjISCQkJGDVqlXw8/NzVahERFQPo0ePxv79+/HII49g7dq1SEpKQmpqKr788stae3kQNUSJ2YqTOSU4k1eK9AvFWPzbCRSba5vN8+ozpsQGGzCwbShiggxoGaRHhL8Oob4ahPpp4adVcZkFIvJaLksOJ06ciIkTJ161XOVEUa/XY926da4KiYiIGkl4eDh++OEHLFq0CElJSdiwYQO6du2KpUuXYsSIEXKHRx7IbpeQbTTh+MViHL9QjBM5JTh+sRgnLpYgq9BUp3MIAtBCKyE2PAhh/jqE+moR4qNFqJ8Gob5ahPpq0MJXh+ggPRQKJoBERJfjqGciIromgiBgypQpuOmmm3Dvvffizz//xMiRI/H000/jzTffdPvJasg9pB08j+lf70GJxVbvYwe3a4GOkX7OGT27R/tjzx+/YMSIPhzDR0R0DZgcEhFRg3Ts2BHbtm3D888/j/fffx/vvfceNm3ahJUrV6JDhw5yh0duQJIkHMwyYufJPJzMKcHJXMcsoWfzSmG+yqygAXo12rTwQZsWvogL9UF0kB4xwQa0D/eDj7bq1xhRFLHHlRdCRNTMMTkkIqIG0+l0eO+995CYmIiJEydi79696NmzJ95//308/PDDHMPlxQrLRAz95ybkFJvrVP7RQfFo08IXbcJ80TrUB8E+Gr5/iIiaCJNDIiJqNCNHjsS+ffvw4IMPYsOGDZg8eTLS0tKwaNEiBAQEyB0euZgkScgsNOH3oxfx/Z+ZOJ1bioyCshrLViz2HqhX489zhXh0UDwmDohHy0B9E0dNREQVmBwSEVGjioyMxLp16zBv3jy88MILWLVqFbZv346VK1eiX79+codHLnChyIRfDl3AZ5tP4tiF4iuWXf5IX7SP8EOoL1sEiYjcDZNDIiJqdAqFAjNmzHBOVnPy5EkMHDgQr732GmbMmME1EZuRLek5uO/T7TU+F6BXIypQj6gAHdqG++HhgXEI89M1cYRERFRXTA6JiMhl+vbtiz179mDKlCn4+uuvMWvWLGzYsAHLli3jmogeTpIkfPL7CcxNPVxlf8tAPe7s0RIJHcLQPTZIpuiIiOhaMDkkIiKXCggIwFdffYVhw4bhySefxM8//4xu3bphyZIlXBPRQ6VfKMbYBX+gyFR9IfrfZiRAyTUEiYg8Evv1EBGRywmCgIcffhi7d+9Gt27dcPHiReeaiCZT3RY4J/fw01/ZGPXB5mqJ4bOJ7bDnH8OYGBIReTAmh0RE1GQ6dOiAbdu24amnngIAvP/+++jTpw8OHDggc2R0NZIk4eU1f2HK8t0oEx0L1mtUCozsGonNzydg2s1tEeSjkTlKIiJqCCaHRETUpCrWRFy7di3CwsKwf/9+9OrVCwsWLIAkSXKHR7WYtnIPlm497dwe1S0Kf76UiI/u64HoIIOMkRERUWNhckhERLIYMWIE9u3bh9tuuw0mkwlTp07FmDFjcPHiRblDo8tsP5mHtfuyqux7f/wN0GuUMkVERESuwOSQiIhkEx4ejrVr1+Ldd9+FRqPBDz/8gK5duyI1NVXu0KiSx1bsqbL9zWP9uUYhEVEzxOSQiIhkpVAoMH36dOzYsQMdO3ZEdnY2Ro4cicceewzFxVdeUJ1c79dMASVmm3P7wJxb0Sc+WMaIiIjIVZgcEhGRW+jWrRt2796N6dOnAwAWL16Mbt26YfPmzfIG5sXSLxRj9elLXUefTWwHHy1XwSIiaq6YHBIRkdvQ6/V499138csvvyA2NhYnTpzA4MGD8fzzz8NsNssdntcpMlddruLRwa1lioSIiJoCk0MiInI7CQkJ2LdvHyZOnAhJkvDWW2+hd+/e2LNnz9UPpkaTkV/mfBwXYoBWxQloiIiaMyaHRETklgICAvDFF19g9erVaNGiBfbv34/evXtj1qxZKCsru/oJqMH2nC10Ptao+JWBiKi54//0RETk1saMGYO//voL48aNg81mwxtvvIGuXbti48aNcofW7FUsdg8AD90YJ18gRETUJJgcEhGR2wsLC8M333yD1atXIyoqCunp6UhISMCjjz6K/Px8ucNrtk5cLHE+bh/uJ2MkRETUFJgcEhGRxxgzZgwOHjyIxx9/HADw6aefolOnTvj3v/8NSZJkjq75OXL+0lIiwT4aGSMhIqKmwOSQiIg8SkBAABYsWIDffvsN7du3R3Z2NsaNG4fExEQcPHhQ7vCaDUmSUFxpttLoIIOM0RARUVNgckhERB5p0KBB2Lt3L1588UVoNBps2LABXbt2xdNPP82upo1AEIQq22qlUEtJIiJqLpgcEhGRx9LpdHj11Vdx6NAh3HHHHbDZbHj//ffRtm1bLFq0CDab7eonoVpVJISdIv2qJYtERNT8MDkkIiKP17p1a3z33XdIS0tDp06dkJubiylTpmDo0KFyh+bRrHbHOE6VgokhEZE3cGlyGBcXB0EQqtxmzpx5xWMkSUJycjKioqKg1+sxZMgQHDhwwJVhEhFRM3HLLbdg7969eO+99xAYGIi//vpL7pA8liRJqJjjR8HkkIjIK7i85fCVV15BVlaW8/biiy9esfxbb72Fd955Bx9++CF27tyJiIgIDBs2DEVFRa4OlYiImgG1Wo2nnnoKR48exUMPPSR3OB7LZr80+ytbDomIvIPLk0M/Pz9EREQ4b76+vrWWlSQJ8+fPxwsvvIC//e1v6NKlC5YuXYrS0lJ89dVXrg6ViIiakRYtWuCf//yn3GF4LGul5FDB8YZERF7B5cnhm2++iZCQENxwww14/fXXYbFYai178uRJZGdnIzEx0blPq9XipptuwpYtW1wdKhEREZWzV1o3UsmWQyIir6By5cmffvpp9OjRA0FBQdixYwdmzZqFkydP4tNPP62xfHZ2NgAgPDy8yv7w8HCcPn26xmPMZjPMZrNz22g0Oh+LotjQS/BIFdftrdcPsA4A1oG3Xz/AOgC8+9obqnK3UiaHRETeod7JYXJyMubMmXPFMjt37kSvXr3w97//3bmva9euCAoKwl133eVsTazN5dNlS5JU6xTaKSkptcaTlpZ2xTibO2+/foB1ALAOvP36Ae+ug9LSUrlD8Fh2+6XHzA2JiLxDvZPDadOmYfz48VcsExcXV+P+fv36AQDS09NrTA4jIiIAOFoQIyMjnfsvXLhQrTWxwqxZs5CUlOTcNhqNiImJAQAMGzYMarX6irE2R6IoIi0tzWuvH2AdAKwDb79+gHUAALm5uXKH4LGUlRa9t1jtVyhJRETNRb2Tw9DQUISGhl7Ti+3ZswcAqiR+lcXHxyMiIgJpaWno3r07AMBisWDTpk148803azxGq9VCq9XW+JxarfbaL0QArx9gHQCsA2+/fsC768BTrzsuLq7acIrnn38eb7zxRpPF4KtVwV+ngtFkxbkCU5O9LhERycdlYw63bt2Kbdu2ISEhAQEBAdi5cyf+/ve/Y/To0YiNjXWW69ChA1JSUjB27FgIgoDp06dj7ty5aNu2Ldq2bYu5c+fCYDDgvvvuc1WoREREbueVV17Bo48+6ty+0mzfrjLy+gicOn0Gg7pHN/lrExFR03NZcqjVarFq1SrMmTMHZrMZrVq1wqOPPooZM2ZUKXfkyBEUFhY6t2fMmIGysjI88cQTyM/PR9++fbF+/Xr4+fm5KlQiIiK3U7EUlJxeGd0JqamnMGJgvKxxEBFR03BZctijRw9s27btquWkSlNlA47JaJKTk5GcnOyiyIiIiNzfm2++iVdffRUxMTEYN24cnnvuOWg0mlrL1zZ7tyiK1zxrq6fNeMt4XcuT4vWkWAHG62qeFK8rYq3PuVy6lAURERHVX32XggJqn717/fr1MBgMDYrH02a8Zbyu5UnxelKsAON1NU+KtzFjrc/M3c0uOaxoiSwtLYXRaPTYyQgaQhRFr75+gHUAsA68/foB1gEAFBUVAajeS0UOrl4K6vLZuwsLCxEbG4v+/ftf89AMURTx66+/IiEhwSPeQ4zXtTwpXk+KFWC8ruZJ8boi1vp8FgqSO3xiNqJz5845l7IgIiICgOPHj6N169ayxpCTk4OcnJwrlomLi4NOp6u2PyMjA9HR0di2bRv69u1bp9fj5yEREVV29uxZREdfeYKxZtdyGBUVhYMHD6JTp044e/Ys/P395Q6pyVWs9eit1w+wDgDWgbdfP8A6AC61ngUHB8sdikuXgqpJVFQUzp49Cz8/PwjCta1i72nvIcbrWp4UryfFCjBeV/OkeF0RqyRJKCoqQlRU1FXLNrvkUKFQoGXLlgAAf39/t38DuJK3Xz/AOgBYB95+/QDrAHB8NniKui4FdTUKheKqvxDXlae9hxiva3lSvJ4UK8B4Xc2T4m3sWAMCAupUrtklh0RERJ6srktBERERNTYmh0RERG6krktBERERNTbP6WdTD1qtFi+//DK0Wq3cocjC268fYB0ArANvv36AdQCwDhrK0+qP8bqWJ8XrSbECjNfVPCleuWNtdrOVEhERERERUf01y5ZDIiIiIiIiqh8mh0RERERERMTkkIiIiIiIiJgcEhEREREREbwgOaxYNFin0yEyMhITJkxAZmam3GE1iVOnTuGRRx5BfHw89Ho92rRpg5dffhkWi0Xu0JrU66+/jhtvvBEGgwGBgYFyh9MkFixYgPj4eOh0OvTs2RO///673CE1md9++w2jRo1CVFQUBEHA6tWr5Q6pyaWkpKB3797w8/NDWFgY7rjjDhw5ckTusJrMwoUL0bVrV+cCwv3798ePP/4od1hERERur9knhwkJCfjmm29w5MgR/Oc//8Hx48dx1113yR1Wkzh8+DDsdjsWLVqEAwcO4N1338XHH3+M2bNnyx1ak7JYLBg3bhwef/xxuUNpEqtWrcL06dPxwgsvYM+ePRg0aBCGDx+OM2fOyB1akygpKUG3bt3w4Ycfyh2KbDZt2oSpU6di27ZtSEtLg9VqRWJiIkpKSuQOrUlER0fjjTfewK5du7Br1y7cfPPNGDNmDA4cOCB3aERERG7N65ay+P7773HHHXfAbDZDrVbLHU6Te/vtt7Fw4UKcOHFC7lCa3JIlSzB9+nQUFBTIHYpL9e3bFz169MDChQud+zp27Ig77rgDKSkpMkbW9ARBwHfffYc77rhD7lBkdfHiRYSFhWHTpk0YPHiw3OHIIjg4GG+//TYeeeQRuUMhIiJyW82+5bCyvLw8rFixAjfeeKNXJoYAUFhYiODgYLnDIBexWCzYvXs3EhMTq+xPTEzEli1bZIqK5FZYWAgAXvm3b7PZ8PXXX6OkpAT9+/eXOxwiIiK35hXJ4fPPPw8fHx+EhITgzJkzWLNmjdwhyeL48eP44IMPMGXKFLlDIRfJycmBzWZDeHh4lf3h4eHIzs6WKSqSkyRJSEpKwsCBA9GlSxe5w2ky+/fvh6+vL7RaLaZMmYLvvvsOnTp1kjssIiIit+aRyWFycjIEQbjibdeuXc7yzz33HPbs2YP169dDqVTiwQcfhCf3pq3v9QNAZmYmbrvtNowbNw6TJ0+WKfLGcy114E0EQaiyLUlStX3kHaZNm4Z9+/Zh5cqVcofSpNq3b4+9e/di27ZtePzxx/HQQw/h4MGDcodFRETk1lRyB3Atpk2bhvHjx1+xTFxcnPNxaGgoQkND0a5dO3Ts2BExMTHYtm2bx3Yxqu/1Z2ZmIiEhAf3798fixYtdHF3TqG8deIvQ0FAolcpqrYQXLlyo1ppIzd+TTz6J77//Hr/99huio6PlDqdJaTQaXHfddQCAXr16YefOnXjvvfewaNEimSMjIiJyXx6ZHFYke9eiosXQbDY3ZkhNqj7Xn5GRgYSEBPTs2RNffPEFFAqPbCyupiHvgeZMo9GgZ8+eSEtLw9ixY53709LSMGbMGBkjo6YkSRKefPJJfPfdd9i4cSPi4+PlDkl2kiR59P/7RERETcEjk8O62rFjB3bs2IGBAwciKCgIJ06cwEsvvYQ2bdp4bKthfWRmZmLIkCGIjY3FvHnzcPHiRedzERERMkbWtM6cOYO8vDycOXMGNpsNe/fuBQBcd9118PX1lTc4F0hKSsKECRPQq1cvZ2vxmTNnvGasaXFxMdLT053bJ0+exN69exEcHIzY2FgZI2s6U6dOxVdffYU1a9bAz8/P2ZIcEBAAvV4vc3SuN3v2bAwfPhwxMTEoKirC119/jY0bN+Knn36SOzQiIiK31qyXsti/fz+efvpp/PnnnygpKUFkZCRuu+02vPjii2jZsqXc4bnckiVLMGnSpBqfa8b/7NVMnDgRS5curbb/119/xZAhQ5o+oCawYMECvPXWW8jKykKXLl3w7rvves0SBhs3bkRCQkK1/Q899BCWLFnS9AHJoLbxpV988QUmTpzYtMHI4JFHHsHPP/+MrKwsBAQEoGvXrnj++ecxbNgwuUMjIiJya806OSQiIiIiIqK6aR4D0IiIiIiIiKhBmBwSERERERERk0MiIiIiIiJickhERERERERgckhERERERERgckhERERERERgckhERERERERgckhERERERERgckhERERERERgckhERERERERgckhERERERERgckhEREREREQA/h9+8SAU7qP53AAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.book_plots import set_figsize, figsize\n", "import matplotlib.pyplot as plt\n", "from kf_book.nonlinear_plots import plot_nonlinear_func\n", "from numpy.random import normal\n", "import numpy as np\n", "\n", "# create 500,000 samples with mean 0, std 1\n", "gaussian = (0., 1.)\n", "data = normal(loc=gaussian[0], scale=gaussian[1], size=500000)\n", "\n", "def f(x):\n", " return (np.cos(4*(x/2 + 0.7))) - 1.3*x\n", "\n", "plot_nonlinear_func(data, f)" ] }, { "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. We call these points *sigma points*. From the output histogram we can compute a mean and standard deviation which would give us an updated, albeit approximated Gaussian.\n", "\n", "Let me show you a scatter plot of the data before and after being passed through `f(x)`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 30000\n", "plt.subplot(121)\n", "plt.scatter(data[:N], range(N), alpha=.2, s=1)\n", "plt.title('Input')\n", "plt.subplot(122)\n", "plt.title('Output')\n", "plt.scatter(f(data[:N]), range(N), alpha=.2, s=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data itself appears to be Gaussian, which it is. By that I mean it looks like white noise scattered around the mean zero. In contrast `g(data)` has a defined structure. There are two bands, with a significant number of points in between. On the outside of the bands there are scattered points, but with many more on the negative side.\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 and particle 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 sigma points we will build an accurate output distribution.\n", "\n", "\"Enough points\" is the rub. The graph above was created with 500,000 sigma points, and the output is still not smooth. What's worse, this is only for 1 dimension. The number of points required increases by the power of the number of dimensions. If you only needed 500 points for 1 dimension, you'd need 500 squared, or 250,000 points for two dimensions, 500 cubed, or 125,000,000 points for three dimensions, and so on. So while this approach does work, it is very computationally expensive. Ensemble filters and particle filters use clever techniques to significantly reduce this dimensionality, but the computational burdens are still very large. The unscented Kalman filter uses sigma points but drastically reduces the amount of computation by using a deterministic method to choose the points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sigma Points - Sampling from a Distribution" ] }, { "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; this extends 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. Then we can compute the mean and covariance of the transformed points, and use that as our estimate of the mean and probability distribution." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.ukf_internal as ukf_internal\n", "ukf_internal.show_2d_transform()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the left we show an ellipse depicting the $1\\sigma$ distribution of two state variables. The arrows show how several 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. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's write a function which passes 10,000 points randomly drawn from the Gaussian\n", "\n", "$$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}, \n", "\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$\n", "\n", "through the nonlinear system:\n", "\n", "$$\\begin{cases}\\begin{aligned}\\bar x&=x+y\\\\\n", "\\bar y&= 0.1x^2 + y^2\\end{aligned} \\end{cases}$$ " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean x=-0.055, y=43.117\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy.random import multivariate_normal\n", "from kf_book.nonlinear_plots import plot_monte_carlo_mean\n", "\n", "def f_nonlinear_xy(x, y):\n", " return np.array([x + y, .1*x**2 + y*y])\n", "\n", "mean = (0., 0.)\n", "p = np.array([[32., 15.], [15., 40.]])\n", "# Compute linearized mean\n", "mean_fx = f_nonlinear_xy(*mean)\n", "\n", "#generate random points\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=10000).T\n", "plot_monte_carlo_mean(xs, ys, f_nonlinear_xy, mean_fx, 'Linearized Mean');" ] }, { "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 in the way of the Extended Kalman filter (we will be learning this in the next chapter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Quick Example\n", "\n", "I'm soon going to proceed into the math the Unscented Kalman Filter (UKF) uses to choose sigma points and then perform the computation. But let's just start with an example so you can see the destination, so to speak. \n", "\n", "We will learn that the UKF can use many different algorithms to generate the sigma points. Several algorithms are provided by FilterPy. Here's one possibility:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from filterpy.kalman import JulierSigmaPoints\n", "\n", "sigmas = JulierSigmaPoints(n=2, kappa=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This will become clearer later, but the object will generate weighted sigma points for any given mean and covariance. Let's just look at an example, where the point's size indicate how much it is weighted:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.ukf_internal import plot_sigmas\n", "plot_sigmas(sigmas, x=[3, 17], cov=[[1, .5], [.5, 3]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see we have 5 points centered around the mean (3, 17) in an odd pattern. It may seem absurd that this will do as well or better than 500,000 randomly generated points, but it will!\n", "\n", "Okay, now let's implement the filter. We will implement a standard linear filter in 1D; we aren't quite ready to tackle a nonlinear filter yet. The design of the filter is not much different than what we have learned so far, with one difference. The KalmanFilter class uses the matrix $\\mathbf F$ to compute the state transition function. Matrices mean **linear** algrebra, which work for linear problems, but not nonlinear ones. So, instead of a matrix we provide a function, just like we did above. The KalmanFilter class uses another matrix $\\mathbf H$ to implement the measurement function, which converts a state into the equivalent measurement. Again, a matrix implies linearity, so instead of a matrix we provide a function. Perhaps it is clear why $\\mathbf H$ is called the 'measurement function'; for the linear Kalman filter it is a matrix, but that is just a fast way to compute a function that happens to be linear. \n", "\n", "Without further ado, here are the state transistion function and measurement function for a 1D tracking problem, where the state is $\\mathbf x = [x \\, \\, \\dot x]^ \\mathsf T$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def fx(x, dt):\n", " xout = np.empty_like(x)\n", " xout[0] = x[1] * dt + x[0]\n", " xout[1] = x[1]\n", " return xout\n", "\n", "def hx(x):\n", " return x[:1] # return position [x] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's be clear, this is a linear example. There is no need to use a UKF for a linear problem, but I'm starting with the simplest possible example. But notice how I wrote `fx()` to compute $\\mathbf{\\bar x}$ as a set of equations instead of a matrix multiplication. This is to illustrate that I could implement any arbitrary nonlinear function here; we are not constrained to linear equations.\n", "\n", "The rest of the design is the same. Design $\\mathbf P$, $\\mathbf R$, and $\\mathbf Q$. You know how to do that, so let's just finish up the filter and run it." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.random import randn\n", "from filterpy.kalman import UnscentedKalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", "\n", "ukf = UnscentedKalmanFilter(dim_x=2, dim_z=1, dt=1., hx=hx, fx=fx, points=sigmas)\n", "ukf.P *= 10\n", "ukf.R *= .5\n", "ukf.Q = Q_discrete_white_noise(2, dt=1., var=0.03)\n", "\n", "zs, xs = [], []\n", "for i in range(50):\n", " z = i + randn()*.5\n", " ukf.predict()\n", " ukf.update(z)\n", " xs.append(ukf.x[0])\n", " zs.append(z)\n", " \n", "plt.plot(xs);\n", "plt.plot(zs, marker='x', ls='');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There really isn't a lot new here. You have to create an object that creates sigma points for you, and provide functions instead of matrices for $\\mathbf F$ and $\\mathbf H$, but the rest is the same as before. This should give you enough confidence to plow through a bit of math and algorithms so you can understand what the UKF is doing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing Sigma Points\n", "\n", "At the start of the chapter I used 500,000 randomly generated sigma points to compute the the probability distribution of a Gaussian passed through a nonlinear function. While the computed mean is quite accurate, computing 500,000 points for every update would cause our filter to be extremely 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.\n", "\n", "Let's consider the simplest possible case and see if it offers any insight. The simplest possible system is the **identity function**: $f(x) = x$. If our algorithm does not work for the identity function then the filter cannot 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. This filter diverges. \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 $\\mu$ 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 will not work. If we didn't alter $\\mu$ then this would be the standard Kalman filter. We must conclude that one sample will not work.\n", "\n", "What is the next lowest number we can choose? Two. 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", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_3_sigma_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can pass these points through a nonlinear function f(x) and compute the resulting mean and variance. The mean can be computed as the average of the 3 points, but that is not very general. For example, for a very nonlinear problem we might want to weight the center point much higher than the outside points, or we might want to weight the outside points higher. \n", "\n", "A more general approach is to compute the weighted mean $\\mu = \\sum_i w_i\\, f(\\mathcal{X}_i)$, where the calligraphic $\\mathcal{X}$ are the sigma points. We need the sums of the weights to equal one. Given that requirement, our task is to select $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the transformed sigma points. \n", "\n", "If we weight the means it also makes sense to weight the covariances. It is possible to use different weights for the mean ($w^m$) and for the covariance ($w^c$). I use superscripts to allow space for indexes in the following equations. We can write\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{Constraints:}\\\\\n", "1 &= \\sum_i{w_i^m} \\\\\n", "1 &= \\sum_i{w_i^c} \\\\\n", "\\mu &= \\sum_i w_i^mf(\\mathcal{X}_i) \\\\\n", "\\Sigma &= \\sum_i w_i^c{(f(\\mathcal{X})_i-\\mu)(f(\\mathcal{X})_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "The first two equations are the constraint that the weights must sum to one. The third equation is how you compute a weight mean. The forth equation may be less familiar, but recall that the equation for the covariance of two random variables is:\n", "\n", "$$COV(x,y) = \\frac{\\sum(x-\\bar x)(y-\\bar{y})}{n}$$\n", "\n", "These constraints do not form a unique solution. For example, if you make $w^m_0$ smaller you can compensate by making $w^m_1$ and $w^m_2$ larger. You can use different weights for the mean and covariances, or the same weights. 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", "We want an algorithm that satisfies the constraints, preferably with only 3 points per dimension. Before we go on I want to make sure the idea is clear. Below are three different examples for the same covariance ellipse with different sigma points. The size of the sigma points is proportional to the weight given to each." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_selections()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The points do not lie along the major and minor axis of the ellipse; nothing in the constraints require me to do that. I show the points evenly spaced, but the constraints do not require that. \n", "\n", "The arrangement and weighting of the sigma points affect how we sample the distribution. Points that are close together will sample local effects, and thus probably work better for very nonlinear problems. Points that are far apart, or far off the axis of the ellipse will sample non-local effects and non Gaussian behavior. However, by varying the weights used for each point we can mitigate this. If the points are far from the mean but weighted very slightly we will incorporate some of the knowledge about the distribution without allowing the nonlinearity of the problem to create a bad estimate. \n", "\n", "Please understand there are infinite ways to select sigma points. The constraints I choose are just one way to do it. For example, not all algorithms for creating the sigma points require the weights to sum to one. In fact, the algorithm I favor in this book does not have that property." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Unscented Transform\n", "\n", "For the moment, assume an algorithm for selecting the sigma points and weights exists. How are the sigma points used to implement a filter?\n", "\n", "The *unscented transform* is the core of the algorithm yet it is remarkably simple. It passes the sigma points $\\boldsymbol{\\chi}$ through a nonlinear function yielding a transformed set of points. \n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n", "\n", "It then computes the mean and covariance of the transformed points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_transform(with_text=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean and covariance of the sigma points are computed as:\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_{i=0}^{2n} w^m_i\\boldsymbol{\\mathcal{Y}}_i \\\\\n", "\\Sigma &= \\sum_{i=0}^{2n} w^c_i{(\\boldsymbol{\\mathcal{Y}}_i-\\mu)(\\boldsymbol{\\mathcal{Y}}_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "These equations should be familiar - they are the constraint equations we developed above. \n", "\n", "In short, the unscented transform takes points sampled from some arbitary probability distribution, passes them through an arbitrary, nonlinear function and produces a Gaussian for each transformed points. I hope you can envision how we can use this to implement a nonlinear Kalman filter. Once we have Gaussians all of the mathematical apparatus we have already developed comes into play!\n", "\n", "The name \"unscented\" might be confusing. It doesn't really mean much. It was a joke fostered by the inventor that his algorithm didn't \"stink\", and soon the name stuck. There is no mathematical meaning to the term." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Accuracy of the Unscented Transform\n", "\n", "Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now pass 5 sigma points through the same function, and compute their mean with the unscented transform. We will use the FilterPy function *MerweScaledSigmaPoints()* to create the sigma points and `unscented_transform` to perform the transform; we will learn about these functions later. In the first example in this chapter I used `JulierSigmaPoints`; they both choose sigma points, but in different ways which I will explain later." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean x=-0.097, y=0.549\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import unscented_transform, MerweScaledSigmaPoints\n", "import scipy.stats as stats\n", "\n", "\n", "#initial mean and covariance\n", "mean = (0., 0.)\n", "p = np.array([[32., 15], [15., 40.]])\n", "\n", "# create sigma points and weights\n", "points = MerweScaledSigmaPoints(n=2, alpha=.3, beta=2., kappa=.1)\n", "sigmas = points.sigma_points(mean, p)\n", "\n", "### pass through nonlinear function\n", "sigmas_f = np.empty((5, 2))\n", "for i in range(5):\n", " sigmas_f[i] = f_nonlinear_xy(sigmas[i, 0], sigmas[i ,1])\n", "\n", "### use unscented transform to get new mean and covariance\n", "ukf_mean, ukf_cov = unscented_transform(sigmas_f, points.Wm, points.Wc)\n", "\n", "#generate random points\n", "np.random.seed(100)\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=5000).T\n", "\n", "plot_monte_carlo_mean(xs, ys, f_nonlinear_xy, ukf_mean, 'Unscented Mean')\n", "ax = plt.gcf().axes[0]\n", "ax.scatter(sigmas[:,0], sigmas[:,1], c='r', s=30);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I find this result remarkable. Using only 5 points we were able to compute the mean with amazing accuracy. The error in x is only -0.097, and the error in y is 0.549. In contrast, a linearized approach (used by the EKF, which we will learn in the next chapter) gave an error of over 43 in y. If you look at the code that generates the sigma points you'll see that it has no knowledge of the nonlinear function, only of the mean and covariance of our initial distribution. The same 5 sigma points would be generated if we had a completely different nonlinear function. \n", "\n", "I will admit to choosing a nonlinear function that makes the performance of the unscented tranform striking compared to the EKF. But the physical world is filled with very nonlinear behavior, and the UKF takes it in stride. I did not 'work' to find a function where the unscented transform happened to work well. You will see in the next chapter how more traditional techniques struggle with strong nonlinearities. This graph is the foundation of why I advise you to use the UKF or similar modern technique whenever possible." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Unscented Kalman Filter\n", "\n", "We can now present the UKF algorithm. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Step\n", "\n", "The UKF's predict step computes the prior using the process model $f()$. $f()$ is assumed to be nonlinear, so we generate sigma points $\\mathcal{X}$ and their corresponding weights $W^m, W^c$\n", "according to some function:\n", "\n", "$$\\begin{aligned}\n", "\\boldsymbol\\chi &= \\text{sigma-function}(\\mathbf x, \\mathbf P) \\\\\n", "W^m, W^c &= \\text{weight-function}(\\mathtt{n, parameters})\\end{aligned}$$\n", "\n", "We pass each sigma point through $f(\\mathbf x, \\Delta t)$. This projects the sigma points forward in time according to the process model, forming the new prior, which is a set of sigma points we name $\\boldsymbol{\\mathcal Y}$:\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi}, \\Delta t)$$\n", "\n", "We compute the mean and covariance of the prior using the *unscented transform* on the transformed sigma points. \n", "\n", "$$\\mathbf{\\bar x}, \\mathbf{\\bar P} = \n", "UT(\\mathcal{Y}, w_m, w_c, \\mathbf Q)$$\n", "\n", "These are the equations for the unscented transform:\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{\\bar x} &= \\sum_{i=0}^{2n} w^m_i\\boldsymbol{\\mathcal Y}_i \\\\\n", "\\mathbf{\\bar P} &= \\sum_{i=0}^{2n} w^c_i({\\boldsymbol{\\mathcal Y}_i - \\mathbf{\\bar x})(\\boldsymbol{\\mathcal Y}_i-\\mathbf{\\bar x})^\\mathsf{T}} + \\mathbf Q\n", "\\end{aligned}\n", "$$\n", "\n", "This table compares the linear Kalman filter with the Unscented Kalman Filter equations. I've dropped the subscript $i$ for readability.\n", "\n", "$$\\begin{array}{l|l}\n", "\\text{Kalman} & \\text{Unscented} \\\\\n", "\\hline \n", "& \\boldsymbol{\\mathcal Y} = f(\\boldsymbol\\chi) \\\\\n", "\\mathbf{\\bar x} = \\mathbf{Fx} & \n", "\\mathbf{\\bar x} = \\sum w^m\\boldsymbol{\\mathcal Y} \\\\\n", "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q & \n", "\\mathbf{\\bar P} = \\sum w^c({\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})(\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})^\\mathsf T}+\\mathbf Q\n", "\\end{array}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Step\n", "\n", "Kalman filters perform the update in measurement space. Thus we must convert the sigma points of the prior into measurements using a measurement function $h(x)$ that you define.\n", "\n", "$$\\boldsymbol{\\mathcal{Z}} = h(\\boldsymbol{\\mathcal{Y}})$$\n", "\n", "We compute the mean and covariance of these points using the unscented transform. The $z$ subscript denotes that these are the mean and covariance of the measurement sigma points.\n", "\n", "$$\\begin{aligned}\n", "\\boldsymbol\\mu_z, \\mathbf P_z &= \n", "UT(\\boldsymbol{\\mathcal Z}, w_m, w_c, \\mathbf R) \\\\\n", "\\boldsymbol\\mu_z &= \\sum_{i=0}^{2n} w^m_i\\boldsymbol{\\mathcal Z}_i \\\\\n", "\\mathbf P_z &= \\sum_{i=0}^{2n} w^c_i{(\\boldsymbol{\\mathcal Z}_i-\\boldsymbol{\\mu}_z)(\\boldsymbol{\\mathcal Z}_i-\\boldsymbol{\\mu}_z)^\\mathsf T} + \\mathbf R\n", "\\end{aligned}\n", "$$\n", "\n", "Next we compute the residual and Kalman gain. The residual of the measurement $\\mathbf z$ is trivial to compute:\n", "\n", "$$\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z$$\n", "\n", "To compute the Kalman gain we first compute the [cross covariance](https://en.wikipedia.org/wiki/Cross-covariance) of the state and the measurements, which is defined as: \n", "\n", "$$\\mathbf P_{xz} =\\sum_{i=0}^{2n} w^c_i(\\boldsymbol{\\mathcal Y}_i-\\mathbf{\\bar x})(\\boldsymbol{\\mathcal Z}_i-\\boldsymbol\\mu_z)^\\mathsf T$$\n", "\n", "And then the Kalman gain is defined as\n", "\n", "$$\\mathbf{K} = \\mathbf P_{xz} \\mathbf P_z^{-1}$$\n", "\n", "If you think of the inverse as a *kind of* matrix reciprocal, you can see that the Kalman gain is a simple ratio which computes:\n", "\n", "$$\\mathbf{K} \\approx \\frac{\\mathbf P_{xz}}{\\mathbf P_z} \n", "\\approx \\frac{\\text{belief in state}}{\\text{belief in measurement}}$$\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "$$\\mathbf x = \\bar{\\mathbf x} + \\mathbf{Ky}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\mathbf P = \\mathbf{\\bar P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}$$\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. The linear algebra is slightly different from the linear Kalman filter, but the algorithm is the same Bayesian algorithm we have been implementing throughout the book. \n", "\n", "This table compares the equations of the linear KF and UKF equations.\n", "\n", "$$\\begin{array}{l|l}\n", "\\textrm{Kalman Filter} & \\textrm{Unscented Kalman Filter} \\\\\n", "\\hline \n", "& \\boldsymbol{\\mathcal Y} = f(\\boldsymbol\\chi) \\\\\n", "\\mathbf{\\bar x} = \\mathbf{Fx} & \n", "\\mathbf{\\bar x} = \\sum w^m\\boldsymbol{\\mathcal Y} \\\\\n", "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T+\\mathbf Q & \n", "\\mathbf{\\bar P} = \\sum w^c({\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})(\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})^\\mathsf T}+\\mathbf Q \\\\\n", "\\hline \n", "& \\boldsymbol{\\mathcal Z} = h(\\boldsymbol{\\mathcal{Y}}) \\\\\n", "& \\boldsymbol\\mu_z = \\sum w^m\\boldsymbol{\\mathcal{Z}} \\\\\n", "\\mathbf y = \\mathbf z - \\mathbf{Hx} &\n", "\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z \\\\\n", "\\mathbf S = \\mathbf{H\\bar PH}^\\mathsf{T} + \\mathbf R & \n", "\\mathbf P_z = \\sum w^c{(\\boldsymbol{\\mathcal Z}-\\boldsymbol\\mu_z)(\\boldsymbol{\\mathcal{Z}}-\\boldsymbol\\mu_z)^\\mathsf{T}} + \\mathbf R \\\\ \n", "\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf S^{-1} &\n", "\\mathbf K = \\left[\\sum w^c(\\boldsymbol{\\mathcal Y}-\\bar{\\mathbf x})(\\boldsymbol{\\mathcal{Z}}-\\boldsymbol\\mu_z)^\\mathsf{T}\\right] \\mathbf P_z^{-1} \\\\\n", "\\mathbf x = \\mathbf{\\bar x} + \\mathbf{Ky} & \\mathbf x = \\mathbf{\\bar x} + \\mathbf{Ky}\\\\\n", "\\mathbf P = (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar P} & \\mathbf P = \\bar{\\mathbf P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}\n", "\\end{array}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Van der Merwe's Scaled Sigma Point Algorithm\n", "\n", "There are many algorithms for selecting sigma points. Since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1]. It performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", "\n", "This formulation uses 3 parameters to control how the sigma points are distributed and weighted: $\\alpha$, $\\beta$, and $\\kappa$. Before we work through the equations, let's look at an example. I will plot the sigma points on top of a covariance ellipse showing the first and second standard deviations, and scale the points based on the mean weights." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.plot_sigma_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the sigma points lie between the first and second standard deviation, and that the larger $\\alpha$ spreads the points out. Furthermore, the larger $\\alpha$ weights the mean (center point) higher than the smaller $\\alpha$, and weights the rest 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": [ "### Sigma Point Computation\n", "\n", "The first sigma point is the mean of the input. This is the sigma point displayed in the center of the ellipses in the diagram above. We will call this $\\boldsymbol{\\chi}_0$.\n", "\n", "$$ \\mathcal{X}_0 = \\mu$$\n", "\n", "For notational convenience we define $\\lambda = \\alpha^2(n+\\kappa)-n$, where $n$ is the dimension of $\\mathbf x$. The remaining sigma points are computed as\n", "\n", "$$ \n", "\\boldsymbol{\\chi}_i = \\begin{cases}\n", "\\mu + \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right ]_{i}& i=1..n \\\\\n", "\\mu - \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} &i=(n+1)..2n\\end{cases}\n", "$$\n", "The $i$ subscript chooses the i$^{th}$ row vector of the matrix.\n", "\n", "In other words, we scale the covariance matrix by a constant, take the square root of it, and ensure symmetry by both adding and subtracting it from the mean. We will discuss how you take the square root of a matrix later.\n", "\n", "### Weight Computation\n", "\n", "This formulation uses one set of weights for the means, and another set for the covariance. The weights for the mean of $\\mathcal{X}_0$ is computed as\n", "\n", "$$W^m_0 = \\frac{\\lambda}{n+\\lambda}$$\n", "\n", "The weight for the covariance of $\\mathcal{X}_0$ is\n", "\n", "$$W^c_0 = \\frac{\\lambda}{n+\\lambda} + 1 -\\alpha^2 + \\beta$$\n", "\n", "The weights for the rest of the sigma points $\\boldsymbol{\\chi}_1 ... \\boldsymbol{\\chi}_{2n}$ are the same for the mean and covariance. They are\n", "\n", "$$W^m_i = W^c_i = \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n$$\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 $\\pm 1\\sigma$ times some scaling factor. There is an $n$ term in the denominator, so with more dimensions the points will be spread out and weighed less.\n", "\n", "**Important note:** Ordinarily these weights do not sum to one. I get many questions about this. Getting weights that sum to greater than one, or even negative values is expected. I cover this in more detail below.\n", "\n", "\n", "### Reasonable Choices for the Parameters\n", "\n", "$\\beta=2$ is a good choice for Gaussian problems, $\\kappa=3-n$ where $n$ is the dimension of $\\mathbf x$ is a good choice for $\\kappa$, and $0 \\le \\alpha \\le 1$ is an appropriate choice for $\\alpha$, where a larger value for $\\alpha$ spreads the sigma points further from the mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the UKF\n", "\n", "Let's solve some problems so you can gain confidence in how easy the UKF is to use. We will start with a linear problem you already know how to solve with the linear Kalman filter. Although the UKF was designed for nonlinear problems, it finds the same optimal result as the linear Kalman filter for linear problems. We will write a filter to track an object in 2D using a constant velocity model. This will allow us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", "\n", "Designing a Kalman filter requires you to specify the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times so I will give you the matrices without a lot of discussion. We want a constant velocity model, so we define $\\bf{x}$ to be\n", "\n", "$$ \\mathbf x = \\begin{bmatrix}x & \\dot x & y & \\dot y \\end{bmatrix}^\\mathsf{T}$$\n", "\n", "With this ordering of state variables the state transition matrix is\n", "\n", "$$\\mathbf F = \\begin{bmatrix}1 & \\Delta t & 0 & 0 \\\\\n", "0&1&0&0 \\\\\n", "0&0&1&\\Delta t\\\\\n", "0&0&0&1\n", "\\end{bmatrix}$$\n", "\n", "which implement the Newtonian equations\n", "\n", "$$\\begin{aligned}\n", "x_k &= x_{k-1} + \\dot x_{k-1}\\Delta t \\\\\n", "y_k &= y_{k-1} + \\dot y_{k-1}\\Delta t\n", "\\end{aligned}$$\n", "\n", "Our sensors provide position but not velocity, so the measurement function is\n", "\n", "$$\\mathbf H = \\begin{bmatrix}1&0&0&0 \\\\ 0&0&1&0\n", "\\end{bmatrix}$$\n", "\n", "The sensor readings are in meters with an error of $\\sigma=0.3$ meters in both *x* and *y*. This gives us a measurement noise matrix of \n", "\n", "$$\\mathbf R = \\begin{bmatrix}0.3^2 &0\\\\0 & 0.3^2\\end{bmatrix}$$\n", "\n", "Finally, let's assume that the process noise can be represented by the discrete white noise model - that is, that over each time period the acceleration is constant. We can use `FilterPy`'s `Q_discrete_white_noise()` to create this matrix for us, but for review the matrix is\n", "\n", "$$\\mathbf Q = \\begin{bmatrix}\n", "\\frac{1}{4}\\Delta t^4 & \\frac{1}{2}\\Delta t^3 \\\\\n", "\\frac{1}{2}\\Delta t^3 & \\Delta t^2\\end{bmatrix} \\sigma^2$$\n", "\n", "My implementation of this filter is:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import KalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", "from numpy.random import randn\n", "\n", "std_x, std_y = .3, .3\n", "dt = 1.0\n", "\n", "np.random.seed(1234)\n", "kf = KalmanFilter(4, 2)\n", "kf.x = np.array([0., 0., 0., 0.])\n", "kf.R = np.diag([std_x**2, std_y**2])\n", "kf.F = np.array([[1, dt, 0, 0], \n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])\n", "kf.H = np.array([[1, 0, 0, 0],\n", " [0, 0, 1, 0]])\n", " \n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "\n", "zs = [np.array([i + randn()*std_x, \n", " i + randn()*std_y]) for i in range(100)] \n", "xs, _, _, _ = kf.batch_filter(zs)\n", "plt.plot(xs[:, 0], xs[:, 2]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should hold no surprises for you. Now let's implement a UKF. Again, this is purely for educational purposes; using a UKF for a linear problem confers no benefit. `FilterPy` implements the UKF with the class `UnscentedKalmanFilter`. \n", "\n", "The first thing to do is implement the functions `f(x, dt)` and `h(x)`. `f(x, dt)` implements the state transition function, and `h(x)` implements the measurement function. These correspond to the matrices $\\mathbf F$ and $\\mathbf H$ in the linear filter.\n", "\n", "Below is a reasonable implementation of these two functions. Each is expected to return a 1D NumPy array or list containing the result. You may give them more readable names than `f` and `h`." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def f_cv(x, dt):\n", " \"\"\" state transition function for a \n", " 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 F @ x\n", "\n", "def h_cv(x):\n", " return x[[0, 2]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next you specify how to compute the sigma points and weights. We gave Van der Merwe's version above, but there are many different choices. FilterPy uses a class named `SigmaPoints` which must implement a method:\n", "\n", "```python\n", "def sigma_points(self, x, P)\n", "```\n", "\n", "and contain attributes `Wm` and `Wc`, which hold the weights for computing the mean and covariance, respectively.\n", "\n", "FilterPy derives the class `MerweScaledSigmaPoints` from `SigmaPoints` and implements the aforementioned methods.\n", "\n", "When you create the UKF you will pass in the $f()$ and $h()$ functions and the sigma point object, as in this example:\n", "\n", "```python\n", "from filterpy.kalman import MerweScaledSigmaPoints\n", "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "\n", "points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1)\n", "ukf = UKF(dim_x=4, dim_z=2, fx=f_cv, hx=h_cv, dt=dt, points=points)\n", "```\n", "\n", "The rest of the code is the same as for the linear kalman filter. I'll use the same measurements and compute the standard deviation of the difference between the two solutions." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "UKF standard deviation 0.013 meters\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "\n", "import numpy as np\n", "\n", "sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=1.)\n", "ukf = UKF(dim_x=4, dim_z=2, fx=f_cv,\n", " hx=h_cv, dt=dt, points=sigmas)\n", "ukf.x = np.array([0., 0., 0., 0.])\n", "ukf.R = np.diag([0.09, 0.09]) \n", "ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "ukf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "\n", "uxs = []\n", "for z in zs:\n", " ukf.predict()\n", " ukf.update(z)\n", " uxs.append(ukf.x.copy())\n", "uxs = np.array(uxs)\n", "\n", "plt.plot(uxs[:, 0], uxs[:, 2])\n", "print(f'UKF standard deviation {np.std(uxs - xs):.3f} meters')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gave me a standard deviation of 0.013 meters, which is quite small. \n", "\n", "The implementation of the UKF is not that different from the linear Kalman filter. Instead of implementing the state transition and measurement functions as the matrices $\\mathbf F$ and $\\mathbf H$ you supply nonlinear functions `f()` and `h()`. The rest of the theory and implementation remains the same. The code implementing `predict()` and `update()` differs, but from a designer's point of view the problem formulation and filter design is very similar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking an Airplane\n", "\n", "Let's tackle our first nonlinear problem. We will write a filter to track an airplane using radar as the sensor. To keep the problem as similar to the previous one as possible we will track in two dimensions. We will track one dimension on the ground and the altitude of the aircraft. Each dimension is independent so we can do this with no loss of generality.\n", "\n", "Radars work by emitting radio waves or microwaves. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to return it can compute the *slant distance* to the target. Slant distance is the straight line distance from the radar to the object. Bearing is computed using the *directive gain* of the antenna.\n", "\n", "We compute the (x,y) position of the aircraft from the slant distance and elevation angle as illustrated by this diagram:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.ekf_internal as ekf_internal\n", "ekf_internal.show_radar_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *elevation angle* $\\epsilon$ is the angle above the line of sight formed by the ground.\n", "\n", "We will assume that the aircraft is flying at a constant altitude. Thus we have a three variable state vector:\n", "\n", "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}= \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state transition function is linear \n", "\n", "$$\\mathbf{\\bar x} = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}\n", "$$\n", "\n", "and can be computed with:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def f_radar(x, dt):\n", " \"\"\" state transition function for a constant velocity \n", " aircraft with state vector [x, velocity, altitude]'\"\"\"\n", " \n", " F = np.array([[1, dt, 0],\n", " [0, 1, 0],\n", " [0, 0, 1]], dtype=float)\n", " return F @ x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we design the measurement function. As in the linear Kalman filter the measurement function converts the filter's prior into a measurement. We need to convert the position and velocity of the aircraft into the elevation angle and range from the radar station.\n", "\n", "Range is computed with the Pythagorean theorem:\n", "\n", "$$\\text{range} = \\sqrt{(x_\\text{ac} - x_\\text{radar})^2 + (y_\\text{ac} - y_\\mathtt{radar})^2}$$\n", "\n", "The elevation angle $\\epsilon$ is the arctangent of $y/x$:\n", "\n", "$$\\epsilon = \\tan^{-1}{\\frac{y_\\mathtt{ac} - y_\\text{radar}}{x_\\text{ac} - x_\\text{radar}}}$$\n", "\n", "We need to define a Python function to compute this. I'll take advantage of the fact that a function can own a variable to store the radar's position. While this isn't necessary for this problem (we could hard code the value, or use a global), this gives the function more flexibility." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def h_radar(x):\n", " dx = x[0] - h_radar.radar_pos[0]\n", " dy = x[2] - h_radar.radar_pos[1]\n", " slant_range = math.sqrt(dx**2 + dy**2)\n", " elevation_angle = math.atan2(dy, dx)\n", " return [slant_range, elevation_angle]\n", "\n", "h_radar.radar_pos = (0, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a nonlinearity that we are not considering, the fact that angles are modular. The residual is the difference between the measurement and the prior projected into measurement space. The angular difference between 359° and 1° is 2°, but 359° - 1° = 358°. 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 I will show you how to handle this problem.\n", "\n", "We need to simulate the radar and the aircraft. By now this should be second nature for you, so I offer the code without discussion." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "from numpy.linalg import norm\n", "from math import atan2\n", "\n", "class RadarStation:\n", " \n", " def __init__(self, pos, range_std, elev_angle_std):\n", " self.pos = np.asarray(pos) \n", " self.range_std = range_std\n", " self.elev_angle_std = elev_angle_std\n", "\n", " \n", " def reading_of(self, ac_pos):\n", " \"\"\" Returns (range, elevation angle) to aircraft. \n", " Elevation angle is in radians.\n", " \"\"\"\n", " \n", " diff = np.subtract(ac_pos, self.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 elevation angle to aircraft with \n", " simulated noise\"\"\"\n", " \n", " rng, brg = self.reading_of(ac_pos) \n", " rng += randn() * self.range_std\n", " brg += randn() * self.elev_angle_std \n", " return rng, brg \n", "\n", "class ACSim: \n", " def __init__(self, pos, vel, vel_std):\n", " self.pos = np.asarray(pos, dtype=float)\n", " self.vel = np.asarray(vel, dtype=float)\n", " self.vel_std = vel_std \n", " \n", " def update(self, dt):\n", " \"\"\" Compute and returns next position. Incorporates \n", " random variation in velocity. \"\"\"\n", " \n", " dx = self.vel*dt + (randn() * self.vel_std) * dt \n", " self.pos += dx \n", " return self.pos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for elevation angle [3]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n", "\n", "The design of $\\mathbf Q$ requires some discussion. The state is $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are down range distance and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of Q. The third element is altitude, which we assume is independent of $x$. That results in a block design for $\\mathbf Q$:\n", "\n", "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & \\boldsymbol 0 \\\\ \\boldsymbol 0 & Q_\\mathtt{y}\\end{bmatrix}$$\n", "\n", "I'll start with the aircraft positioned directly over the radar station, flying at 100 m/s. A typical height finder radar might update only once every 3 seconds so we will use that for our epoch period. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math\n", "from kf_book.ukf_internal import plot_radar\n", "\n", "dt = 3. # 12 seconds between readings\n", "range_std = 5 # meters\n", "elevation_angle_std = math.radians(0.5)\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", "h_radar.radar_pos = radar_pos\n", "\n", "points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n", "kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2,2] = 0.1\n", "\n", "kf.R = np.diag([range_std**2, elevation_angle_std**2])\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", "np.random.seed(200)\n", "pos = (0, 0)\n", "radar = RadarStation(pos, range_std, elevation_angle_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", "for _ in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x) \n", "plot_radar(xs, time)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This may or may not impress you, but it impresses me! In the Extended Kalman filter chapter we will solve the same problem, but it will take a significant amount of mathematics. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tracking Maneuvering Aircraft" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous example produced good results, but it assumed the aircraft did not change altitude. Here are the filter results if the aircraft starts climbing after one minute." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actual altitude: 2515.6\n", "UKF altitude : 1042.1\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.ukf_internal import plot_altitude\n", "\n", "# reset aircraft position\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "np.random.seed(200)\n", "time = np.arange(0, 360 + dt, dt)\n", "xs, ys = [], []\n", "for t in time:\n", " if t >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " ys.append(ac.pos[1])\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", "plot_altitude(xs, time, ys)\n", "print(f'Actual altitude: {ac.pos[1]:.1f}')\n", "print(f'UKF altitude : {xs[-1][2]:.1f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filter is unable to track the changing altitude. What do we have to change in our design?\n", "\n", "I hope you answered \"add climb rate to the state\", like so:\n", "\n", "\n", "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude} \\\\ \\mathtt{climb\\, rate}\\end{bmatrix}= \\begin{bmatrix}x \\\\\\dot x\\\\ y \\\\ \\dot y\\end{bmatrix}$$\n", "\n", "This requires the following change to the state transition function, which is still linear.\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix} 1 & \\Delta t & 0 &0 \\\\ 0& 1& 0 &0\\\\ 0&0&1&\\Delta t \\\\ 0&0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\\\dot x\\\\ y\\\\ \\dot y\\end{bmatrix} \n", "$$\n", "\n", "The measurement function stays the same, but we must alter $\\mathbf Q$ to account for the dimensionality change of $\\mathbf x$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def f_cv_radar(x, dt):\n", " \"\"\" state transition function for a constant velocity \n", " aircraft\"\"\"\n", " F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]], dtype=float)\n", " return F @ x\n", " \n", "def cv_UKF(fx, hx, R_std):\n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", " kf = UKF(4, len(R_std), dt, fx=fx, hx=hx, points=points)\n", "\n", " kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", " kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", " kf.R = np.diag(R_std)\n", " kf.R = kf.R @ kf.R # square to get variance\n", " kf.x = np.array([0., 90., 1100., 0.])\n", " kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", " return kf" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actual altitude: 2515.6\n", "UKF altitude : 2500.1\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(200)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "kf_cv = cv_UKF(f_cv_radar, h_radar, R_std=[range_std, elevation_angle_std])\n", "time = np.arange(0, 360 + dt, dt)\n", "xs, ys = [], []\n", "for t in time:\n", " if t >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " ys.append(ac.pos[1])\n", " kf_cv.predict()\n", " kf_cv.update([r[0], r[1]]) \n", " xs.append(kf_cv.x)\n", "\n", "plot_altitude(xs, time, ys)\n", "print(f'Actual altitude: {ac.pos[1]:.1f}')\n", "print(f'UKF altitude : {xs[-1][2]:.1f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A significant amount of noise has been introduced into the altitude estimate, but we are now accurately tracking altitude." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sensor Fusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's consider an example of sensor fusion. We have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system. A full implementation must account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", "\n", "The radar's accuracy in the last examples allowed us to estimate velocities to within one m/s or so, I will degrade that accuracy to illustrate the effect of sensor fusion. Let's change the range error to $\\sigma=500$ meters and then compute the standard deviation of the estimated velocity. I'll skip the first several measurements because the filter is converging during that time, causing artificially large deviations.\n", "\n", "The standard deviation without using Doppler is:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Velocity std 3.4 m/s\n" ] } ], "source": [ "range_std = 500.\n", "elevation_angle_std = math.degrees(0.5)\n", "np.random.seed(200)\n", "pos = (0, 0)\n", "radar = RadarStation(pos, range_std, elevation_angle_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "kf_sf = cv_UKF(f_cv_radar, h_radar, R_std=[range_std, elevation_angle_std])\n", "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", "for _ in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf_sf.predict()\n", " kf_sf.update([r[0], r[1]]) \n", " xs.append(kf_sf.x)\n", "\n", "xs = np.asarray(xs)\n", "plot_radar(xs, time, plot_x=False, plot_vel=True, plot_alt=False)\n", "print(f'Velocity std {np.std(xs[10:, 1]):.1f} m/s')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For Doppler we need to include the velocity in $x$ and $y$ into the measurement. The `ACSim` class stores velocity in the data member `vel`. To perform the Kalman filter update we just need to call `update` with a list containing the slant distance, elevation angle, and velocity in $x$ and $y$:\n", "\n", "$$z = [\\mathtt{slant\\_range},\\, \\text{elevation angle},\\, \\dot x,\\, \\dot y]$$\n", "\n", "The measurement contains four values so the measurement function also needs to return four values. The slant range and elevation angle will be computed as before, and we do not need to compute the velocity in $x$ and $y$ as they are provided by the state estimate." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def h_vel(x):\n", " dx = x[0] - h_vel.radar_pos[0]\n", " dz = x[2] - h_vel.radar_pos[1]\n", " slant_range = math.sqrt(dx**2 + dz**2)\n", " elevation_angle = math.atan2(dz, dx)\n", " return slant_range, elevation_angle, x[1], x[3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can implement our filter." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Velocity std 0.9 m/s\n" ] } ], "source": [ "h_radar.radar_pos = (0, 0)\n", "h_vel.radar_pos = (0, 0)\n", "\n", "range_std = 500.\n", "elevation_angle_std = math.degrees(0.5)\n", "vel_std = 2.\n", "\n", "np.random.seed(200)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "radar = RadarStation((0, 0), range_std, elevation_angle_std)\n", "\n", "kf_sf2 = cv_UKF(f_cv_radar, h_vel, \n", " R_std=[range_std, elevation_angle_std, vel_std, vel_std])\n", "\n", "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", "for t in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " # simulate the doppler velocity reading\n", " vx = ac.vel[0] + randn()*vel_std\n", " vz = ac.vel[1] + randn()*vel_std\n", " kf_sf2.predict()\n", " kf_sf2.update([r[0], r[1], vx, vz]) \n", " xs.append(kf_sf2.x)\n", "xs = np.asarray(xs)\n", "plot_radar(xs, time, plot_x=False, plot_vel=True, plot_alt=False)\n", "print(f'Velocity std {np.std(xs[10:,1]):.1f} m/s')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By incorporating the velocity sensor we were able to reduce the standard deviation from 3.5 m/s to 1.3 m/s. \n", "\n", "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to the *Complementary filter*, which blends the high update rate inertial velocity measurements with the accurate but slowly updated position estimates of the GPS to produce high rate and accurate position and velocity estimates. The high rate velocity estimates are integrated between the GPS updates to produce accurate and high rate position estimates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multiple Position Sensors\n", "\n", "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. These systems emit beacons in the form of radio waves. The sensor extracts the range and/or bearing to the beacon from the signal. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays the *radial* - the direction from the VOR station on the ground to the aircraft. The pilot uses a chart to find the intersection point of the radials, which identifies the location of the aircraft.\n", "\n", "That is a manual approach with low accuracy. A Kalman filter will produce far more accurate position estimates. Assume we have two sensors, each of which provides a bearing only measurement to the target, as in the chart below. The width of the perimeters are proportional to the $3\\sigma$ of the sensor noise. The aircraft must be positioned somewhere within the intersection of the two perimeters with a high degree of probability." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_two_sensor_bearing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We compute the bearing between a sensor and the target as:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def bearing(sensor, target_pos):\n", " return math.atan2(target_pos[1] - sensor[1], \n", " target_pos[0] - sensor[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filter receives the measurement from the two sensors in a vector. The code will accept any iterable container, so I use a Python list for efficiency. We can implement that as:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "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": [ "Assume a constant velocity model for the aircraft. For a change of pace I compute the new positions explicitly rather than using matrix-vector multiplication:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "def fx_VOR(x, dt):\n", " x[0] += x[1] * dt\n", " x[2] += x[3] * dt\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we implement the measurement function. It converts the prior to an array containing the measurement to both stations. I'm not a fan of global variables, but I put the position of the stations in the global variables `sa_pos` and `sb_pos` to demonstrate this method of sharing data with $h()$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "sa_pos = [-400, 0]\n", "sb_pos = [400, 0]\n", "\n", "def hx_VOR(x):\n", " # measurement to A\n", " pos = (x[0], x[2])\n", " return measurement(sa_pos, sb_pos, pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we write boilerplate which constructs the filter, runs it, and plots the results:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def moving_target_filter(pos, std_noise, Q, dt=0.1, kappa=0.0):\n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n", " f = UKF(dim_x=4, dim_z=2, dt=dt, \n", " hx=hx_VOR, fx=fx_VOR, points=points)\n", " f.x = np.array([pos[0], 1., pos[1], 1.])\n", "\n", " q = Q_discrete_white_noise(2, dt, Q)\n", " f.Q[0:2, 0:2] = q\n", " f.Q[2:4, 2:4] = q\n", " f.R *= std_noise**2\n", " f.P *= 1000 \n", " return f\n", "\n", "def plot_straight_line_target(f, std_noise):\n", " xs, txs = [], []\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], ls='--', lw=2, c='k')\n", " plt.show()\n", "\n", "np.random.seed(123)\n", "target_pos = [100, 200]\n", "\n", "std_noise = math.radians(0.5)\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", "plot_straight_line_target(f, std_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks quite good to me. The beginning of the track exhibits large errors, but the filter settles down and produces good estimates.\n", "\n", "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors at (0,0). This will cause a nonlinearity in the computation of the residuals because the mean angle will be near zero. As the angle goes below 0 the measurement function will compute a large positive angle of nearly $2\\pi$. The residual between the prediction and measurement will thus be very large, nearly $2\\pi$ instead of nearly 0. This makes it impossible for the filter to perform accurately, as seen in the example below." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "target_pos = [0, 0]\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", "plot_straight_line_target(f, std_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This performance is unacceptable. `FilterPy`'s UKF code allows you to specify a function which computes the residuals in cases of nonlinear behavior like this,. The final example in this chapter demonstrates its use." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effects of Sensor Error and Geometry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geometry of the sensors relative to the tracked object imposes a physical limitation that can be extremely difficult to deal with when designing filters. If the radials of the VOR stations are nearly parallel to each other then 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. These scatter plots show the error distribution for a 1°$\\sigma$ error for two different bearings." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.plot_scatter_of_bearing_error()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Explain Filter Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that for small angular errors the positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer for both the one sensor and multiple sensor problem. " ] }, { "cell_type": "markdown", "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 may need to revisit some of the earlier 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 positions. 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." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.plot_scatter_moving_target()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter 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° 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 take that into account. \n", "\n", "This graph makes it look easy because we have plotted 100 measurements for each position update. The movement of the aircraft is obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", "\n", "Now consider that the bearing gives us no distance information. Suppose we set the initial estimate to 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° 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. Here are two plots showing the effects of different sensor placements. I used a square and a triangle as a symbol for the two sensors, and drew a distribution of the errors due to each sensor using the same symbol shape and color. 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 $y$." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with figsize(10,5):\n", " ukf_internal.plot_iscts_two_sensors()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the first plot I placed the sensors nearly orthogonal to the target's initial position so we get these lovely 'x' shape intersections. 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", "In the second plot the airplane starts very near one sensor, and then flies past the second sensor. The intersections of the errors are very non-orthogonal, and the resulting position errors become very spread out." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation of the UKF\n", "\n", "FilterPy implements the UKF, but it is instructive to learn how to translate equations into code. Implementing the UKF is quite straightforward. First, let's write code to compute the mean and covariance of the sigma points. \n", "\n", "We will store the sigma points and weights in matrices, like so:\n", "\n", "$$ \n", "\\begin{aligned}\n", "\\text{weights} &= \n", "\\begin{bmatrix}\n", "w_0& w_1 & \\dots & w_{2n}\n", "\\end{bmatrix} \n", "\\\\\n", "\\text{sigmas} &= \n", "\\begin{bmatrix}\n", "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} & \\dots & \\mathcal{X}_{0,n-1} \\\\\n", "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} & \\dots & \\mathcal{X}_{1,n-1} \\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", "\\mathcal{X}_{2n,0} & \\mathcal{X}_{2n,1} & \\dots & \\mathcal{X}_{2n,n-1}\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "That's a lot of subscripts to describe something very simple, so here's an example for a two dimensional problem ($n$=2):" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0. ],\n", " [ 0.173, 0.017],\n", " [ 0. , 0.172],\n", " [-0.173, -0.017],\n", " [ 0. , -0.172]])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "points = MerweScaledSigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n", "points.sigma_points(x=[0.,0], P=[[1.,.1],[.1, 1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sigma point for the mean is on the first row. Its position is (0, 0), which is equal to the mean (0,0). The second sigma point is at position (0.173, 0.017), and so on. There are are $2n+1 = 5$ rows, one row per sigma point. If $n=3$, then there would be 3 columns and 7 rows.\n", "\n", "The choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code clearer as I can refer to the i$^{th}$ sigma point as `sigmas[i]` instead of `sigmas[:, i]`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weights\n", "\n", "Computing the weights with NumPy is easy. Recall that the Van der Merwe scaled sigma point implementation states:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\lambda&=\\alpha^2(n+\\kappa)-n \\\\ \n", "W^m_0 &= \\frac{\\lambda}{n+\\lambda} \\\\\n", "W^c_0 &= \\frac{\\lambda}{n+\\lambda} + 1 -\\alpha^2 + \\beta \\\\\n", "W^m_i = W^c_i &= \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n\n", "\\end{aligned}\n", "$$\n", " \n", "Code for these is:\n", "\n", "```python\n", "lambda_ = alpha**2 * (n + kappa) - n\n", "Wc = np.full(2*n + 1, 1. / (2*(n + lambda_))\n", "Wm = np.full(2*n + 1, 1. / (2*(n + lambda_))\n", "Wc[0] = lambda_ / (n + lambda_) + (1. - alpha**2 + beta)\n", "Wm[0] = lambda_ / (n + lambda_)\n", "```\n", "\n", "I use the underscore in `lambda_` because `lambda` is a reserved word in Python. A trailing underscore is the Pythonic workaround." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sigma Points\n", "\n", "The equations for the sigma points are:\n", "\n", "$$\n", "\\begin{cases}\n", "\\mathcal{X}_0 = \\mu \\\\\n", "\\mathcal{X}_i = \\mu + \\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i, & i=1..n \\\\\n", "\\mathcal{X}_i = \\mu - \\left[\\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} & i=(n+1)..2n\n", "\\end{cases}\n", "$$\n", "\n", "The Python is not difficult once we understand the $\\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i$ term.\n", "\n", "The term $\\sqrt{(n+\\lambda)\\Sigma}$ is a matrix because $\\Sigma$ is a matrix. The subscript $i$ in $[\\sqrt{(n+\\lambda)\\Sigma}]_i$ is choosing the i-th row vector of the matrix. What is the square root of a matrix? There is no unique definition. One definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$: if $\\Sigma = SS$ then $S = \\sqrt{\\Sigma}$.\n", "\n", "We will choose an alternative definition that has numerical properties which make it easier to compute. We can define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n", "\n", "$$\n", "\\Sigma = \\mathbf{SS}^\\mathsf T\n", "$$\n", "\n", "This definition is favored because $\\mathbf S$ is computed using the [*Cholesky decomposition*](https://en.wikipedia.org/wiki/Cholesky_decomposition) [5]. It decomposes a Hermitian, positive-definite matrix into a triangular matrix and its conjugate transpose. The matrix can be either upper \n", "or lower triangular, like so:\n", "\n", "$$A=LL^{∗} \\\\ A=U^{∗}U$$\n", "\n", "The asterick denotes the conjugate transpose; we have only real numbers so for us we can write:\n", "\n", "$$A=LL^\\mathsf T \\\\ A=U^\\mathsf T U$$\n", "\n", "$\\mathbf P$ has these properties, so we can treat $\\mathbf S = \\text{cholesky}(\\mathbf P)$ as the square root of $\\mathbf P$.\n", "\n", "SciPy provides `cholesky()` method in `scipy.linalg`. If your language of choice is Fortran, C, or C++, libraries such as LAPACK provide this routine. Matlab provides `chol()`.\n", "\n", "By default `scipy.linalg.cholesky()` returns a upper triangular matrix, so I elected to write the code to expect an upper triangular matrix. For this reason I access the result by row, so that the first sigma point, which is the center point, is affected by a full row of non-zero values. If you provide your own square root implementation you will need to take this into account. You will find UKF algorithms in the literature that take the values column first. This is fine if the cholesky is lower-triangular, or if you are using a different algorithm that computes a symmetric matrix so row vs column order doesn't matter. " ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cholesky:\n", "[[1.414 0.071]\n", " [0. 1.731]]\n", "\n", "square of cholesky:\n", "[[2.005 0.122]\n", " [0.122 2.995]]\n" ] } ], "source": [ "import scipy\n", "a = np.array([[2., .1], [.1, 3]])\n", "s = scipy.linalg.cholesky(a)\n", "print(\"cholesky:\")\n", "print(s)\n", "print(\"\\nsquare of cholesky:\")\n", "print(s @ s.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we can implement the sigma points with this code:\n", "\n", "```python\n", "sigmas = np.zeros((2*n+1, n))\n", "U = scipy.linalg.cholesky((n+lambda_)*P) # sqrt\n", "\n", "sigmas[0] = X\n", "for k in range (n):\n", " sigmas[k+1] = X + U[k]\n", " sigmas[n+k+1] = X - U[k]\n", "```\n", "\n", "Now let's implement the unscented transform. Recall the equations\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_i w_i^m\\mathcal{X}_i \\\\\n", "\\Sigma &= \\sum_i w_i^c{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "We implement the sum of the means with\n", "\n", "```python\n", "x = np.dot(Wm, sigmas)\n", "```\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 and Fortran to achieve much faster speeds than Python can reach. A typical speedup is 20x to 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 of products, we call the built in `numpy.dot(x, y)` method. The dot product of two vectors is the sum of the element-wise multiplications of each element. If passed a 1D array and a 2D array it will compute the sum of inner products:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([410, 520, 630])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.array([10, 100])\n", "b = np.array([[1, 2, 3],\n", " [4, 5, 6]])\n", "np.dot(a, b)" ] }, { "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", "```python\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", "\n", "This introduces another feature of NumPy. The state variable `x` is one dimensional, as is `sigmas[k]`, so the difference `sigmas[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 $\\mathbf{yy}^\\mathsf{T}$ for the 1D array $\\mathbf{y}$. An alternative implementation could be:\n", "\n", "```python\n", "y = (sigmas[k] - x).reshape(kmax, 1) # convert into 2D array\n", "P += Wc[K] * np.dot(y, y.T)\n", "```\n", "\n", "This code is slower and not idiomatic, so we will not use it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Step\n", "\n", "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", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\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.\n", "\n", "```python\n", "def predict(self, sigma_points_fn):\n", " \"\"\" Performs the predict step of the UKF. On return, \n", " self.xp and self.Pp contain the predicted state (xp) \n", " and covariance (Pp). 'p' stands for prediction.\n", " \"\"\"\n", "\n", " # calculate sigma points for given mean and covariance\n", " sigmas = sigma_points_fn(self.x, self.Pp)\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.Wm, self.Wc, self.Q)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The update step converts the sigmas into measurement space via the function `h(x)`.\n", "\n", "$$\\mathcal{Z} = h(\\mathcal{Y})$$\n", "\n", "The mean and 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", "$$\\mathbf P_{xz} =\\sum_{i=0}^{2n} w^c_i(\\boldsymbol{\\mathcal Y}_i-\\mu)(\\boldsymbol{\\mathcal Z}_i-\\mu_z)^\\mathsf T$$\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "$$\\begin{aligned}\n", "K &= \\mathbf P_{xz} \\mathbf P_z^{-1}\\\\\n", "{\\mathbf x} &= \\mathbf{\\bar x} + \\mathbf{Ky}\n", "\\end{aligned}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\mathbf P = \\mathbf{\\bar P} - \\mathbf{KP}_z\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This function can be implemented as follows, assuming it is a method of a class that stores the necessary matrices and data.\n", "\n", "```python\n", "def update(self, z):\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 UT\n", " zp, Pz = unscented_transform(sigmas_h, self.Wm, self.Wc, self.R)\n", "\n", " # compute cross variance of the state and the measurements\n", " Pxz = np.zeros((self._dim_x, self._dim_z))\n", " for i in range(self._num_sigmas):\n", " Pxz += self.Wc[i] * np.outer(sigmas_f[i] - self.xp,\n", " sigmas_h[i] - zp)\n", "\n", " K = np.dot(Pxz, inv(Pz)) # Kalman gain\n", "\n", " self.x = self.xp + np.dot(K, z - zp)\n", " self.P = self.Pp - np.dot(K, Pz).dot(K.T)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### FilterPy's Implementation\n", "\n", "FilterPy has generalized the code somewhat. You can specify different sigma point algorithms, specify how to compute the residual of the state variables (you can not subtract angles because they are modular), provide a matrix square root function, and more. See the help for details.\n", "\n", "https://filterpy.readthedocs.org/#unscented-kalman-filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Batch Processing\n", "\n", "The Kalman filter is recursive - estimates are based on the current measurement and prior estimate. But it is very common to have a set of data that have been already collected which we want to filter. In this case the filter can be run in a *batch* mode, where all of the measurements are filtered at once.\n", "\n", "Collect your measurements into an array or list.\n", "\n", "```python\n", "zs = read_altitude_from_csv()\n", "```\n", "\n", "Then call the `batch_filter()` method.\n", "\n", "```python\n", "Xs, Ps = ukf.batch_filter(zs)\n", "```\n", "\n", "The function takes the list/array of measurements, filters it, and returns an array of state estimates (`Xs`) and covariance matrices (`Ps`) for the entire data set. \n", "\n", "Here is a complete example drawing from the radar tracking problem above." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = 12. # 12 seconds between readings\n", "range_std = 5 # meters\n", "bearing_std = math.radians(0.5)\n", "\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", "h_radar.radar_pos = radar_pos\n", "\n", "points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n", "kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2 ,0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2, 2] = 0.1\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2])\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", "radar = RadarStation((0, 0), range_std, bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "np.random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "zs = []\n", "for i in range(len(t)):\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " zs.append([r[0], r[1]])\n", "\n", "xs, covs = kf.batch_filter(zs)\n", "ukf_internal.plot_radar(xs, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing the Results\n", "\n", "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", "If we are collecting data and post-processing it we have measurements after the questionable one that informs us 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 turn was initiated.\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", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in position in meters:\n", "\t [-1.4166 -0.2815 1.2679 -1.2405 -2.1863]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ms, P, K = kf.rts_smoother(xs, covs)\n", "ukf_internal.plot_rts_output(xs, Ms, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From these charts we can see that the improvement in the position is small, but the improvement in the velocity is good, and spectacular for the altitude. The difference in the position are very small, so I printed the difference between the UKF and the smoothed results for the last 5 points. I recommend always using the RTS smoother if you can post-process your data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing the Sigma Parameters\n", "\n", "I have found the literature on choosing values for $\\alpha$, $\\beta$, and $\\kappa$ to be rather lacking. Van der Merwe's dissertation contains the most information, but it is not exhaustive. So let's explore what they do. \n", "\n", "Van der Merwe suggests using $\\beta=2$ for Gaussian problems, and $\\kappa=3-n$. So let's start there and vary $\\alpha$. I will let $n=1$ to minimize the size of the arrays we need to look at and to avoid having to compute the square root of matrices." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 3. -3.]\n", "mean weights: [0.6667 0.1667 0.1667]\n", "cov weights: [2.6667 0.1667 0.1667]\n", "lambda: 2\n", "sum cov 2.9999999999999996\n" ] } ], "source": [ "from kf_book.ukf_internal import print_sigmas\n", "print_sigmas(mean=0, cov=3, alpha=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So what is going on here? We can see that for a mean of 0 the algorithm chooses sigma points of 0, 3, and -3, but why? Recall the equation for computing the sigma points:\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= \\mu\\\\\n", "\\mathcal{X}_i &= \\mu \\pm \\sqrt{(n+\\lambda)\\Sigma}\n", "\\end{aligned}$$\n", "\n", "My choice of $n=1$ reduces everything to scalars, allowing us to avoid computing the square root of matrices. So, for our values the equation is\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= 0 \\\\\n", "\\mathcal{X}_i &= 0 \\pm \\sqrt{(1+2)\\times 3} \\\\\n", "&= \\pm 3\n", "\\end{aligned}$$\n", "\n", "So as $\\alpha$ gets larger the sigma points get more spread out. Let's set it to an absurd value." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 600. -600.]\n", "mean weights: [1. 0. 0.]\n", "cov weights: [-39996. 0. 0.]\n", "lambda: 119999\n", "sum cov -39996.00000000001\n" ] } ], "source": [ "print_sigmas(mean=0, cov=3, alpha=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the sigma points spread over 100 standard deviations. If our data was Gaussian we'd be incorporating data many standard deviations away from the mean; for nonlinear problems this is unlikely to produce good results. But suppose our distribution was not Gaussian, but instead had very fat tails? We might need to sample from those tails to get a good estimate, and hence it would make sense to make $\\kappa$ larger (not 200, which was absurdly large to make the change in the sigma points stark). \n", "\n", "With a similar line of reasoning, suppose that our distribution has nearly no tails - the probability distribution looks more like an inverted parabola. In such a case we'd probably want to pull the sigma points in closer to the mean to avoid sampling in regions where there will never be real data.\n", "\n", "Now let's look at the change in the weights. When we have $k+n=3$ the weights were 0.6667 for the mean, and 0.1667 for the two outlying sigma points. On the other hand, when $\\alpha=200$ the mean weight shot up to 0.99999 and the outlier weights were set to 0.000004. Recall the equations for the weights:\n", "\n", "$$\\begin{aligned}\n", "W_0 &= \\frac{\\lambda}{n+\\lambda} \\\\\n", "W_i &= \\frac{1}{2(n+\\lambda)}\n", "\\end{aligned}$$\n", "\n", "We can see that as $\\lambda$ gets larger the fraction for the weight of the mean ($\\lambda/(n+\\lambda)$) approaches 1, and the fraction for the weights of the rest of the sigma points approaches 0. This is invariant on the size of your covariance. So as we sample further and further away from the mean we end up giving less weight to those samples, and if we sampled very close to the mean we'd give very similar weights to all.\n", "\n", "However, the advice that Van der Merwe gives is to constrain $\\alpha$ in the range $0 \\gt \\alpha \\ge 1$. He suggests $10^{-3}$ as a good value. Let's try that." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 0.0036 -0.0036]\n", "mean weights: [-999999. 500000. 500000.]\n", "cov weights: [-999996. 500000. 500000.]\n", "lambda: -0.999999\n", "sum cov 3.9999989999923855\n" ] } ], "source": [ "print_sigmas(mean=0, cov=13, alpha=.001, kappa=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Robot Localization - A Fully Worked Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is time to undertake a significant problem. Most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world problem. This example will not teach you how to tackle any problem, but illustrates the type of things you will have to consider as you design and implement a filter. \n", "\n", "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape using a sensor to detect landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house, or a robot in a warehouse.\n", "\n", "The robot has 4 wheels in the same configuration used by automobiles. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n", "\n", "The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", "\n", "Both the process model and measurement models are nonlinear. The UKF accommodates both, so we provisionally conclude that the UKF is a viable choice for this problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Robot Motion Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires a complicated set of differential equations. \n", "\n", "For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. This is a depiction of the model:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ekf_internal.plot_bicycle()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see the front tire is pointing in direction $\\alpha$ relative to the wheelbase. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. We can compute the turn angle $\\beta$ with\n", "\n", "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n", "\n", "and the turning radius R is given by \n", "\n", "$$R = \\frac{d}{\\beta}$$\n", "\n", "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n", "\n", "With $\\theta$ being the robot's orientation we compute the position $C$ before the turn starts as\n", "\n", "$$\\begin{aligned}\n", "C_x &= x - R\\sin(\\theta) \\\\\n", "C_y &= y + R\\cos(\\theta)\n", "\\end{aligned}$$\n", "\n", "After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n", "\n", "$$\\begin{aligned} \\bar x &= C_x + R\\sin(\\theta + \\beta) \\\\\n", "\\bar y &= C_y - R\\cos(\\theta + \\beta) \\\\\n", "\\bar \\theta &= \\theta + \\beta\n", "\\end{aligned}\n", "$$\n", "\n", "Once we substitute in for $C$ we get\n", "\n", "$$\\begin{aligned} \\bar x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", "\\bar y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", "\\bar \\theta &= \\theta + \\beta\n", "\\end{aligned}\n", "$$\n", "\n", "You do not need to understand this math in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the State Variables\n", "\n", "For our robot we will maintain the position and orientation:\n", "\n", "$$\\mathbf x = \\begin{bmatrix}x & y & \\theta\\end{bmatrix}^\\mathsf{T}$$\n", "\n", "I could include velocities into this model, but as you will see the math will already be quite challenging.\n", "\n", "The control input $\\mathbf{u}$ is the commanded velocity and steering angle\n", "\n", "$$\\mathbf{u} = \\begin{bmatrix}v & \\alpha\\end{bmatrix}^\\mathsf{T}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the System Model\n", "\n", "We model our system as a nonlinear motion model plus white noise.\n", "\n", "$$\\bar x = x + f(x, u) + \\mathcal{N}(0, Q)$$\n", "\n", "Using the motion model for a robot that we created above, we can write:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "from math import tan, sin, cos, sqrt\n", "\n", "def move(x, dt, u, wheelbase):\n", " hdg = x[2]\n", " vel = u[0]\n", " steering_angle = u[1]\n", " dist = vel * dt\n", "\n", " if abs(steering_angle) > 0.001: # is robot turning?\n", " beta = (dist / wheelbase) * tan(steering_angle)\n", " r = wheelbase / tan(steering_angle) # radius\n", "\n", " sinh, sinhb = sin(hdg), sin(hdg + beta)\n", " cosh, coshb = cos(hdg), cos(hdg + beta)\n", " return x + np.array([-r*sinh + r*sinhb, \n", " r*cosh - r*coshb, beta])\n", " else: # moving in straight line\n", " return x + np.array([dist*cos(hdg), dist*sin(hdg), 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use this function to implement the state transition function `f(x)`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I will design the UKF so that $\\Delta t$ is small. If the robot is moving slowly then this function should give a reasonably accurate prediction. If $\\Delta t$ is large or your system's dynamics are very nonlinear this method will fail. In those cases you will need to implement it using a more sophisticated numerical integration technique such as Runge Kutta. Numerical integration is covered briefly in the **Kalman Filter Math** chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the Measurement Model\n", "\n", "The sensor provides a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. If $p$ is the position of a landmark, the range $r$ is\n", "\n", "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n", "\n", "We assume that the sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n", "\n", "$$\\phi = \\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$$\n", "\n", "Thus our measurement function is\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{z}& = h(\\mathbf x, \\mathbf P) &+ \\mathcal{N}(0, R)\\\\\n", "&= \\begin{bmatrix}\n", "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", "\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta \n", "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n", "\\end{aligned}$$\n", "\n", "I will not implement this yet as there is a difficulty that will be discussed in the *Implementation* section below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design Measurement Noise\n", "\n", "It is reasonable to assume that the range and bearing measurement noise is independent, hence\n", "\n", "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we begin coding we have another issue to handle. The residual is $y = z - h(x)$. Suppose z has a bearing of $1^\\circ$ and $h(x)$ is $359^\\circ$. Subtracting them gives $-358^\\circ$. This will throw off the computation of the Kalman gain because the correct angular difference is $2^\\circ$. So we will have to write code to correctly compute the bearing residual." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "def normalize_angle(x):\n", " x = x % (2 * np.pi) # force in range [0, 2 pi)\n", " if x > np.pi: # move to [-pi, pi)\n", " x -= 2 * np.pi\n", " return x" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.9999999999999774\n" ] } ], "source": [ "print(np.degrees(normalize_angle(np.radians(1-359))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state vector has the bearing at index 2, but the measurement vector has it at index 1, so we need to write functions to handle each. Another issue we face is that as the robot maneuvers different landmarks will be visible, so we need to handle a variable number of measurements. The function for the residual in the measurement will be passed an array of several measurements, one per landmark." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "def residual_h(a, b):\n", " y = a - b\n", " # data in format [dist_1, bearing_1, dist_2, bearing_2,...]\n", " for i in range(0, len(y), 2):\n", " y[i + 1] = normalize_angle(y[i + 1])\n", " return y\n", "\n", "def residual_x(a, b):\n", " y = a - b\n", " y[2] = normalize_angle(y[2])\n", " return y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now implement the measurement model. The equation is\n", "$$h(\\mathbf x, \\mathbf P)\n", "= \\begin{bmatrix}\n", "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", "\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta \n", "\\end{bmatrix}$$\n", "\n", "The expression $\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$ can produce a result outside the range $[-\\pi, \\pi)$, so we should normalize the angle to that range.\n", "\n", "The function will be passed an array of landmarks and needs to produce an array of measurements in the form `[dist_to_1, bearing_to_1, dist_to_2, bearing_to_2, ...]`." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "def Hx(x, landmarks):\n", " \"\"\" takes a state variable and returns the measurement\n", " that would correspond to that state. \"\"\"\n", " hx = []\n", " for lmark in landmarks:\n", " px, py = lmark\n", " dist = sqrt((px - x[0])**2 + (py - x[1])**2)\n", " angle = atan2(py - x[1], px - x[0])\n", " hx.extend([dist, normalize_angle(angle - x[2])])\n", " return np.array(hx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our difficulties are not over. The unscented transform computes the average of the state and measurement vectors, but each contains a bearing. There is no unique way to compute the average of a set of angles. For example, what is the average of 359$^\\circ$ and 3$^\\circ$? Intuition suggests the answer should be 1$^\\circ$, but a naive $\\frac{1}{n}\\sum x$ approach yields 181$^\\circ$.\n", "\n", "One common approach is to take the arctan of the sum of the sins and cosines.\n", "\n", "$$\\bar{\\theta} = atan2\\left(\\frac{\\sum_{i=1}^n \\sin\\theta_i}{n}, \\frac{\\sum_{i=1}^n \\cos\\theta_i}{n}\\right)$$\n", "\n", "`UnscentedKalmanFilter.__init__()` has an argument `x_mean_fn` for a function which computes the mean of the state, and `z_mean_fn` for a function which computes the mean of the measurement. We will code these function as:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "def state_mean(sigmas, Wm):\n", " x = np.zeros(3)\n", "\n", " sum_sin = np.sum(np.dot(np.sin(sigmas[:, 2]), Wm))\n", " sum_cos = np.sum(np.dot(np.cos(sigmas[:, 2]), Wm))\n", " x[0] = np.sum(np.dot(sigmas[:, 0], Wm))\n", " x[1] = np.sum(np.dot(sigmas[:, 1], Wm))\n", " x[2] = atan2(sum_sin, sum_cos)\n", " return x\n", "\n", "def z_mean(sigmas, Wm):\n", " z_count = sigmas.shape[1]\n", " x = np.zeros(z_count)\n", "\n", " for z in range(0, z_count, 2):\n", " sum_sin = np.sum(np.dot(np.sin(sigmas[:, z+1]), Wm))\n", " sum_cos = np.sum(np.dot(np.cos(sigmas[:, z+1]), Wm))\n", "\n", " x[z] = np.sum(np.dot(sigmas[:,z], Wm))\n", " x[z+1] = atan2(sum_sin, sum_cos)\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These functions take advantage of the fact that NumPy's trigometric functions operate on arrays, and `dot` performs element-wise multiplication. NumPy is implemented in C and Fortran, so `sum(dot(sin(x), w))` is much faster than writing the equivalent loop in Python.\n", "\n", "With that done we are now ready to implement the UKF. I want to point out that when I designed this filter I did not just design all of functions above in one sitting, from scratch. I put together a basic UKF with predefined landmarks, verified it worked, then started filling in the pieces. \"What if I see different landmarks?\" That lead me to change the measurement function to accept an array of landmarks. \"How do I deal with computing the residual of angles?\" This led me to write the angle normalization code. \"What is the *mean* of a set of angles?\" I searched on the internet, found an article on Wikipedia, and implemented that algorithm. Do not be daunted. Design what you can, then ask questions and solve them, one by one.\n", "\n", "You've seen the UKF implemention already, so I will not describe it in detail. There are two new things here. When we construct the sigma points and filter we have to provide it the functions that we have written to compute the residuals and means.\n", "\n", "```python\n", "points = SigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", " subtract=residual_x)\n", "\n", "ukf = UKF(dim_x=3, dim_z=2, fx=fx, hx=Hx, dt=dt, points=points,\n", " x_mean_fn=state_mean, z_mean_fn=z_mean,\n", " residual_x=residual_x, residual_z=residual_h)\n", "```\n", "\n", "Next, we need to pass extra data into our `f(x, dt)` and `h(x)` functions. We want to use `move(x, dt, u, wheelbase)` for `f(x, dt)`, and `Hx(x, landmarks)` for `h(x)`. We can do this, we just have to pass the extra parameters into `predict()` and `update()` as keyword arguments like so:\n", "\n", "```python\n", " ukf.predict(u=u, wheelbase=wheelbase) \n", " ukf.update(z, landmarks=landmarks)\n", "```\n", "\n", "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once per second. We are not using Runge Kutta to integrate the differential equations of motion, so a small time step makes the simulation more accurate." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "\n", "dt = 1.0\n", "wheelbase = 0.5\n", "\n", "def run_localization(\n", " cmds, landmarks, sigma_vel, sigma_steer, sigma_range, \n", " sigma_bearing, ellipse_step=1, step=10):\n", "\n", " plt.figure()\n", " points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", " subtract=residual_x)\n", " ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=move, hx=Hx,\n", " dt=dt, points=points, x_mean_fn=state_mean, \n", " z_mean_fn=z_mean, residual_x=residual_x, \n", " residual_z=residual_h)\n", "\n", " ukf.x = np.array([2, 6, .3])\n", " ukf.P = np.diag([.1, .1, .05])\n", " ukf.R = np.diag([sigma_range**2, \n", " sigma_bearing**2]*len(landmarks))\n", " ukf.Q = np.eye(3)*0.0001\n", " \n", " sim_pos = ukf.x.copy()\n", " \n", " # plot landmarks\n", " if len(landmarks) > 0:\n", " plt.scatter(landmarks[:, 0], landmarks[:, 1], \n", " marker='s', s=60)\n", " \n", " track = []\n", " for i, u in enumerate(cmds): \n", " sim_pos = move(sim_pos, dt/step, u, wheelbase)\n", " track.append(sim_pos)\n", "\n", " if i % step == 0:\n", " ukf.predict(u=u, wheelbase=wheelbase)\n", "\n", " if i % ellipse_step == 0:\n", " plot_covariance_ellipse(\n", " (ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,\n", " facecolor='k', alpha=0.3)\n", "\n", " x, y = sim_pos[0], sim_pos[1]\n", " z = []\n", " for lmark in landmarks:\n", " dx, dy = lmark[0] - x, lmark[1] - y\n", " d = sqrt(dx**2 + dy**2) + randn()*sigma_range\n", " bearing = atan2(lmark[1] - y, lmark[0] - x)\n", " a = (normalize_angle(bearing - sim_pos[2] + \n", " randn()*sigma_bearing))\n", " z.extend([d, a]) \n", " ukf.update(z, landmarks=landmarks)\n", "\n", " if i % ellipse_step == 0:\n", " plot_covariance_ellipse(\n", " (ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,\n", " facecolor='g', alpha=0.8)\n", " track = np.array(track)\n", " plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n", " plt.axis('equal')\n", " plt.title(\"UKF Robot localization\")\n", " plt.show()\n", " return ukf" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Final P: [0.0092 0.0187 0.0007]\n" ] } ], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15]])\n", "cmds = [np.array([1.1, .01])] * 200\n", "ukf = run_localization(\n", " cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1)\n", "print('Final P:', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Steering the Robot\n", "\n", "The steering simulation in the run above is not realistic. The velocity and steering angles never changed, which doesn't pose much of a problem for the Kalman filter. We could implement a complicated PID controlled robot simulation, but I will just generate varying steering commands using NumPy's `linspace` method. I'll also add more landmarks as the robot will be traveling much farther than in the first example." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15], [20, 5],\n", " [0, 30], [50, 30], [40, 10]])\n", "dt = 0.1\n", "wheelbase = 0.5\n", "sigma_range=0.3\n", "sigma_bearing=0.1\n", "\n", "def turn(v, t0, t1, steps):\n", " return [[v, a] for a in np.linspace(\n", " np.radians(t0), np.radians(t1), steps)] \n", " \n", "# accelerate from a stop\n", "cmds = [[v, .0] for v in np.linspace(0.001, 1.1, 30)]\n", "cmds.extend([cmds[-1]]*50)\n", "\n", "# turn left\n", "v = cmds[-1][0]\n", "cmds.extend(turn(v, 0, 2, 15))\n", "cmds.extend([cmds[-1]]*100)\n", "\n", "#turn right\n", "cmds.extend(turn(v, 2, -2, 15))\n", "cmds.extend([cmds[-1]]*200)\n", "\n", "cmds.extend(turn(v, -2, 0, 15))\n", "cmds.extend([cmds[-1]]*150)\n", "\n", "cmds.extend(turn(v, 0, 1, 25))\n", "cmds.extend([cmds[-1]]*100)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final covariance [0.0013 0.0043 0.0004]\n" ] } ], "source": [ "ukf = run_localization(\n", " cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1, step=1,\n", " ellipse_step=20)\n", "print('final covariance', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can incorporate more error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further away from these landmarks." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final covariance [0.0026 0.0657 0.0008]\n" ] } ], "source": [ "ukf = run_localization(\n", " cmds, landmarks[0:2], sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1, step=1,\n", " ellipse_step=20)\n", "print('final covariance', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working because of the need to handle the modular math of angles. On the other hand, if you have implemented an extended Kalman filter (EKF) perhaps you are bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. The EKF for the same problem requires some fairly difficult mathematics. For many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", "\n", "The advantage of the UKF over the EKF is not only the relative ease of implementation. It is somewhat premature to discuss this because you haven't learned the EKF yet, but the EKF linearizes the problem at one point and passes that point through a linear Kalman filter. In contrast, the UKF takes $2n+1$ samples. Therefore the UKF is often more accurate than the EKF, especially when the problem is highly nonlinear. While it is not true that the UKF is guaranteed to always outperform the EKF, in practice it has been shown to perform at least as well, and usually much better than the EKF. \n", "\n", "Hence my recommendation is to always start by implementing the UKF. If your filter has real world consequences if it diverges (people die, lots of money lost, power plant blows up) of course you will have to engage in sophisticated analysis and experimentation to choose the best filter. That is beyond the scope of this book, and you should be going to graduate school to learn this theory. \n", "\n", "Finally, I have spoken of the UKF as *the* way to perform sigma point filters. This is not true. The specific version I chose is Julier's scaled unscented filter as parameterized by Van der Merwe in his 2004 dissertation. If you search for Julier, Van der Merwe, Uhlmann, and Wan you will find a family of similar sigma point filters that they developed. Each technique uses a different way of choosing and weighting the sigma points. But the choices don't stop there. For example, the SVD Kalman filter uses singular value decomposition (SVD) to find the approximate mean and covariance of the probability distribution. Think of this chapter as an introduction to the sigma point filters, rather than a definitive treatment of how they work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [1] Rudolph Van der Merwe. \"Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models\" dissertation (2004).\n", "\n", "- [2] Simon J. Julier. \"The Scaled Unscented Transformation\". Proceedings of the American Control Conference 6. IEEE. (2002)\n", "\n", "- [3] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n", "\n", "- [4] 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", "- [5] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 4 }