CTRA_KNet.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "22b66fa9-f423-4dbf-8e0b-5802001fcb0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as func\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.interpolate import interp1d\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d331a05-88f6-4372-9b29-e0c58a59d4a2",
   "metadata": {},
   "source": [
    "# 1. Data Preperation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a87044c9-9226-445f-9605-c9b5a1b4e544",
   "metadata": {},
   "source": [
    "## 1.1 Path and File names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cf42ea35-4f9b-40ee-80a2-b1072ed9bf31",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dates and directory\n",
    "date = '2013-04-05'  # TODO: Add other datasets\n",
    "directory = '/Users/sidhu/Documents/Master Thesis/KNet-Local/Data/' + date + '/'\n",
    "\n",
    "# Ground Truth\n",
    "GT_f = 'groundtruth.csv'\n",
    "\n",
    "# GPS\n",
    "GPS_f = 'gps.csv'\n",
    "GPS_RTK_f = 'gps_rtk.csv'\n",
    "\n",
    "# IMU\n",
    "IMU_f = 'ms25.csv'\n",
    "IMU_EULER_f = 'ms25_euler.csv'\n",
    "\n",
    "# Odometry\n",
    "od_1_f = 'odometry_mu.csv'\n",
    "od_2_f = 'odometry_mu_100hz.csv'\n",
    "od_3_f = 'odometry_cov.csv'\n",
    "od_4_f = 'odometry_cov_100hz.csv'\n",
    "\n",
    "# Wheels\n",
    "wheels_f = 'wheels.csv'\n",
    "\n",
    "# KVH\n",
    "kvh_f = 'kvh.csv'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a679829-abc8-4c81-9c7c-1a547b97631a",
   "metadata": {},
   "source": [
    "## 1.2 Data Loading"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02726f24-4886-425d-929f-579a7842e96c",
   "metadata": {},
   "source": [
    "### 1.2.1 Ground Truth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6b25ed81-ac1a-40a3-8a05-d94cdb1005bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "GROUNDTRUTH CSV File Format:\n",
    "                                Field | Description                               | Unit\n",
    "                                0     | UTIME of the measurements                 | microsecond\n",
    "                                1-3   | x, y, z                                   | m\n",
    "                                4-6   | roll, pitch, heading                      | rad\n",
    "\"\"\"\n",
    "\n",
    "gt      = np.loadtxt(directory + GT_f, delimiter = \",\")\n",
    "# NED (North, East Down)\n",
    "gtTime  = gt[:, 0] * 1e-6\n",
    "x       = gt[:, 1]\n",
    "y       = gt[:, 2]\n",
    "z       = gt[:, 3]\n",
    "roll    = gt[:, 4]\n",
    "pitch   = gt[:, 5]\n",
    "heading = gt[:, 6]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5c156bd-72d6-4920-ae74-24be725fb6fe",
   "metadata": {},
   "source": [
    "### 1.2.2 GPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3e916c55-bfc3-4a59-9934-693dc2a508ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" \n",
    "GPS CSV File Format:\n",
    "                                Field | Description                               | Unit\n",
    "                                0     | UTIME of the GPS fix                      | microsecond\n",
    "                                1     | Fix mode                                  |\n",
    "                                2     | Number of satellites used in the fix      |\n",
    "                                3     | Latitude                                  | rad\n",
    "                                4     | Longitude                                 | rad\n",
    "                                5     | Altitude                                  | m\n",
    "                                6     | Track                                     | m\n",
    "                                7     | Speed                                     | m/s\n",
    "\"\"\"\n",
    "gps     = np.loadtxt(directory + GPS_f, delimiter = \",\")\n",
    "gpsTime = gps[:, 0] * 1e-6\n",
    "lat     = gps[:, 3]\n",
    "lng     = gps[:, 4]\n",
    "alt     = gps[:, 5]\n",
    "\n",
    "gpsRTK     = np.loadtxt(directory + GPS_RTK_f, delimiter = \",\")\n",
    "gpsRTKTime = gpsRTK[:, 0] * 1e-6\n",
    "latRTK     = gpsRTK[:, 3]\n",
    "lngRTK     = gpsRTK[:, 4]\n",
    "altRTK     = gpsRTK[:, 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "385893a5-fe66-4ce3-bd9c-943c8365ccb1",
   "metadata": {},
   "source": [
    "### 1.2.3 IMU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "befc62f3-9758-4dc3-a666-afb82165e50a",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "IMU CSV File Format:\n",
    "                                Field | Description                               | Unit\n",
    "                                0     | UTIME of the measurements                 | microsecond\n",
    "                                1-3   | 3-DOF magnetic field strength vector      | Gauss\n",
    "                                4-6   | 3-DOF acceleration vector                 | m/s2\n",
    "                                7-9   | 3-DOF angular rate (roll, pitch, heading) | rad/s\n",
    "\"\"\"\n",
    "imu     = np.loadtxt(directory + IMU_f, delimiter = \",\")\n",
    "imuTime = imu[:, 0] * 1e-6\n",
    "# magX    = imu[:, 1]\n",
    "# magY    = imu[:, 2]\n",
    "# magZ    = imu[:, 3]\n",
    "accelX  = imu[:, 4]\n",
    "accelY  = imu[:, 5]\n",
    "accelZ  = imu[:, 6]\n",
    "gyroX   = imu[:, 7]\n",
    "gyroY   = imu[:, 8]\n",
    "gyroZ   = imu[:, 9]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a478883-09af-42ca-b5fb-327e23f46730",
   "metadata": {},
   "source": [
    "## 1.3 Data Preprocessing\n",
    "\n",
    "Idea: Interpolate Data so we get periodic measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1232f5dd-8a19-4205-9f25-26a3a67e0051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fca03d13370>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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W1AfTE81yjSQFIXJUKJok4JX/xE/XzvYBPvLzFXQNxfjUhVP4zCXTCOZBp738xQiRgxJJg+5QjMpCr92hjEtaa+56bCOhWJLHPnMeC+pL7A4pa3Lz+keIPDcYTaA1eXFmO1p2dw5RVezNq4QAkhSEyEnptX5lHYXTopTiby6YzO6OId7c3WV3OFklSUGIHNTSFwFgQrGMPjpdNy+dRH2pn7se20A0kbQ7nKyRpCBEDmruCQEwsVTKZp+ugMfF3e+bz66OIX7xyh67w8kaSQpC5KBE0ly5yyNDUoflohmVXDyzkvte3ZNeACfXyV+MEDko1ZewrXXA5kjGv5vOnkj3UIy1+3rsDiUrhpUUlFLfVUptVUqtV0o9ppQqyXjtq0qpnUqpbUqpqzK2L7O27VRK3TmczxdCHN3lsyfQWB7gO09vJRLPn/bw0fCuaRUEPE4eWrHf7lCyYrhXCs8B87TWC4DtwFcBlFJzgJuAucAy4L+VUk6llBP4CXA1MAf4sLWvEGIEeVwOvv6euexsH+TaH7/C0xtaSORJ88dIK/K5+fi7Gnl83UFW7um2O5xRN6ykoLV+VmudqgL1JlBvPb4OeERrHdVa7wF2Akus206t9W6tdQx4xNpXCDHCLplVxb23LALg0w+t5dx7/srdT25m88F+tNY2Rze+fPaSadSV+PnaYxuIJXI7uY5kn8IngKetx3VAU8Zrzda2Y21/B6XUHUqp1Uqp1R0dHSMYphD548q51Tzz9xfys5sXcebEEn71+l6u+fErXP6Dl/jBc9vZ2T5od4jjQsDj4hvvNa+8/rzuoN3hjKoTzmxRSi0Hqo/y0l1a6z9Z+9wFJICHRiowrfW9wL0AixcvltMaIU6Ty+lg2bxqls2rpnsoxlMbWnhi/UH+71938OPnd3BWQwk3nd3AexbW4vc47Q53zLpoZiUOBSv2dPG+M+twOMZmldPhOmFS0FpffrzXlVK3Ae8GLtOHrkkPABMzdqu3tnGc7UKIUVZW4OHmpZO4eekk2vsj/Ontgzyyaj//+If1fPfZbXzjvXO5Zn6N3WGOSW6ng/n1JfxudTN/evsgkysKaCwvoKrYS3mBl4oij3lf6KG80EtN0IfPPf6SrBpO26JSahnwA+AirXVHxva5wMOYfQi1wPPAdEBhdkhfhpkMVgEf0VpvOt7nLF68WK9evfq04xRCHJvWmhV7uvnOU1tY19zHPy2bxacvnmp3WGNSe3+E5Vva2d0xyO7OIfZ2DdE1GKMvHH/HvkpBbdBPY0UgnUBmVhdxxsQSinzZqUmllFqjtV58Su8ZZlLYCXiBVHGQN7XWf2u9dhdmP0MC+Hut9dPW9muAHwFO4H6t9d0n+hxJCkKMvljC4PO/eYtnN7fy1r9cSTAgxfROVixh0D0Uo3MwStdQjM6BKE09IfZ2DrHHuvVb9aiUghlVRSydUsb1Z9ZxxsTRWx3vdJLCsKplaa2nHee1u4F3HPC11k8BTw3nc4UQI8/jcrB0Shl/2dRKUkYnnRKPy0F10Ef1MVa601rTE4qz6WAfa/b1sHZ/L79d3cQDb+xjSmUB37xuHu+aVpHlqI9OSigKIdL2doXwuBwUS3XVEaWUoqzAwwXTK7lgeiUAA5E4T6xv4auPbuCxtw6MmaQgZS6EEAAYhuYvG1u5aEYlrhxdanIsKfK5+fCSBubVFfPXre1jZu6I/MsLIQB4c08Xrf0RrpXRR1n1gUVmbaWOwajdoQDSfCSEsDz+9kGKvC6WzTvatKT8kjQ0kXiSaMIgEk8e9jiaMIgnDWIJ62Y9jic1sUTSvE8ah+0XTxoozL4Hj8tBWYGXuhJzZFKFtWTqno4hqorsX/9CkoIQAjAPhMYYacI4Fq010YRBOJYkFE8SjpkH7LD1OGwdwFOPw/EkkYzH4Zhx9P2PeB5Pjsz34HE6cDsVbpcDrSFuJYuk8c6f/4lfrWLjN64atZFIJ0uSghACgPedWcf/rmnmmU2tXHfGUavPHJdhaIZiCQYiCYaiicPOrFP3xzxwZzwPHXGgj8SNww7ap0op8Lud+N1OfG4nfo8z/bzY72ZCsdd87nFZ+zjwuZ14Xce+97gcuJ2H7t+5TeFxOo56gNda0xuKc6A3zM72QR54Yy9v7e9lKJZk8lefYtu3luF12TfpTZKCEAKApVPKqSvx8/s1zemkoLVmb1eIt/b3mGPtw3EGIgn6I3H6I2YCMLfFGYwmOMoJ8HG5HOrQQdqTceB2O6kqcmccyB2HHbj9bgd+z6F9D3uvx0kg47nXdfSDs12UUpQWeCgt8DCvLsj1Z9YRTSSZ+c9/AeBrj27k+x9caFt8khSEEAB0DEZJGAZN3SGe39LG8i1tLN/STseA2QGqFBR5XRT73RT53BT5XNSV+JldXWRtc1FsbS/wut5xdu11Ow6dsVsHbbeMcgLA63Ky+p8vZ/G3lvPn9QclKQgxXsSTBgd6wuaZqcdJwO0c98M393eF+D+Pb+TFbYeqEd/+wGoKvS4umlHJu6ZVcNakEqZXFeHM0SJwY0Fq6VS7S3NLUhDiJO1oG+Cjv1hB+8DhQwe9LgcFXrNZo8DrJOBxpe8LvebjAo959lzgdVHgceJxOXA5Hbgdyrx3KtxOBy6H2Snpdzsp9LqoLfGP+IG4NxTj2U1t/OfzOzjQGz7sNZdDcdt5jVw8s4qzJ5fa2radbxxjpIlLkoIQJ+nf/7KNSDzJd26Yj6E14ViSoWiSUCzBUCxBKJYkFE0yFDM7WrsGYwxGze2D0cRpnQH63A5uOKueu6+fd8rt4oPRBBua+9JNQXu7Qsfc9/OXTefDSyZSE/SfcoxiZIyVkV+SFIQ4CUlD88K2dm47r5EPL2k4rZ8RTxqEokkGYwniCYOEYY5tjyfN+0TSIGFYY9zjSXpDcX6/ppmHV+xn2dxq5tQW43Y6cCjSVw+D0QQdA1He2NXF8i1tvLn75JaLvHhmJZ+5eBqLJ5Xm7LoA481QNHHinbJAkoIQJ0FrjdYa/zDq47udDoIBxylVH60t8fOx+1fysftXntZnLqgPcvnsCVw0o5LpEwoJeOQ/+bEqMUJzI4Yrb/5Cnt7QwmNvHWB/d4jOwRgJwyCR1CQMcyKJx+kg4HUR8FhtwlZHYoHHRcDrJOh3U1HopbLQXEyjotBLRaGX8kKPtLuOMK01kbhBUpuTqbRhXlobWpPUGq1Tz82x8Yeem9sGowla+yK09oVp6YtYtzDdQzHAHBKoMNtwPS5zjHnA66Km2EdtiZ+Gcj/z64JMqShMn0W7nA5qgn72dR+7CWY0XDijkqe/cAG7O4boHIzyxPqDrNrbc9g+dSV+LpxRyRVzqlgyuZxCb978Z51Txkonfl789by2s5NPP7SWqiIvC+qDnNlQYnXqOXA5FQ6liCUMwvGE1UZsthMPRBK09UcYiibpC5vjsI+m2OeiosibThqVRYdWX3IoiMQNinwuplQWMqWygOIsLbAx3qxv7uX//nUnK/d0H3XRktPhcZoljWuCPmZWF6FQaA4lknjSLGfQG4qxpaU/PfwSoKrIy/sX1fOZi6dS5HMTiScpsqF66OyaYmbXFNMzFOOHy7czq7qIr1w1k/OmVsjymTnE5ZSkkDVd1hni/9y+hFnVxaf9cyLxJB0DUToHo3QOmgtqdGY87xiIsqWln5d3RBmIHLt9sLLIy+TyAiYEfSSSBlqDw2GewTqUMs+OtcYwsM6MzTPgVBmC1AEtmXGWnLT20akzaiPz8eFn16mRLsV+N/WlfqZWFnL57AnMmFBoyySfvlCcn760i3tf3kVpwMPV86pprCjAqRRKmWf0qXb01HfkUGS8pszvD3P/Ao+L6qCPCcU+ygs8p9RmHokn2dcVYl1TL89taeNnL+1ixe4ufvepc3E6FMapzs4aQd97dhsDkQS/veNMZlYX2RaHGB3h2KnP1h4NeZEUeqykUFbgGdbP8bmdTCwLMLEscMJ9I/Ek3UMxDK3xuZ30huLs7hhkV8cQuzoG2d8VYkNzr9VxqNLNH1offrBT1sEwdSB0ODIPigqnQ+FOb7P2UcraL/Ogab0HiCfN+jH94Thv7Ori0bUH+O4z25hSWcA182q4en41c2qKRz1BtPZFuO/V3Ty8Yj9DsSQfWFTPv7xnjq1XUj63k5nVRcysLuKDZ0/ksbea+eJv1/HE+hZcDnVaZRZGQl84zu9WN/GhsydKQshRB3sjdocA5ElSSNUpdzmyN8nI53ZSW3JoeF9FoZdpVYVZ+/xT0T4Q4ZlNbTy9oYX/fnEn//XCTupL/Vw+ewLnT6tgwcTgiFRv1FqzvzvEyj3dPLWhhVd2dKKBdy+o4VMXTmVO7elfxY2Wq+fV8MXfrmN/d4iDfREaywtsiWPF7i7iSc31p1GTSIwPPrd5fArY3CSYF0nBa40Yidh0ljfWVRX5uGXpJG5ZOomuwSjPbW7juc1t/Gblfn71+l4AaoM+5tYFmVJRQEN5gEKvC6/LiddtdtR6XQ4icYOBiFkbZzCaYDCSoC8c52BfmOaeMHsz1qmtK/Fz+/mTuXnppJO68rJLauy406Eo8rlo67fnbK4nZF7t1pXKPIJclWqYLLB5oEB+JIUxMn18PCgv9HLTkgZuWtJAOJZk08E+3m7qZV1zH5sP9vHStg5iyZP/Hn1uB7VBP/VlAd6zMMjc2iALJwaz0jw1EgIeF9XFPra1DnDhjEqe29zGPe/Pfhypv93U37LIPamTVjsGM2TKk6RgXilEJSmcEr/HyeLGMhY3lqW3JQ1N+0CEUCxJNG4QTZglkaMJI12aociXKu/gStdzGc/Om1bOs5vauHhmpW0L2qfq74/9NCpOV3u/OfKtvtTeK+c8SQrmgUmaj4bP6VB5Vwrhk+dP4dG1B3hifQtnNpTYEkOpNUiiczBGubVSl8gtD6/cD8D508ptjWP8n8adhGRGu7AQp6qh/NCZ2zXz7Fm/ODXiaGtrvy2fL0bfyj1miZJvP7WV3R2DtsWRF0khNfporFQhFONDS1+Ye57eyryvP5Pe9skLJtsSS6V1ddAbGplJfWLsefHLF6cfv+f/vkooZk8tpLxoPkr15o/ULFmR+9Y39/LB//fGYYMTtn1rmW2d4xErDlmUJndNKg/gcTmIJQyGYkkSNk2UzIu/sFTNm/LC4U1eE/njj28dNCujfvlivvcBcxWspizXPcr085d3oxTMHYNzOcTIqc8YcrzpgD1NhXmRFHzWPAUZkipOltupSBia9c19LJpUCsD/rmm2LZ7nNrdx5ZwJLJxYYlsMYnQppXj27y9MPy/w2jOJLS+SQlWR2R7b3GPfmZ4YXz598VTOnFjC537zFo+9dYAPLq7nF6/sYfNBe87eCrxO3trfa1s7s8iOzKVd7aqAkBdJYU5tMR6Xgzd2ddkdihgnSgIefvupc3nvwlp+/PwO3jWtgkKvix8/v8OWeK47o472gehhVVxFbrNr7Yu8SApel5Nr5lXz29VNtpUpEOOP2+ngmvnVgNkE+ZFzGvjLplbW7Os5wTtHXqoJa0/nUNY/W+SXvEgKAF+6YiZJQ/Oj5fac6YnxZyAS55tPbGF6VSGXzKziMxdPxeVQ/GFt9vsWUqOOkjaW7hb5IS+GpII5Aemj50ziwTf38bcXTWGSTdUuxfjx8vZODvSGcTkUX/n9OjoHoyQMzZKMsh/ZkrrCrQ4Ov1qtEMeTN1cKANefWUfS0Oxos2+2oBg/LptdxacunMKZDSW83dRLW3+UW5ZO4pr52Z/VnCqSFhojC7GI3JU3VwqZpNyFOBk+t5OvXjPb7jCAQ8OqpX6XGG15lRRS7bGnsjzjcBiGZktrP9vbBmjpi5BImiurAWirenpm0c30Q2tjZuvxke87fNvx94NDS1oqDq3a5kgvd2l+J86MVdqcGctfOlOvOQ4ti+mwtgf9bmtNai8lfnfWvtt843GmijrKXBsxuvIqKaQXTMlCqYJHVu7nP57Zlp5NfapSIarDtqmjbEvtl7H1iPdq6//SS35yeDIaKS6HoqzAQ0Whl4oiL5WFXubUFnPz0oZ0+XJxelKF8OpK8qtCrci+vEoKqWJio9181BeO87XHNrCgvoS7rpnNwolBakv86QNj6tPTB3Qb6uloaz1oM1EcShhJQ2MYZmVZQ2sMQ5O0tmttXm0lre0JQ9MbitM5GKVz0BxDbz6O0TkYZXvrAH9Y28wbuzr56c2LpG7PMGxpGaDQ62J2jazPLEZX3iQFrTU/fn4HVUVe5taNbv2Yg71hDA1/c8EUrl1gT6nlE1GppqNRXrblwTf28i9/2sR/v7CLL1w+fVQ/K5e19kWoCfrGxWp14vRpmxZxypQ3p25r9/ew4UAfX7piBsU+96h+lt/qFHx83QHe2t+Dkcdjy285t5F3L6jhJy/spDd0ek1pAlr6IzIcNQ+MhT6jEblSUEr9A/A9oFJr3anM05n/BK4BQsBtWuu11r63Av9svfVbWusHRiKGE3n87YP43A7es7B21D9rUnmAW8+dxK9X7OeZTW14nA6qgz587kM5+KgdzBx+pnCyqeRQc5TZs5DZz5B5YpnZJ3Go6epQf4T5OL0zCrMT2uV04HYqXI5D9y6nIpowiMSThGLmLRJPErOW5ownDQytKfK66ByKEUsaPLmhhY+eM+kkfyuRqaM/wrTKCrvDEKNsIGp/ef9hJwWl1ETgSmB/xuargenW7Rzgp8A5Sqky4OvAYsxj3hql1ONa61GtG6C1ZvmWdi6YXpleW2E0KaX4xnXz+PvLZ/Dyjg62tAzQ0hd+R5XWww7YR+koPuLhUemMB5qM0U368BFOqf20PvSuw7frw/ZJPTYMTTxpEIkbJJIJ4klNwjBIGBqP04Hf4yTgcVIa8OBzO/C6nHhcjvQSqAORBE9uOAjAXY9tlKRwmlxOBwnD/rNIMbpSx4iiLBynjmUkPvmHwD8Cf8rYdh3wP9o87X1TKVWilKoBLgae01p3AyilngOWAb8ZgTiOqWMwyoHecNZXzSot8HDdGXVcd0ZWPzbreoZiPLu5ldV7e1izv4fdHUevzzO/LpjlyHJHRaGHzkEphpfrwtbkxJKC0W3iPp5hJQWl1HXAAa31uiM6wOqApoznzda2Y20/2s++A7gDoKGhYThh0twTBqBRSluMqHtf3sW3n9p6wv2KfS6+fcN83r1g9JvucpXH5RgT7c1idO2y1mauLwmcYM/Rc8KkoJRaDlQf5aW7gK9hNh2NOK31vcC9AIsXLx5WT+1AxKxBnyoVIIZv08G+wxLCexbWcs7kMs5qKGXGhMLD6sKL4WvuCacrpYrc9fKOTsAssWKXEx4ltdaXH227Umo+MBlIXSXUA2uVUkuAA8DEjN3rrW0HMJuQMre/eBpxn5JCWaN5xEWP6B+ZVlnIexbWEvTbd9mbq+JJg/aBKBOKZfRRrkuNVHTZWBngtE/ntNYbtNZVWutGrXUjZlPQWVrrVuBx4GPKtBTo01q3AM8AVyqlSpVSpZhXGc8M/9c4vikVZrOR1KIfOWc1lPKFyw7NO/jh8u0s/MazNN75JI13PsmPlm+n5zRnc4vDvbqzk1jCsKU6q8iuVG2rwlEeNn88o9We8hTmcNSdmENSPw6gte5WSn0TWGXt92+pTufRVFrgweNy0NonC+yMpC9eMYMvXjGD5p4QP3lhF79ZeWgA2o+W70ivXRHwOLnn/Qt49/waqY10GlJLgJ4zRZJCrttuVXCutJYQtsOIJQXraiH1WAOfPcZ+9wP3j9TnnqzpVYVsaxvI9sfmhfrSAN+5YT7fuWE+APu7Qvz0pZ38ZqU5piAUS/L537zF53/zFj/44EJuOKveznDHne6hGAUeJ0U2nj2K7NjRbh6jqmxMCnnTGzi3tphNNi26nm8aygN854YF7L3nWvZ85xp+96lz0/WmvvS7dVz3k9feMWdDHFtlkZehWFKGpOaBeNLsUygNeGyLIS+G47ywrZ3frTaXUEwkDRkZcxLiSYODvWFa+iK09UeIJzU+twO/24nf48TtdGAYh4rphWJJhqIJhmIJQtEkg9EEQ9EE4XgSQ2veu7CWV3Z00jkYZV1TLx/42et8+uJp1AR9FHideJxOvG4HHqcjPflN/p1Mk60+se2tA1RMs+8MUmSP22lfM2teJIXUPAWAuV9/hjm1xVw9r5r3nVk/Ym13Wmta+iIkDfMAORCJE4olzTUcjihlnZrTkTQM4kmzAmnSsGYKW8/jhiaZNGcOJ6zX40mzhEQ0bhBLJonGDSIJg3AswVA0SSiWYCCSoD+SYCASf8cIobFkXXMff/vrNcfdx+ty0FAWYFZNMdfMq+aqudV52Sdx7tRyqoq8/NsTm/njZ9+VXnBH5C6/x75/YzUWqvKdyOLFi/Xq1auH9TN2dQyyrqmXTQf7Wb23m3XNfTgdivOmljOnppiSgIeSgJvSgJtin5tCn4vSgIf6Uj9KKSJx8+y3yOdiKJqkNxRjV8cQb+zq4v7X9ozQbzq21Jf6qQ36qSr24nE6iCSShK06RwlD40wv0qMo8DoJeFwUeJ0UeFwEvC4KvU58bidOh8LtcBA3DLoGY/zgue0smlTKP187m+6hGEMxs2aSWTfp0OP+SJx9XSHW7u+hczDGRTMq+a+PnJmXbesvbmvntl+u4vxpFfzggwupkuGpOanxzicB2P3ta0bkBEgptUZrvfhU3pMXVwoAUysLqSjwUl7opbE8wIL6Eh5fd5BXdnTyijVhZLiKfS4KvC4KvS6K/W78bicupzpshbTMJOxyKJwOh3nvVLgcVrE567k79bpTWQdWhdftxGs1r3hcDnxu82AcsGoQFfncFPtc6SYej9MxJs6utda8ububJ9aZI5KuP6OWMxtObjJW0tA8vGIf//rnzXzk5yv49e3nEAzkV2K4eGYV99wwn3/98yYu/t6LfPScBq6YU82ZDSWyTkUOsvO/2bxICmv39/Cr1/byl02tI9bBWWGtKnbGxBI+sKieiWX2TUsfy/rCcR5d28xDK/azs32QoN/N3e+bx0eWnHzpEqdDccu5jdSW+Pn0r9dy8335mRhuWtLA0inlfP+57dz/2l5+/soe/G4n06oKqQn68Lmd6X4fn9uJN+N55sJSXutkwm+dUPg9hz8v9LnSEz5F/sn55qMv/+86fr+mGY/TwYeXTGTZvBqmVhbgcjrSzRVJQ1PsN5uNPK7Dz7piCSNdPlqcHK01a/f38PCKJp5Yf5BowmDhxBJuPqeB9yysHVab+F+3tvGpB9cwtbKQB28/x9bx3HbqC8d5Y1cXK/d0s6N9gPb+KJGEWb48EjdLmg+nT+lHHzqD6888alkyMYpSzUd777l2RH6eNB8dwTA0b+zqMh9rzWcumXbKpQKOTBLi2AxD8/s1zdz36h62tZnLR964qJ4PL2lg3ghVSL101gTuu/VsPvXgGj7ws9d58PZz8vIqLeh3s2xeNcvmHa0smckwdHrNi9T65BrzRCccN/uHMu8j1uNvPrGZ/13TJEkhT+V0UnA4FC98+WK+8MhbPL2x1RwJJEaM1prmnjDrmntZ39zHqzs62dzSz7y6Yr5zw3zeu7B2VNavuHBGJQ/9zTl8/Jer+Nj9K3n00+dRWmDfuO6xyuFQ+D3OUx7JsulgP4+ubSYST8pIpyxKrUzot/k7z+mkAOaZvt/tpKrIS22J3+5wcsZrOzv52mMb2NcVAszveU5NMd+9cQE3Lqof9bWEz2oo5b5bF/ORn6/gUw+u4cFPLsHrkgPYSLh6fjUPvrmPpza0yOzzLNrfbf63NKXS3hL/edE2sq1tgFk1xXaHkVP+5Y8b0wnh2vk1PPrp83jsM+fxgcUTs7a4/OLGMr73wYWs3NvNl/93fV6vhT2Szp1STl2Jn2c2tdodSl5JzWa2u/8y568UwFxe0sYJgjnp/tvO5tG1zSzf0s6TG1p4ckML9aV+fvKRs1g4sSRrcbx3YS0HesL8+1+2UhP08bVrZmfts3OVUoqKIq8s6pNl8aT5fXtsPljlRVKYV1fM0xvlrGckNVYU8KUrZ/KlK2fS2hfhhW3tfP1Pm3h4xf6sJgWAv71oCi19Ye59eTfVxT4+cX52l13NRdF4Ek8ejezSWrPxQD994ThnNJTYMiS3fcCsbWX3iLq8SAqTygsYiCSk42yUVAd9fHhJAw++sc+Wom1KKf7Pu+fQ3h/l357YTHXQxzXza7IeRy4JeJwMRRN2h5E1v1/TzFd+vx4wD8pPfO78rC9q1GElhaoie2er50WfgtcaVhpLyuXwaDK0PmySVDa5nA5+dNMZLJpUyt//9m1W7R31ZTpyWl1pgAO94RPvmCPObChNF6HrGIjy53UHsx7DWFh1DfIkKaTKAMTHcIG4XBBLGrhtnNfhczv5+ccWU1/i5/ZfrWKHrJ9x2iaW+jnYG06vBJbrplUV8vqdlzFzQhEAK/Zk/6QilZTiNp+85kVSSE1AG8tVQ8e7ne2DNHeHKbOxDjxAWYGHBz6xBK/bya33r6SlL3/OdkfS+dMriCc1dzy4hiZrqGSuqyzy8oMPLQTguc1tWf989xhp0ciLpOBzm79mvpz1ZJNhaH63qokb/vs1iv0u/vbiqXaHxMSyAL+87Wz6Iwne/9+v8/L2DsZDOZex5LypFXzz+nms2tPNpd9/kT+sabY7pKyYkzF0fVtrdq80U53bg1F7j1N50dFsWInX5ciLHJgVkXiSpze2cP+re9lwoI+zG0v57o0LqRsjEwTn1QV5+G/O4QuPvM3H7l/J3Npi3ndmHe9eUEt18NgdeYahiVvrWiSShx6ba1mY9YTMmlnmfcIwSBpmJVdD6/R9IqlJao1hZNwbmqQmvS21jkbmew/tyzu2Jaw25/pSP/Prgpw/vWJUJ+zdsnQSl8+u4oJ/f4E/rG3m/YtyfyKbUoq7rpnN3U9t4aofvcwjdyxl6ZTyrHx2qoP5oM19OXmRFFLlLZwyWWHYdrQN8NCK/Ty6tpn+SIJJ5QF++KGFXLewbkyU6M60oL6Ep79wAX9Y28zDK/bzrSe38K0nt1Be4MHndhJLGsSThw76qcWM7KAUOJXC4VA4lVkq3aHMCrFOhwOnw3zd0NA2EEFrcx3f+249m/n1I1NX6mgicfN7uXz2hFH7jLHmby6cwtbWAf6wtpmb7n0TgMtmVfGN6+ZSXzp6dbZSVwr7uoZG7TNORl4khbh1qWB3r/541huK8es39/GD57bjcjhYNq+am5ZMZOnk8jGXDDL53E4+es4kPnrOJHZ3DPKXTa0094SJxg08Lgdup8LtNNescFtrV7id5poWLqf5usth3nvdTjxOB163A6+1bKjL6bAO5tYB3Dqgmwf1ozzO3Ddj/1OZBR6JJ3ljdxdf/cMGvvL7dfzl7y8cte9vzb4eAC6YXjFqnzEWff+DC3nfmXXcfN8KAJ7f2s7zW9vTr8+vC3LJrCoumlHBnJrgaa+UZhiaLa39LN/czg+XbwegczA2/F9gGPIiKSTHyFCv8URrzba2AV7f2cXLOzp4dUdn+ozxnvfPp6Jw/E1smlJZyGcunmZ3GMPmczu5ZGYVy+ZVj3pbf9I6oRrLiX+0nD+9gr33XEsiafCr1/fyrSe3pF/bcKCPDQf6+PHzO0b8c5c0lo34zzwVeZEUEqmaItKncFzNPSFe3dHJa7u6eGNXZ/qMpbE8wCfOn8x7F9aOWAlsMXwBj5NQ3FwPZLTmh7zd1EuRz0VDHpYnT3E5HXzygil88oIpACSSBqv39fDS9g5e3t7BpoP9w/r5UyoKuGx2FVfOreaMifavpJcXSSF1pSA54Z0O9IZ58I19PLupld2dZltmZZGX86dVcN60Cs6bWj6q7aji9M2sLiJpaNY193LWSS5teqoMw5znY/eBaixxOR0snVLO0inl/NOyWXaHM+LyIimkLn0NmaZwmFV7u7nlvhXEk5rzp1Xw0aWTuGB6BdOrCrNW6VScvotmVFLkdXHPU1t55I6lo9LEM31CIb9d3UTnYHRcNhmKU5cXSSE9U1CyAmCuvPVfL+zkvld2Uxv088AnluTl6mXjXUnAwz+/ezb/9IcNPLWxhXcvqB3xz0gNx/zDmmY+dZH9c1DE6MuTpGCVuZDaRwD8bnUTP35+B5fOquLu982jJjg25haIU3fjoonc9+oevvboBjYd7OeiGZWcMbFkWIUfI/EkTd0h1jf38cI2c8RNU09+zGoWeZIUinzmr9kfTlAj/aR4rCRpaC0JYZxzOhQ/vXkR33piM//vpV389MVdOJTZL1RR6KXA66LA47TuXbiciljCIJY0iMbNCXmxpEEkbtA9FKNzIMpARnXUsgIPHzt3Ev9wxUwbf0uRTXmRFMqs9Xu7hqJAkb3BjAGLGs1OyRe3ddgciRgJUysL+eXHl9AbirFmXw/rm/s42BumayjGUDRBx2CUfV0hBqMJEobG63JYNyce67HP7WBubTEVhV4qCj3UBP3Mrw8ytbLQtsq3wh55lRR6huI2RzI2pDoMPz0G6hSJkVMS8HDZ7Alclkezj8XIy4txZjGrOqrXxrLOY0nQ76aswEPPkL0zJ4UQY09eHCVTHcx21vofa3wuR7rAmhBCpOTFUbI/bHacFfvyorXspPSG45T43XaHIYQYY/IiKXRY6wbL5BtTNJEkFEtSEpCkIIQ4XF4khdQC5KnStPmuL2x2uAdtXiVNCDH25MVRsnMwitOh0vMV8l2/lRSkOc2ktUZr0JhzN8zH1n3m44zXsbYb2no/HPN96fdYHBkltBUKpUBhLvCS/nxt/Ww0xT43BXJCI7IkL/7SmnvC1AR9uKSoFwADkbF15dQ1GGXV3m52tA3S3BOmPxInHE8SiSeJJYxDq5UdsbqZoTls5TLztUMrlhmp/XXGwds6uKcOuuNFodfF/Log1yyo4UOLJ6bXHRdipI2No8Io6w3F03MVBLT0RQCYUHzsZSmzoXsoxjef2Myf1x1Mj4SqKPRSGnDjczvxu50EPC7rzJrDFqtxpFcp47DVypRS6VXKDp2Rm2fjDqWsM/JDjznKNqXMs3bzDP7QmbzD2ma+TVnbMvd95/sc1mPrfwDp5JW0LinSVxlaW7Gq9PuUMv9+D/aGWbGni3/540Y2Nvfx7zcuyOq/lcgfw04KSqnPAZ8FksCTWut/tLZ/Fbjd2v55rfUz1vZlwH8CTuAXWut7hhvDiRhaS9XPDPu6zDo2DeX2FcGLJpJ8/Fer2HKwn1vPa+TaBTXMri4+7RWs8oHWmjseXMPruzvtDkXksGElBaXUJcB1wEKtdVQpVWVtnwPcBMwFaoHlSqkZ1tt+AlwBNAOrlFKPa603DyeOE6ko9LKzfXA0P2JcSS2Y8uiaZm5712RbYvjP5TtY19TLz24+i2XzamyJYaxJJK36Q4Mxuodi9EfiDETidA7GONAb5kBPmJe2dzCrWkq1iNEz3CuFTwP3aK2jAFrr1CKm1wGPWNv3KKV2Akus13ZqrXcDKKUesfYd1aQwtbKAx946QCiWIODJixaz47pmfjWza4p5ZFWTLUnBMDQPvrGPaxfU5F1CiCUMNrf0s6NtgKbuEPu6Q+zvDtHUHTru2rylATd1pX6uP6OWW86dlMWIRb4Z7hFyBnCBUupuIAJ8WWu9CqgD3szYr9naBtB0xPZzjvaDlVJ3AHcANDQ0DCvIxooCwGw2mV1TPKyflQuUUrgcihKbhqT2hGIMRBMsnjQ6q4WNNTvaBvjLxlZe39XFW009ROLWuscKakv8NJQFuHz2BCYU+6go8lJR4KGswEOx302Rz0VpwCOjj0TWnPAvTSm1HKg+ykt3We8vA5YCZwO/U0pNGYnAtNb3AvcCLF68eFjjRIp95iQtqfVzyGA0YVufQvuAOZmwqsjeju7RFEsY/HndQX7x6h62tPSjFMytLebDSxo4u7GMOTXF1Jb4ZRSRGHNOmBS01pcf6zWl1KeBR7XWGliplDKACuAAMDFj13prG8fZPmqe3tgCwCs7OzlvWsVof9y4MKHYS3t/xJbPTs2TyNUZ1cs3t/H1xzdxoDfMjAmFfOO9c1k2r9r20V5CnIzhXpP+EbgEeMHqSPYAncDjwMNKqR9gdjRPB1ZijsqbrpSajJkMbgI+MswYTujxtw8C8O4F+dV+fTwFHhetNiWF1EgwPY7mCZyMSDzJvz6+iUdWNTGruohf3nY2F8+slJFvYlwZblK4H7hfKbURiAG3WlcNm5RSv8PsQE4An9VaJwGUUn8HPIM5JPV+rfWmYcZwQg3lBWxt7T9uR16+2dcdorG8wJbP1lY2yKVjZftAhFvvX8WWln4+ffFUvnj5DGkaEuPSsJKC1joG3HyM1+4G7j7K9qeAp4bzuafqnhvmc91PXuM//rKVi2ZUZvOjxyTD0OzpHOLKOfYsxuJymtkgV0p394XifOy+lezvDvHL287mkllVdockxGnLi1OZhRNLaCgLYGgIx5J2h2O7/kicpKEpt6lqbDRxaPRNLrjvtT1sbR3g3lsWS0IQ415eJAWAv7lwCltb+1ny7eXc+Yf1vLGrK734Tr7xuc1Zw6GMBdqzaVvrAAAzc2QSVm8oRpHXxfnTZRCDGP/yZvDzLUsnMaemiIdW7OfxdQd5ZFUThV4X50wu49yp5Zw3tYJZ1UU4cuX09Th8biezqot4dnMbn7tsetY/3+syk1IyR5qPqoq8DEQTROLJdMIVYrzKm6QAsGhSGYsmlfGt6xO8tK2DV3Z28sauLp7fak7ELg24OXdqORfPrOLy2RNyuojeNfNr+MFz222Z5R2Jm014nhypWrvpYD/VxT5ZA1zkhLxKCikBj4ur59dw9XxziGpLX5g3dnXx+q4uXtvZyVMbWnEoWDK5jKvmVnPl3GrqSvw2Rz2yElbTWddgjEBZdv8MdrQPEvA4cybpHuyLMLWqQIaeipyQl0nhSDVBPzecVc8NZ9WjtWbjgX6e2dTKM5ta+cafN/ONP29mfl2Qq+ZO4D0La5lk01DOkdIXivPzV/ZwwfQK6kuzm+xiCYNnNrVyyayqnDmIlhd4aLNpzocQI02SwhGUUsyvDzK/PsiXr5rJ7o5BntnUxjObWvnes9v5/nPbuXRmFZ+5ZBqLxmntnt5wjHA8yTXza7J+YH5i/UG6h2LceFZ9Vj93NBX5XOxst6fTXoiRJo2gJzClspBPXzyVP372Xbzx1Uv53KXTWbu/hxt/9jobmvvsDu+01JcG8LudbG8byOrnxpMGP1q+g9k1xTk1X8TnchKOy1BnkRskKZyCmqCfL10xg2e+eCEuh+Kxt0a9bNOocDoUM6uL0kNDjyVu1fff1zXE5oP97O0comswSixxekN5H3h9L/u7Q3z5yhk5NcqrczBKeY70jwghzUenoarIx6Wzqnh83QHuvHrWuCxnUFnk5bnNbfzD79YRTSQZiCSsRV0S9IfN++Od/RZ6XZQE3JQGPJQE3JQVeNKPC70uHErhcppLS7b1RVi7v4fXd3VxycxKLs2xCV5dQzEqi+yZCCjESJOkcJpuWtKQ7mt4z8Jau8M5ZR9eMpH2gSiv7+rE73ZS5HdT7HNRE/RR7DPr+Bf5zG1FPjcBj9lEMhBJ0BeO0xOK0Rsy73tCcfZ1hcx1EiLvbFt3OhRTKgr4ylUzuf38yTnTwZzSG4plvcNeiNEiSeE0XTi9kimVBXznqS3MrC5ixoTxNTv30lkTuHTWyNc+SiQNQvEkhqFJGpqk1pQGPLhzZE7CkbTWtA9Ec3ptCJFfcvO/1CxwOhT/+aEziSUNlv3oZe74n9U8sf4g/ZG43aHZyuV0UOxzUxLwUF7oparIl7MJAaA/kiAUS1ITlKQgcoNcKQzD/PogT33hAh54fS+/WdnEs5vbcDkUZzeWcemsKs6dWs7smmKcOdSpKg7X0hcGoKZEkoLIDZIUhqmqyMdXrprFFy+fwdtNvTy/tZ0XtrZz91NbACj2uVgyuYwzG0qZU1vM3JpiKou8Odeunq9a+sxJa3KlIHKFJIUR4nI6WNxYxuLGMv5p2Sxa+sKs2N3Nij1drNjdzfIt7el9i30uJlcWMqWigMkZt8aKAgplgfZxpaXXTArVQeloFrlBjkCjpCbo5/oz67j+zDoA+sJxtrb0s7mln90dQ+zpHGLlnu53zHWoDfqYU1vMnJpiFtSX8K5pFfg9UnlzrNra2o/X5aBKhqSKHCFJIUuCfjfnTCnnnCnlh20Px5Ls6x5iT8cQuzuH2N42wOaD/fx1azuGBr/bySWzKlk2r4ZLZ1XJlcQYsr1tgD++dYBLZ1XldGe6yC9yhLGZ3+NkVnUxs6qLD9seiSdZvbeHpze28MymNp7a0IrH5eDC6RUsm1fDZbOqKJVZtFkVSxi83dTLqzs7eWlbO+ua+wh4nNx2XqPdoQkxYlRqEfWxbPHixXr16tV2h2GbpKFZu7+Hpze08peNLRzsi+B0KJY0lnHl3AlcMWcC9aUB2+IzDE13KEbPUIy+cJy+cBxDg9up8DgduF0O3E4HLofCYz1OveayHrudDjxOx5gqf9ExEOXtpl7e2t/D2029vN3USyiWxKFgfn0J186v5v1n1du2rKkQJ6KUWqO1XnxK75GkML5orVnf3Mdzm9t4dnMr29sGAZhbW2yt/TCBmROKRmx0k2FouoZitPSFaemL0NoX4WBfmNa+CC19EVr6wrT1RYmN0NKmDkU6QZjJxEoYLgdel9O6N28+t9O8WY/9Huuxx4nf7STgceL3uDIem9szF8MJxZLm79UfodX6Hdv6I+ztDHGg1xxu6nIoZtUUcVZDKe+aVsHSKeUE/e4R+X2FGE2SFPLQns4hnt3UyrOb21i7vwetoaEswMUzK7loRiWLJ5URDBw6gPUMxdjS2k9vKE7C0MyuLiISN+gLx+mPmGUr9nQMsb19kD2dg0c94HucDiYEvdQE/dQEfdQE/VQXeykv9BL0uyn2u3EoiCc18aSRcct4ntDEDYN4wtweSxokMl7PfB5LGESTBtG4uT0aTxJNGESs+3AsSSSRJBJPEomffnJyOhQTirxMCPqoK/GzsL6EMxpKmFcblM5+MS5JUshz7QMRnt/SznOb23hjV1e6oF1FoZeAx0nPUIyB6Inr/ntdDqZVFTKlspC6ktSB3zz415T4KAt4xlQzTyatdTpRhOJJwrEE4ZhBKJYgFE8SiZmJJHUh5XU5079feaFXJhqKnCJJQaRFE2ZH9cYDfezpHCISTxL0u6kvDTCrpojSgIc1+3ooK/DgdTnSZ/glATdVRT45OAqRA04nKcjooxzldTl517QK3jWt4pj7zKsLZjEiIcR4IIOrhRBCpElSEEIIkSZJQQghRJokBSGEEGmSFIQQQqRJUhBCCJEmSUEIIUSaJAUhhBBp42JGs1KqA9g3yh9TAXSO8mecjrEaF4zd2CSuUzdWYxurccHYjS0zrkla68pTefO4SArZoJRafarTwbNhrMYFYzc2ievUjdXYxmpcMHZjG25c0nwkhBAiTZKCEEKINEkKh9xrdwDHMFbjgrEbm8R16sZqbGM1Lhi7sQ0rLulTEEIIkSZXCkIIIdIkKQghhEjLu6SglPqmUmq9UuptpdSzSqlaa7tSSv1YKbXTev2sjPfcqpTaYd1uHcXYvquU2mp9/mNKqRJre6NSKmzF/LZS6mcZ71mklNpgxf1jpdSIL5l2rLis175qffY2pdRVGduXWdt2KqXuHOmYrM/4gFJqk1LKUEotzthu6/d1vNis12z7zo6I41+VUgcyvqdrThRjNmX7+zhBLHutv5u3lVKrrW1lSqnnrOPCc0qp0izFcr9Sql0ptTFj21FjOd5x7Zi01nl1A4ozHn8e+Jn1+BrgaUABS4EV1vYyYLd1X2o9Lh2l2K4EXNbjfwf+3XrcCGw8xntWWvEqK/6rsxjXHGAd4AUmA7sAp3XbBUwBPNY+c0YhrtnATOBFYHHGdlu/rxPEZut3dkSM/wp8+SjbjxrjaMZylBiy/n2cIJ69QMUR2/4DuNN6fGfqv4ssxHIhcFbm3/ixYjnWce14t7y7UtBa92c8LQBSPe3XAf+jTW8CJUqpGuAq4DmtdbfWugd4Dlg2SrE9q7VOWE/fBOqPt78VX7HW+k1t/gX8D3B9FuO6DnhEax3VWu8BdgJLrNtOrfVurXUMeMTad6Tj2qK13nay+2fr+zpBbLZ+ZyfpWDFm01j6Po7lOuAB6/EDjNLf0pG01i8D3ScZy7GOa8eUd0kBQCl1t1KqCfgo8H+szXVAU8Zuzda2Y20fbZ/AzPApk5VSbymlXlJKXWBtq7PiyWZsmXGNte8s01j5vo401r6zv7OaFe7PaP4YC/9+YyGGTBp4Vim1Ril1h7Vtgta6xXrcCkywJ7TjxnLK36Nr5GOzn1JqOVB9lJfu0lr/SWt9F3CXUuqrwN8BXx8rsVn73AUkgIes11qABq11l1JqEfBHpdTcMRDXqDuZuI5i1L+vYcSWVceLEfgp8E3MA943ge9jJn3xTudrrQ8opaqA55RSWzNf1FprpdSYGN8/3FhyMilorS8/yV0fAp7CTAoHgIkZr9Vb2w4AFx+x/cXRik0pdRvwbuAyq4kDrXUUiFqP1yildgEzrNgym5hSMWclLo79nXGc7SMa1zHeM+rf1+nGRha+s0wnG6NS6ufAEycRY7aMhRjStNYHrPt2pdRjmM1bbUqpGq11i9Uk025XfMeJ5ZS/x7xrPlJKTc94eh2QyviPAx+zeuuXAn3W5dgzwJVKqVLr8vpKa9toxLYM+EfgvVrrUMb2SqWU03o8BZgO7Lbi61dKLbVG0XwMGPEz1GPFhfmd3aSU8iqlJltxrQRWAdOVUpOVUh7gJmvfrLD7+zqBMfOdHdG2/D4gNZrlWDFmk61/Q5mUUgVKqaLUY8xjwEYrntRoxFvJ/t9SpmPFcqzj2rFlo7d8LN2AP2D+g64H/gzUWdsV8BPMEQ8bOHzEyCcwO9t2Ah8fxdh2Yrb/vW3dUiOj3g9ssratBd6T8Z7F1u+zC/gvrFnq2YjLeu0u67O3kTGSB3PUw3brtbtG6ft6H2YbaRRoA54ZC9/X8WKz+zs7IsYHrb/19dbBo+ZEMWbzlu3v4zhxTMEc/bTO+ru6y9peDjwP7ACWA2VZiuc3mE2kcetv7PZjxXK849qxblLmQgghRFreNR8JIYQ4NkkKQggh0iQpCCGESJOkIIQQIk2SghBCiDRJCkIIIdIkKQghhEj7/8nHIQgIoblUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First we display the ground truth\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "914e8a34-f1de-4456-aca7-4eb886a7a910",
   "metadata": {},
   "source": [
    "### 1.3.1 GPS Data\n",
    "\n",
    "1. Transform to x and y\n",
    "2. First remove outliers\n",
    "3. Interpolate data\n",
    "4. Get data at periodic time stamps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "071cc745-f194-4b80-8d0f-ae74151f1557",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fca03f1c970>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# STEP 1 \n",
    "# Transform GPS lat and lan into x and y\n",
    "\n",
    "lat0 = lat[0]\n",
    "lng0 = lng[0]\n",
    "\n",
    "dLat = lat - lat0\n",
    "dLng = lng - lng0\n",
    "\n",
    "r = 6400000 # approx. radius of earth (m)\n",
    "x_gps = r * np.cos(lat0) * np.sin(dLng)\n",
    "y_gps = r * np.sin(dLat)\n",
    "\n",
    "plt.plot(x_gps, y_gps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b6e71fc2-52ea-445a-8604-79c34d0ae28f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33724 34720 33724 34720\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# STEP 2\n",
    "# Remove outliers\n",
    "\n",
    "r1 = np.where(x_gps > (np.mean(x_gps) + 2*np.std(x_gps)))\n",
    "r2 = np.where(x_gps < (np.mean(x_gps) - 2*np.std(x_gps)))\n",
    "r = np.concatenate((r1[0],r2[0]))\n",
    "\n",
    "xg = np.delete(x_gps,r)\n",
    "yg = np.delete(y_gps,r)\n",
    "tg = np.delete(gpsTime,r)\n",
    "\n",
    "r1 = np.where(yg > (np.mean(yg) + 2*np.std(yg)))\n",
    "r2 = np.where(yg < (np.mean(yg) - 2*np.std(yg)))\n",
    "r = np.concatenate((r1[0],r2[0]))\n",
    "\n",
    "x_gp = np.delete(xg,r)\n",
    "y_gp = np.delete(yg,r)\n",
    "t_gp = np.delete(tg,r)\n",
    "\n",
    "plt.plot(x_gp, y_gp)\n",
    "print(t_gp.size, gpsTime.size, x_gp.size, x_gps.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2c021043-e553-4c54-92d5-cd20700baf71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc9c00a5ee0>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# STEP 3\n",
    "# Interpolate the data\n",
    "\n",
    "# Fit the function\n",
    "f_x_gp = interp1d(t_gp, x_gp, kind='cubic')\n",
    "f_y_gp = interp1d(t_gp, y_gp, kind='cubic')\n",
    "\n",
    "\n",
    "# STEP 4\n",
    "# Generate periodic time stamps\n",
    "delta_t = 0.05\n",
    "\n",
    "\n",
    "# We need to figure out which area we can extract from the data where we have imu, gps and gt data available\n",
    "l_time = max([imuTime[0], t_gp[0], gtTime[0]])\n",
    "h_time = min([imuTime[-1], t_gp[-1], gtTime[-1]])\n",
    "\n",
    "ts = np.arange(start=np.ceil(l_time), stop=np.floor(h_time), step=delta_t)  # timestamps\n",
    "\n",
    "# Create interpolated data\n",
    "x_gp_inter = f_x_gp(ts)\n",
    "y_gp_inter = f_y_gp(ts)\n",
    "\n",
    "# Compare the 2 interpolations\n",
    "# x axis\n",
    "plt.plot(ts, x_gp_inter)\n",
    "plt.plot(t_gp, x_gp)\n",
    "\n",
    "# y axis\n",
    "#plt.plot(t_gp_new, y_gp_inter)\n",
    "#plt.plot(t_gp, y_gp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64e10557-c07e-41ba-b74f-5bf8652f8555",
   "metadata": {},
   "source": [
    "### 1.3.2 IMU DATA\n",
    "\n",
    "1. Interpolate\n",
    "2. Sample periodically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f33c0e3a-ee04-45b3-b39a-a95068a1578a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fca03f14670>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Analyze IMU data\n",
    "\n",
    "# Acceleration in x\n",
    "plt.plot(imuTime, accelX)\n",
    "# Acceleration in y\n",
    "#plt.plot(imuTime, accelY)\n",
    "# Heading\n",
    "#plt.plot(imuTime, gyroZ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3daf250d-c5b6-4a16-857b-e57494c7e35a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc9e08ed880>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interpolate data so we get same periodic measurements\n",
    "f_x_acc = interp1d(imuTime, accelX, kind='cubic')\n",
    "f_y_acc = interp1d(imuTime, accelY, kind='cubic')\n",
    "f_heading = interp1d(imuTime, gyroZ, kind='cubic')\n",
    "\n",
    "# Create interpolated data\n",
    "# We use again t_gp_new to have same time measurements\n",
    "x_acc_inter = f_x_acc(ts)\n",
    "y_acc_inter = f_y_acc(ts)\n",
    "heading_inter = f_heading(ts)\n",
    "\n",
    "plt.plot(ts, x_acc_inter)\n",
    "plt.plot(imuTime, accelX)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a48de42-8344-4f83-a540-745c9dfe0c35",
   "metadata": {},
   "source": [
    "### 1.3.3 Merge Sensor Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba930c5c-b8e7-4a67-bd57-a23c5d36b894",
   "metadata": {},
   "source": [
    "### ![alt text](CTRA.png \"Model Overview\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d74237-cb15-4ef6-b8bd-012c5bb5944d",
   "metadata": {},
   "source": [
    "## 1.3.3 Ground Truth Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0d8bbbc8-5e42-4dee-9bde-d30608cc6fbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fca04480cd0>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get ground truth for all these sensor data\n",
    "\n",
    "# Useful ground truth we have\n",
    "# x, y, heading\n",
    "\n",
    "f_x_gt = interp1d(gtTime, x, kind='cubic')\n",
    "f_y_gt = interp1d(gtTime, y, kind='cubic')\n",
    "f_heading_gt = interp1d(gtTime, heading, kind='cubic')\n",
    "\n",
    "x_gt_inter = f_x_gt(ts)\n",
    "y_gt_inter = f_y_gt(ts)\n",
    "heading_gt = f_heading_gt(ts)\n",
    "\n",
    "plt.plot(gtTime, x)\n",
    "plt.plot(ts, x_gt_inter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "18db0104-434f-42b2-b9e8-d00df979829b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Merge all sensor data into one ndarray\n",
    "\n",
    "sensor_data = np.zeros((ts.size, 4))  # We will have four measurements at each time step [x, y, heading, acceleration]\n",
    "gt_data = np.zeros((ts.size,3))\n",
    "\n",
    "for i in range(sensor_data.shape[0]):\n",
    "    sensor_data[i][0] = x_gp_inter[i]\n",
    "    sensor_data[i][1] = y_gp_inter[i] \n",
    "    sensor_data[i][2] = heading_inter[i] \n",
    "    sensor_data[i][3] = x_acc_inter[i] \n",
    "    \n",
    "    gt_data[i][0] = x_gt_inter[i]\n",
    "    gt_data[i][1] = y_gt_inter[i]\n",
    "    gt_data[i][2] = heading_gt[i]\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "276d381a-1ac2-41e5-88de-8d2dc0aca05c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert to torch \n",
    "data = torch.from_numpy(sensor_data)\n",
    "gt = torch.from_numpy(gt_data)\n",
    "time_stamps = torch.from_numpy(ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "af91590b-5905-4201-a07a-b0f81a93cf73",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split torch for training and validation set\n",
    "d1, d2, d3, d4, d5 = torch.tensor_split(data, 5)\n",
    "g1, g2, g3, g4, g5 = torch.tensor_split(gt, 5)\n",
    "\n",
    "x_train = [d1, d2, d3]\n",
    "y_train = [g1, g2, g3]\n",
    "\n",
    "x_val = [d4]\n",
    "y_val = [g4]\n",
    "\n",
    "x_test = [d5]\n",
    "y_test = [g5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "287a0edb-a3a6-4349-a2cb-c352d2ee83c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fca044ab820>,\n",
       " <matplotlib.lines.Line2D at 0x7fca044ab850>,\n",
       " <matplotlib.lines.Line2D at 0x7fca044ab970>,\n",
       " <matplotlib.lines.Line2D at 0x7fca044aba90>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts, gt)\n",
    "plt.plot(ts, data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3b5f0e54-7255-40d9-8515-a15847ef93ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc9d00bb460>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gtTime, x)\n",
    "plt.plot(gtTime, y)\n",
    "plt.plot(gtTime, heading)\n",
    "plt.plot(ts[0], 500, 'ro')\n",
    "plt.plot(ts[-1], 500, 'ro')\n",
    "plt.plot(gtTime[0], 400, 'bo')\n",
    "plt.plot(gtTime[-1], 400, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "186803a1-5504-4a98-a1a4-81071c628040",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on the CPU\n"
     ]
    }
   ],
   "source": [
    "if torch.cuda.is_available():\n",
    "    cuda0 = torch.device(\"cuda:0\")  # you can continue going on here, like cuda:1 cuda:2....etc.\n",
    "    torch.set_default_tensor_type('torch.cuda.FloatTensor')\n",
    "else:\n",
    "   cuda0 = torch.device(\"cpu\")\n",
    "   print(\"Running on the CPU\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3da7e97d-ed47-4e7e-8a52-4f9ade5ea6d0",
   "metadata": {},
   "source": [
    "# 2. Model Preperation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4c647eb-cba2-4626-bc79-bf7ae92e3116",
   "metadata": {},
   "source": [
    "## 2.1 System Model Class & KalmanNet\n",
    "\n",
    "This class saves all the necessary information about the state space model and its parameters\n",
    "Note: Removed T & delta_t since I want to incorporate information about the data in the training/testing pipeline not in the System Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6ff7aa2f-d8a8-4d73-b4a5-afcf0b458c4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SystemModel:\n",
    "    \n",
    "    # f: state evolution function needs to be defined\n",
    "    # q: noise \n",
    "    # h: observation function/model\n",
    "    # r: noise\n",
    "    # T: length of trajectory (size of observation array/tensor)\n",
    "    # m: dimension of state vector\n",
    "    # n: dimension of observation vector\n",
    "    def __init__(self, m, n, f, q, h, r, T):\n",
    "\n",
    "        ####################\n",
    "        ### Motion Model ###\n",
    "        ####################\n",
    "        #self.modelname = modelname\n",
    "\n",
    "        self.f = f\n",
    "        self.m = m\n",
    "\n",
    "        self.q = q\n",
    "\n",
    "        #self.delta_t = delta_t\n",
    "        \n",
    "        self.Q = q * q * torch.eye(self.m)\n",
    "\n",
    "        \n",
    "        #########################\n",
    "        ### Observation Model ###\n",
    "        #########################\n",
    "        self.h = h\n",
    "        self.n = n\n",
    "\n",
    "        self.r = r\n",
    "        self.R = r * r * torch.eye(self.n)\n",
    "\n",
    "        #Assign T and T_test\n",
    "        self.T = T\n",
    "        #self.T_test = T_test\n",
    "\n",
    "    #####################\n",
    "    ### Init Sequence ###\n",
    "    #####################\n",
    "    def InitSequence(self, m1x_0, m2x_0):\n",
    "\n",
    "        self.m1x_0 = torch.squeeze(m1x_0).to(cuda0)\n",
    "        self.m2x_0 = torch.squeeze(m2x_0).to(cuda0)\n",
    "\n",
    "\n",
    "    #########################\n",
    "    ### Update Covariance ###\n",
    "    #########################\n",
    "    def UpdateCovariance_Gain(self, q, r):\n",
    "\n",
    "        self.q = q\n",
    "        self.Q = q * q * torch.eye(self.m)\n",
    "\n",
    "        self.r = r\n",
    "        self.R = r * r * torch.eye(self.n)\n",
    "\n",
    "    def UpdateCovariance_Matrix(self, Q, R):\n",
    "\n",
    "        self.Q = Q\n",
    "        self.R = R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f0f34a7e-99d0-4e9e-b40c-22cb5ea317bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "nGRU = 2\n",
    "\n",
    "class KalmanNetNN(torch.nn.Module):\n",
    "\n",
    "    ###################\n",
    "    ### Constructor ###\n",
    "    ###################\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "    ######################################\n",
    "    ### Initialize Kalman Gain Network ###\n",
    "    ######################################\n",
    "\n",
    "    def Build(self, ssModel, infoString = 'fullInfo'):\n",
    "\n",
    "        self.InitSystemDynamics(ssModel.f, ssModel.h, ssModel.m, ssModel.n, infoString = 'fullInfo')\n",
    "        self.InitSequence(ssModel.m1x_0, ssModel.T)\n",
    "\n",
    "        # Number of neurons in the 1st hidden layer\n",
    "        H1_KNet = (ssModel.m + ssModel.n) * (10) * 8\n",
    "\n",
    "        # Number of neurons in the 2nd hidden layer\n",
    "        H2_KNet = (ssModel.m * ssModel.n) * 1 * (4)\n",
    "\n",
    "        self.InitKGainNet(H1_KNet, H2_KNet)\n",
    "\n",
    "\n",
    "\n",
    "    def InitKGainNet(self, H1, H2):\n",
    "\n",
    "        # Input Dimensions (+1 for time input)\n",
    "        D_in = self.m + self.m + self.n  # F1,3,4\n",
    "\n",
    "        # Output Dimensions\n",
    "        D_out = self.m * self.n;  # Kalman Gain\n",
    "\n",
    "        ###################\n",
    "        ### Input Layer ###\n",
    "        ###################\n",
    "        # Linear Layer\n",
    "        self.KG_l1 = torch.nn.Linear(D_in, H1, bias=True)\n",
    "\n",
    "        # ReLU (Rectified Linear Unit) Activation Function\n",
    "        self.KG_relu1 = torch.nn.ReLU()\n",
    "\n",
    "        ###########\n",
    "        ### GRU ###\n",
    "        ###########\n",
    "        # Input Dimension\n",
    "        self.input_dim = H1\n",
    "        # Hidden Dimension\n",
    "        self.hidden_dim = ((self.n * self.n) + (self.m * self.m)) * 10 * 1\n",
    "        # Number of Layers\n",
    "        self.n_layers = nGRU\n",
    "        # Batch Size\n",
    "        self.batch_size = 1\n",
    "        # Input Sequence Length\n",
    "        self.seq_len_input = 1\n",
    "        # Hidden Sequence Length\n",
    "        self.seq_len_hidden = self.n_layers\n",
    "\n",
    "        # batch_first = False\n",
    "        # dropout = 0.1 ;\n",
    "\n",
    "        # Initialize a Tensor for GRU Input\n",
    "        # self.GRU_in = torch.empty(self.seq_len_input, self.batch_size, self.input_dim)\n",
    "\n",
    "        # Initialize a Tensor for Hidden State\n",
    "        self.hn = torch.randn(self.seq_len_hidden, self.batch_size, self.hidden_dim)\n",
    "\n",
    "        # Iniatialize GRU Layer\n",
    "        self.rnn_GRU = nn.GRU(self.input_dim, self.hidden_dim, self.n_layers)\n",
    "\n",
    "        ####################\n",
    "        ### Hidden Layer ###\n",
    "        ####################\n",
    "        self.KG_l2 = torch.nn.Linear(self.hidden_dim, H2, bias=True)\n",
    "\n",
    "        # ReLU (Rectified Linear Unit) Activation Function\n",
    "        self.KG_relu2 = torch.nn.ReLU()\n",
    "\n",
    "        ####################\n",
    "        ### Output Layer ###\n",
    "        ####################\n",
    "        self.KG_l3 = torch.nn.Linear(H2, D_out, bias=True)\n",
    "\n",
    "    ##################################\n",
    "    ### Initialize System Dynamics ###\n",
    "    ##################################\n",
    "    def InitSystemDynamics(self, f, h, m, n, infoString = 'fullInfo'):\n",
    "        \n",
    "        if(infoString == 'partialInfo'):\n",
    "            self.fString ='ModInacc'\n",
    "            self.hString ='ObsInacc'\n",
    "        else:\n",
    "            self.fString ='ModAcc'\n",
    "            self.hString ='ObsAcc'\n",
    "        \n",
    "        # Set State Evolution Function\n",
    "        self.f = f\n",
    "        self.m = m\n",
    "\n",
    "        # Set Observation Function\n",
    "        self.h = h\n",
    "        self.n = n\n",
    "\n",
    "    ###########################\n",
    "    ### Initialize Sequence ###\n",
    "    ###########################\n",
    "    def InitSequence(self, M1_0, T):\n",
    "\n",
    "        self.m1x_posterior = torch.squeeze(M1_0)\n",
    "        self.m1x_posterior_previous = 0 # for t=0\n",
    "\n",
    "        self.T = T\n",
    "        self.x_out = torch.empty(self.m, T)\n",
    "\n",
    "        self.state_process_posterior_0 = torch.squeeze(M1_0)\n",
    "        self.m1x_prior_previous = self.m1x_posterior\n",
    "\n",
    "        # KGain saving\n",
    "        self.i = 0\n",
    "        self.KGain_array = self.KG_array = torch.zeros((self.T,self.m,self.n))\n",
    "\n",
    "    ######################\n",
    "    ### Compute Priors ###\n",
    "    ######################\n",
    "    def step_prior(self):\n",
    "        # Predict the 1-st moment of x\n",
    "        self.m1x_prior = torch.squeeze(self.f(self.m1x_posterior))\n",
    "\n",
    "        # Predict the 1-st moment of y\n",
    "        self.m1y = torch.squeeze(self.h(self.m1x_prior))\n",
    "\n",
    "        # Update Jacobians\n",
    "        #self.JFt = get_Jacobian(self.m1x_posterior, self.fString)\n",
    "        #self.JHt = get_Jacobian(self.m1x_prior, self.hString)\n",
    "\n",
    "        self.state_process_prior_0 = torch.squeeze(self.f(self.state_process_posterior_0))\n",
    "        self.obs_process_0 = torch.squeeze(self.h(self.state_process_prior_0))\n",
    "\n",
    "    ##############################\n",
    "    ### Kalman Gain Estimation ###\n",
    "    ##############################\n",
    "    def step_KGain_est(self, y):\n",
    "        # Feature 1: yt - yt-1\n",
    "        try:\n",
    "            my_f1_0 = y - torch.squeeze(self.y_previous)\n",
    "        except:\n",
    "            my_f1_0 = y - torch.squeeze(self.obs_process_0) # when t=0 \n",
    "        # my_f1_reshape = torch.squeeze(my_f1_0)       \n",
    "        y_f1_norm = func.normalize(my_f1_0, p=2, dim=0, eps=1e-12, out=None)\n",
    "\n",
    "        # Feature 2: yt - y_t+1|t\n",
    "        # my_f2_0 = y - torch.squeeze(self.m1y)\n",
    "        # my_f2_reshape = torch.squeeze(my_f2_0)  \n",
    "        # y_f2_norm = func.normalize(my_f2_reshape, p=2, dim=0, eps=1e-12, out=None)\n",
    "\n",
    "        # Feature 3: x_t|t - x_t-1|t-1\n",
    "        m1x_f3_0 = self.m1x_posterior - self.m1x_posterior_previous\n",
    "        m1x_f3_reshape = torch.squeeze(m1x_f3_0)\n",
    "        m1x_f3_norm = func.normalize(m1x_f3_reshape, p=2, dim=0, eps=1e-12, out=None)\n",
    "\n",
    "        # Reshape and Normalize m1x Posterior\n",
    "        #m1x_post_0 = self.m1x_posterior - self.state_process_posterior_0 # Option 1\n",
    "\n",
    "        # Featture 4: x_t|t - x_t|t-1\n",
    "        m1x_f4_0 = self.m1x_posterior - self.m1x_prior_previous \n",
    "        #m1x_reshape = torch.squeeze(self.m1x_posterior) # Option 3\n",
    "        m1x_f4_reshape = torch.squeeze(m1x_f4_0)\n",
    "        m1x_f4_norm = func.normalize(m1x_f4_reshape, p=2, dim=0, eps=1e-12, out=None)\n",
    "\n",
    "        # Normalize y\n",
    "        #my_0 = y - torch.squeeze(self.obs_process_0) # Option 1\n",
    "        #my_0 = y - torch.squeeze(self.m1y) # Option 2\n",
    "        # my_0 = y\n",
    "        # y_norm = func.normalize(my_0, p=2, dim=0, eps=1e-12, out=None)\n",
    "        #y_norm = func.normalize(y, p=2, dim=0, eps=1e-12, out=None);\n",
    "\n",
    "        # Input for counting\n",
    "        count_norm = func.normalize(torch.tensor([self.i]).float(),dim=0, eps=1e-12,out=None)\n",
    "\n",
    "        # KGain Net Input\n",
    "        KGainNet_in = torch.cat([y_f1_norm,m1x_f3_norm,m1x_f4_norm], dim=0)\n",
    "\n",
    "        # Kalman Gain Network Step\n",
    "        KG = self.KGain_step(KGainNet_in)\n",
    "\n",
    "        # Reshape Kalman Gain to a Matrix\n",
    "        self.KGain = torch.reshape(KG, (self.m, self.n))\n",
    "\n",
    "    #######################\n",
    "    ### Kalman Net Step ###\n",
    "    #######################\n",
    "    def KNet_step(self, y):\n",
    "        # Compute Priors\n",
    "        self.step_prior()\n",
    "\n",
    "        # Compute Kalman Gain\n",
    "        self.step_KGain_est(y)\n",
    "\n",
    "        # Save KGain in array\n",
    "        self.KGain_array[self.i] = self.KGain\n",
    "        self.i += 1\n",
    "\n",
    "        # Innovation\n",
    "        # y_obs = torch.unsqueeze(y, 1)\n",
    "        dy = y - self.m1y\n",
    "\n",
    "        # Compute the 1-st posterior moment\n",
    "        INOV = torch.matmul(self.KGain, dy)\n",
    "        self.m1x_posterior_previous = self.m1x_posterior\n",
    "        self.m1x_posterior = self.m1x_prior + INOV\n",
    "\n",
    "        self.state_process_posterior_0 = self.state_process_prior_0\n",
    "        self.m1x_prior_previous = self.m1x_prior\n",
    "        self.y_previous = y\n",
    "\n",
    "        # return\n",
    "        return torch.squeeze(self.m1x_posterior)\n",
    "\n",
    "    ########################\n",
    "    ### Kalman Gain Step ###\n",
    "    ########################\n",
    "    def KGain_step(self, KGainNet_in):\n",
    "\n",
    "        ###################\n",
    "        ### Input Layer ###\n",
    "        ###################\n",
    "        L1_out = self.KG_l1(KGainNet_in)\n",
    "        La1_out = self.KG_relu1(L1_out)\n",
    "\n",
    "        ###########\n",
    "        ### GRU ###\n",
    "        ###########\n",
    "        GRU_in = torch.empty(self.seq_len_input, self.batch_size, self.input_dim)\n",
    "        GRU_in[0, 0, :] = La1_out\n",
    "        GRU_out, self.hn = self.rnn_GRU(GRU_in, self.hn)\n",
    "        GRU_out_reshape = torch.reshape(GRU_out, (1, self.hidden_dim))\n",
    "\n",
    "        ####################\n",
    "        ### Hidden Layer ###\n",
    "        ####################\n",
    "        L2_out = self.KG_l2(GRU_out_reshape)\n",
    "        La2_out = self.KG_relu2(L2_out)\n",
    "\n",
    "        ####################\n",
    "        ### Output Layer ###\n",
    "        ####################\n",
    "        L3_out = self.KG_l3(La2_out)\n",
    "        return L3_out\n",
    "\n",
    "    ###############\n",
    "    ### Forward ###\n",
    "    ###############\n",
    "    def forward(self, y):\n",
    "        yt = torch.squeeze(y)\n",
    "        '''\n",
    "        for t in range(0, self.T):\n",
    "            self.x_out[:, t] = self.KNet_step(y[:, t])\n",
    "        '''\n",
    "        self.x_out = self.KNet_step(yt)\n",
    "\n",
    "        return self.x_out\n",
    "\n",
    "    #########################\n",
    "    ### Init Hidden State ###\n",
    "    #########################\n",
    "    def init_hidden(self):\n",
    "        weight = next(self.parameters()).data\n",
    "        hidden = weight.new(self.n_layers, self.batch_size, self.hidden_dim).zero_()\n",
    "        self.hn = hidden.data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bd7fbe7-7ec2-4a42-854f-01d1b76ba448",
   "metadata": {},
   "source": [
    "## 2.2 Define the CTRA model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbdb8ae1-0367-4634-b710-ec222059708b",
   "metadata": {},
   "source": [
    "### ![alt text](delta_x.png \"Model Overview\")\n",
    "### ![alt text](delta_y.png \"Model Overview\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "84dc14d0-48ad-436f-92d0-c6ad91c31d8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_CTRA(state):\n",
    "    x = state[0]\n",
    "    y = state[1]\n",
    "    t = state[2]  # heading\n",
    "    v = state[3]  # speed\n",
    "    a = state[4]  # acceleration\n",
    "    w = state[5]  # yaw rate\n",
    "    T = delta_t\n",
    "    sin=torch.sin\n",
    "    cos=torch.cos\n",
    "    \n",
    "    add_state = torch.zeros_like(state)\n",
    "    \n",
    "    add_x = (1/w)*(v + a*T)*sin(t+w*T)  - (v/w)*cos(t) + (a/w**2)*cos(t+w*T) - (a/w**2)*sin(t)\n",
    "    add_y = (1/w)*(-v - a*T)*cos(t+w*T)  + (v/w)*cos(t) + (a/w**2)*sin(t+w*T) - (a/w**2)*sin(t)\n",
    "    \n",
    "    add_state = torch.tensor([add_x, add_y, w*T, a*T, 0, 0])\n",
    "    state = state.float()\n",
    "    \n",
    "    return state + add_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "88394fbb-bb3a-4afe-b843-fdbea4a9d2e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will have four measurements at each time step [x, y, heading, acceleration]\n",
    "def h_NCLT(state):\n",
    "    H = torch.tensor([[1, 0, 0, 0, 0, 0],\n",
    "                     [0, 1, 0, 0, 0, 0],\n",
    "                     [0, 0, 1, 0, 0, 0],\n",
    "                     [0, 0, 0, 0, 1, 0]]).float()\n",
    "    state = state.float()\n",
    "    return torch.matmul(H, state.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ff3e2c6f-ed74-4066-925b-92d73aa26751",
   "metadata": {},
   "outputs": [],
   "source": [
    "# m: dimension of state vector\n",
    "# n: dimension of observation vector\n",
    "# f: state evolution function needs to be defined\n",
    "# q: noise \n",
    "# h: observation function/model\n",
    "# r: noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b8a2ad5b-92cb-4dbd-9a27-bcc0e2ac8ae0",
   "metadata": {},
   "outputs": [],
   "source": [
    "q = 0.001\n",
    "r = 0.111\n",
    "ctra_system = SystemModel(6 , 4 , f_CTRA, q, h_NCLT , r, x_train[0].shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c0ac7bce-9382-4493-ad00-79d4e20a164b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initiliaze system\n",
    "\n",
    "# Initial state vector\n",
    "m1x_0 = torch.ones(6)\n",
    "\n",
    "#Initial covariance\n",
    "m2x_0 = torch.eye(6)*3000\n",
    "ctra_system.InitSequence(m1x_0, m2x_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "da5d8195-a26c-49d3-8128-2c7fd0f0b722",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define our KalmanNet with the given state space model and trajectory length\n",
    "KNet_model = KalmanNetNN()\n",
    "KNet_model.Build(ctra_system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "fc0a368d-e728-4ae0-8fae-e935c502466f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set training parameters\n",
    "n_Epochs, n_Batch, learningRate, weightDecay = 200, 10 , 1e-3, 1e-4\n",
    "\n",
    "\n",
    "N_Epochs = n_Epochs  # Number of Training Epochs\n",
    "N_B = n_Batch # Number of Samples in Batch\n",
    "learningRate = learningRate # Learning Rate\n",
    "weightDecay = weightDecay # L2 Weight Regularization - Weight Decay\n",
    "\n",
    "# MSE LOSS Function\n",
    "loss_fn = nn.MSELoss(reduction='mean')\n",
    "\n",
    "# Use the optim package to define an Optimizer that will update the weights of\n",
    "# the model for us. Here we will use Adam; the optim package contains many other\n",
    "# optimization algoriths. The first argument to the Adam constructor tells the\n",
    "# optimizer which Tensors it should update.\n",
    "optimizer = torch.optim.Adam(KNet_model.parameters(), lr=learningRate, weight_decay=weightDecay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "34ad2307-c8d0-49f7-a3a4-24fc844a355b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = x_val[0]\n",
    "y_val[0].T.shape\n",
    "len(x_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "afc08e1d-38af-43db-9810-71897697c041",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/j_/gxx7k8bn0777lz4mkj9bnjvm0000gn/T/ipykernel_41139/995604436.py:8: UserWarning: The use of `x.T` on tensors of dimension other than 2 to reverse their shape is deprecated and it will throw an error in a future release. Consider `x.mT` to transpose batches of matricesor `x.permute(*torch.arange(x.ndim - 1, -1, -1))` to reverse the dimensions of a tensor. (Triggered internally at  /Users/distiller/project/pytorch/aten/src/ATen/native/TensorShape.cpp:2318.)\n",
      "  return torch.matmul(H, state.T)\n"
     ]
    }
   ],
   "source": [
    "# Training function\n",
    "#def NNTrain(self, n_Examples, train_input, train_target, n_CV, cv_input, cv_target):\n",
    "\n",
    "# NUmber of samples for training and validation\n",
    "N_E = len(x_train)\n",
    "N_CV = len(x_val)\n",
    "\n",
    "# MSE for validation (linear and db)\n",
    "MSE_cv_linear_batch = torch.empty([N_CV])\n",
    "MSE_cv_linear_epoch = torch.empty([N_Epochs])\n",
    "MSE_cv_dB_epoch = torch.empty([N_Epochs])\n",
    "\n",
    "# MSE for training\n",
    "MSE_train_linear_batch = torch.empty([N_B])\n",
    "MSE_train_linear_epoch = torch.empty([N_Epochs])\n",
    "MSE_train_dB_epoch = torch.empty([N_Epochs])\n",
    "\n",
    "##############\n",
    "### Epochs ###\n",
    "##############\n",
    "\n",
    "MSE_cv_dB_opt = 1000\n",
    "MSE_cv_idx_opt = 0\n",
    "\n",
    "for ti in range(0, N_Epochs):\n",
    "\n",
    "    #################################\n",
    "    ### Validation Sequence Batch ###\n",
    "    #################################\n",
    "\n",
    "    # Cross Validation Mode\n",
    "    KNet_model.eval()\n",
    "\n",
    "    for j in range(0, N_CV):\n",
    "        #y_cv = cv_input[j, :, :]\n",
    "        y_cv = x_val[j]\n",
    "        KNet_model.InitSequence(ctra_system.m1x_0, ctra_system.T)\n",
    "\n",
    "        x_out_cv = torch.empty(KNet_model.m, KNet_model.T)\n",
    "        for t in range(0, KNet_model.T):\n",
    "            x_out_cv[:, t] = KNet_model(y_cv[t].float())\n",
    "\n",
    "        # Compute Training Loss\n",
    "        H_gt = torch.tensor([[1, 0, 0, 0, 0, 0],\n",
    "                             [0, 1, 0, 0, 0, 0],\n",
    "                             [0, 0, 0, 1, 0, 0]]).float()\n",
    "        xout = torch.matmul(H_gt, x_out_cv)\n",
    "        MSE_cv_linear_batch[j] = loss_fn(xout, y_val[j].T).item()\n",
    "\n",
    "    # Average\n",
    "    MSE_cv_linear_epoch[ti] = torch.mean(MSE_cv_linear_batch)\n",
    "    MSE_cv_dB_epoch[ti] = 10 * torch.log10(MSE_cv_linear_epoch[ti])\n",
    "\n",
    "    if (MSE_cv_dB_epoch[ti] < MSE_cv_dB_opt):\n",
    "        MSE_cv_dB_opt = MSE_cv_dB_epoch[ti]\n",
    "        MSE_cv_idx_opt = ti\n",
    "        torch.save(KNet_model, 'KNet_model.pt')\n",
    "\n",
    "    ###############################\n",
    "    ### Training Sequence Batch ###\n",
    "    ###############################\n",
    "\n",
    "    # Training Mode\n",
    "    KNet_model.train()\n",
    "\n",
    "    # Init Hidden State\n",
    "    KNet_model.init_hidden()\n",
    "\n",
    "    Batch_Optimizing_LOSS_sum = 0\n",
    "\n",
    "    for j in range(0, N_B):\n",
    "        n_e = random.randint(0, N_E - 1)\n",
    "\n",
    "        y_training = x_train[n_e]\n",
    "        KNet_model.InitSequence(ctra_system.m1x_0, ctra_system.T)\n",
    "\n",
    "        x_out_training = torch.empty(KNet_model.m, KNet_model.T)\n",
    "        for t in range(0, KNet_model.T):\n",
    "            x_out_training[:, t] = KNet_model(y_training[t].float())\n",
    "\n",
    "        # Compute Training Loss\n",
    "        xoutt = torch.matmul(H_gt, x_out_training)\n",
    "        LOSS = loss_fn(xoutt, y_train[n_e].T)\n",
    "        MSE_train_linear_batch[j] = LOSS.item()\n",
    "\n",
    "        Batch_Optimizing_LOSS_sum = Batch_Optimizing_LOSS_sum + LOSS\n",
    "\n",
    "    # Average\n",
    "    MSE_train_linear_epoch[ti] = torch.mean(MSE_train_linear_batch)\n",
    "    MSE_train_dB_epoch[ti] = 10 * torch.log10(MSE_train_linear_epoch[ti])\n",
    "\n",
    "    ##################\n",
    "    ### Optimizing ###\n",
    "    ##################\n",
    "\n",
    "    # Before the backward pass, use the optimizer object to zero all of the\n",
    "    # gradients for the variables it will update (which are the learnable\n",
    "    # weights of the model). This is because by default, gradients are\n",
    "    # accumulated in buffers( i.e, not overwritten) whenever .backward()\n",
    "    # is called. Checkout docs of torch.autograd.backward for more details.\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    # Backward pass: compute gradient of the loss with respect to model\n",
    "    # parameters\n",
    "    Batch_Optimizing_LOSS_mean = Batch_Optimizing_LOSS_sum / N_B\n",
    "    Batch_Optimizing_LOSS_mean.backward()\n",
    "\n",
    "    # Calling the step function on an Optimizer makes an update to its\n",
    "    # parameters\n",
    "    optimizer.step()\n",
    "\n",
    "    ########################\n",
    "    ### Training Summary ###\n",
    "    ########################\n",
    "    print(ti, \"MSE Training :\", MSE_train_dB_epoch[ti], \"[dB]\", \"MSE Validation :\", MSE_cv_dB_epoch[ti],\n",
    "          \"[dB]\")\n",
    "\n",
    "    if (ti > 1):\n",
    "        d_train = MSE_train_dB_epoch[ti] - MSE_train_dB_epoch[ti - 1]\n",
    "        d_cv = MSE_cv_dB_epoch[ti] - MSE_cv_dB_epoch[ti - 1]\n",
    "        print(\"diff MSE Training :\", d_train, \"[dB]\", \"diff MSE Validation :\", d_cv, \"[dB]\")\n",
    "\n",
    "    print(\"Optimal idx:\", MSE_cv_idx_opt, \"Optimal :\", MSE_cv_dB_opt, \"[dB]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69f9e47c-5cf1-4f62-b2ef-c1dd334fd51e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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