Kalman-Filter-CA-2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Kalman Filter Implementation for Constant Acceleration Model (CA) in Python\n",
    "\n",
    "Multisensor Data Fusion with acceleration ($\\ddot x$ and $\\ddot y$) and position ($x$ and $y$).\n",
    "\n",
    "`CC-BY-SA2.0 Lizenz Paul Balzer, Motorblog http://www.cbcity.de`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![Kalman Filter](Kalman-Filter-Step.png)\n",
    "\n",
    "First, we have to initialize the matrices and vectors. Setting up the math."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## State Vector\n",
    "\n",
    "Constant Acceleration Model for Ego Motion in Plane\n",
    "\n",
    "$$x_k= \\left[ \\begin{matrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y \\end{matrix} \\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Motion\n",
    "\n",
    "Formal Definition:\n",
    "\n",
    "$$x_{k+1} = A \\cdot x_{k} + B \\cdot u$$\n",
    "\n",
    "Hence, we have no control input $u$:\n",
    "\n",
    "$$x_{k+1} = \\begin{bmatrix}1 & 0 & \\Delta t & 0 & \\frac{1}{2}\\Delta t^2 & 0 \\\\ 0 & 1 & 0 & \\Delta t & 0 & \\frac{1}{2}\\Delta t^2 \\\\ 0 & 0 & 1 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 1 & 0 & \\Delta t \\\\ 0 & 0 & 0 & 0 & 1 & 0  \\\\ 0 & 0 & 0 & 0 & 0 & 1\\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y\\end{bmatrix}_{k}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Measurement\n",
    "\n",
    "$$y = H \\cdot x$$\n",
    "\n",
    "Acceleration ($\\ddot x$ & $\\ddot y$) as well as position ($x$ & $y$) is measured.\n",
    "\n",
    "$$y = \\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\\\0 & 1 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1\\end{bmatrix} \\cdot x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Setting up the math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]] (6, 1)\n"
     ]
    }
   ],
   "source": [
    "x = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]).T\n",
    "print(x, x.shape)\n",
    "n=x.size # States\n",
    "#plt.scatter(float(x[0]),float(x[1]), s=100)\n",
    "#plt.title('Initial Location')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Initial Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[100.   0.   0.   0.   0.   0.]\n",
      " [  0. 100.   0.   0.   0.   0.]\n",
      " [  0.   0.  10.   0.   0.   0.]\n",
      " [  0.   0.   0.  10.   0.   0.]\n",
      " [  0.   0.   0.   0.   1.   0.]\n",
      " [  0.   0.   0.   0.   0.   1.]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([100.0, 100.0, 10.0, 10.0, 1.0, 1.0])\n",
    "print(P, P.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,5.5])\n",
    "plt.ylim([5.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Dynamic Matrix\n",
    "\n",
    "It is calculated from the dynamics of the Egomotion.\n",
    "\n",
    "$$x_{k+1} = x_{k} + \\dot x_{k} \\cdot \\Delta t +  \\ddot x_k \\cdot \\frac{1}{2}\\Delta t^2$$\n",
    "$$y_{k+1} = y_{k} + \\dot y_{k} \\cdot \\Delta t +  \\ddot y_k \\cdot \\frac{1}{2}\\Delta t^2$$\n",
    "\n",
    "$$\\dot x_{k+1} = \\dot x_{k} + \\ddot x \\cdot \\Delta t$$\n",
    "$$\\dot y_{k+1} = \\dot y_{k} + \\ddot y \\cdot \\Delta t$$\n",
    "\n",
    "$$\\ddot x_{k+1} = \\ddot x_{k}$$\n",
    "$$\\ddot y_{k+1} = \\ddot y_{k}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.    0.    0.1   0.    0.005 0.   ]\n",
      " [0.    1.    0.    0.1   0.    0.005]\n",
      " [0.    0.    1.    0.    0.1   0.   ]\n",
      " [0.    0.    0.    1.    0.    0.1  ]\n",
      " [0.    0.    0.    0.    1.    0.   ]\n",
      " [0.    0.    0.    0.    0.    1.   ]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "dt = 0.1 # Time Step between Filter Steps\n",
    "\n",
    "A = np.matrix([[1.0, 0.0, dt, 0.0, 1/2.0*dt**2, 0.0],\n",
    "              [0.0, 1.0, 0.0, dt, 0.0, 1/2.0*dt**2],\n",
    "              [0.0, 0.0, 1.0, 0.0, dt, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1.0, 0.0, dt],\n",
    "              [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(A, A.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurement Matrix $H$\n",
    "\n",
    "Here you can determine, which of the states is covered by a measurement. In this example, the position ($x$ and $y$) as well as the acceleration is measured ($\\ddot x$ and $\\ddot y$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0. 0. 0.]\n",
      " [0. 1. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 0. 1.]] (4, 6)\n"
     ]
    }
   ],
   "source": [
    "H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(H, H.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurement Noise Covariance $R$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10000.     0.     0.     0.]\n",
      " [    0. 10000.     0.     0.]\n",
      " [    0.     0.   100.     0.]\n",
      " [    0.     0.     0.   100.]] (4, 4)\n"
     ]
    }
   ],
   "source": [
    "ra = 10.0**2   # Noise of Acceleration Measurement\n",
    "rp = 100.0**2  # Noise of Position Measurement\n",
    "R = np.matrix([[rp, 0.0, 0.0, 0.0],\n",
    "               [0.0, rp, 0.0, 0.0],\n",
    "               [0.0, 0.0, ra, 0.0],\n",
    "               [0.0, 0.0, 0.0, ra]])\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SpJ6YtArKgJKknjCgNpNnP/vZrF27drnufoswab+sS6F5b0upHybtb94KSpJ6YtICyiYJSVInWUFJUg9MYpu5ASVJPWFASZI6yYCSJHXSpAWUTRKSpE6ygpKknpi0CsqAkqQesItPktRZkxZQXoOSJHWSFZQk9cSkVVAGlCT1hAElSeokA0qS1DmT2MVnk4QkqZOsoCSpJyatgjKgJKknDChJUicZUJKkTpq0gLJJQpLUSVZQktQDk9hmbkBJUk8YUJKkTjKgJEmdNGkBZZOEJKmTrKAkqQdskpAkdZYBJUnqJANKktRJkxZQNklIkjrJCkqSemLSKigDSpJ6wC4+SVJnTVpAeQ1KktRJQwVUkpckqSSXzrHOU5JsSnJDkkct3hAlSfCz03zjfPXRsKf4LgEKeGaS7atq0wzrfAjYDnhDVd25WAOUJDX6GjTjGqqCqqrbgCuAbYEV05cnOQb4deAfq+rcRR2hJAmYvApqlGtQl7Tfnzc4M8nOwDuBTcBrFmlckqQBCwmnSQioL7ffnz9t/juAXYHTqur7izIqSdLEG6XN/CEVVJKVwG8BVwFvn28HSY4Hjgd4whOeMMJdS5L6WgmNa+gKqqquB64Fdkvy5CQPo2mMCPCaqvrpEPtYU1UrqmrFrrvuOvagJWkSTdopvlFfqPtlYG+a03x7AfsBH6uqixZ7YJKkB+tr0Ixr1IC6BFgNHA28ALgdeOMij0mSNAMDam5T16EOb7+fWFU3LeJ4JEkCRnyro6r6HjAVSJcBaxZ9RJKkh9gcbeZJdkzy6STfTXJlkucl2TnJhUmubr/v1K6bJGcmWZfkm0meNbCf1e36VydZPe4xjxRQSXZob94PvLqqHhj3jiVJo9kMTRLvBf6hqp4G/BJwJXAS8MWq2hf4YjsNzZm0fduv44EPtmPcGTgFeC7wHOCUqVAb1ahvFnsysBtwZlV9Y5w7lCSNZykDKs17qP4acBZAVf20qm4HVgHntKudAxzR3l4FfKQalwI7JtkdOBS4sKo2tu9CdCFw2DjHO/Q1qCQHAicC19AElSRpM1pgk8QuSdYOTK+pqsHLNE8GbgH+OskvAZcDrwd2q6obAarqxiSPbdffA1g/sP2Gdt5s80c2Z0Al2Q94A/A4mlS8F3hFVd09zp1JkpbNrVX1kPdSHbAN8CzgtVV1WZL38rPTeTOZKS1rjvkjm+8U36HAsTRl3yXAIVW1du5NJElLYYmvQW0ANlTVZe30p2kC66b21B3t95sH1t9rYPs9gRvmmD+yOQOqqt5VVamqR1XVgVX1r+PciSRpYZa6i6+qfgSsT/LUdtZBwHeA82le/0r7/bz29vnAMW033wHAHe2pwAuAFybZqW2OeGE7b2R+5Lsk9cRmeKHua4GPJdmWpt/gVTSFzKeSHAv8EHh5u+7ngRcB64B72nWpqo1J/gz4arveqVW1cZzBGFCS1BNLHVBtd/ZM16kOmmHdAk6YZT8fBj680PGM2mYuSdJmYQUlST3he/FJkjrJgJIkdc6Ib1m0RfAalCSpk6ygJKknJq2CMqAkqScMKElSJxlQkqROmrSAsklCktRJVlCS1AOT2GZuQElSTxhQkqROMqAkSZ00aQFlk4QkqZOsoCSpJyatgjKgJKkH7OKTJHWWASVJ6qRJCyibJCRJnWQFJUk9MWkVlAElST1hQEmSOscuPklSZ01aQNkkIUnqJCsoSeqJSaugDKgeq6rlHkLvPfDAA8s9hN7baitPxGwuBpQkqZMmLaB86iNJ6iQrKEnqAdvMJUmdZUBJkjrJgJIkddKkBZRNEpKkTrKCkqSemLQKyoCSpB6wi0+S1FkGlCSpkyYtoGySkCR1khWUJPXEpFVQBpQk9YQBJUnqHLv4JEmdNWkBZZOEJKmTrKAkqScmrYIyoCSpJwwoSVInGVCSpM6ZxC4+myQkSZ1kBSVJPTFpFZQBJUk9YUBJkjpp0gLKa1CSpE6ygpKknpi0CsqAkqQesM1cktRZUyE1ztcI97F1kq8n+bt2eu8klyW5Osm5SbZt52/XTq9rlz9pYB9vaedfleTQcY93rIBKclySs5Mc0U6vbKdPGncgkqS5bY6AAl4PXDkw/Xbg3VW1L3AbcGw7/1jgtqraB3h3ux5Jng4cBewHHAZ8IMnW4xzvuBXUSmA1sH87vU87fdiY+5MkLbMkewL/BfirdjrAgcCn21XOAY5ob69qp2mXH9Suvwr4ZFX9pKquBdYBzxlnPGNdg6qqVwKvHJg+Gzh7nH1JkoazGa5BvQf4A+Dn2unHALdX1X3t9AZgj/b2HsB6gKq6L8kd7fp7AJcO7HNwm5F4DUqSemKBp/h2SbJ24Ov4aft+MXBzVV0+OHuGYdQ8y+baZiR28UlSDyxCF9+tVbVijuW/ArwkyYuA7YFH0VRUOybZpq2i9gRuaNffAOwFbEiyDfBoYOPA/CmD24zECkqSemIpmySq6i1VtWdVPYmmyeGiqvpN4EvAy9rVVgPntbfPb6dpl19UVdXOP6rt8tsb2Bf4yjjHawUlSZrLm4FPJnkr8HXgrHb+WcBHk6yjqZyOAqiqK5J8CvgOcB9wQlXdP84dDx1QSU4D3gL8U1UdMm1ZgP8NHA18AVhVVfeOMyBJ0sw21wt1q+pi4OL29jXM0IVXVZuAl8+y/duAty10HKOc4jsduBk4OMnB05a9jyacLgFeajhJ0uLbTK+D6oyhA6qq7gL+tJ08fWp+klOBE4DLgRdX1Y8XdYSSJGDyAmrUa1BrgNcCK5K8jKa3/WSaVx0fVlV3LvL4JEn4XnzzatsM39xOfpDm7S2uAw6pqlvn2z7J8VM9+LfccsuoY5UkTZCR28yr6nzgCmAX4Bbg4Kq6fsht11TViqpaseuuu45615I00TzFN48kr6N5E0BoXszlaT1J2gz6GjTjGqmCSrKa5pXF1wOfo3ml8SlLMC5J0jSTVkENHVBJjqR5YdZG4BCazr1NwG8necrSDE+SBAsLpy06oNrXPX0CuIemW+/KqloPvJ/mNOEZSzdESdIkmjegkhwAfLadXFVVawcWnw7cARyZZOUSjE+S1LKCGpDkGcDnge2AV1TVlwaXV9VG2k9RBN65JCOUJAGTF1BzdvFV1beAnedZ53QG3llCkrQ0+ho04/LjNiRJneTHbUhST0xaBWVASVIP9Pla0rgMKEnqCQNKktRJkxZQNklIkjrJCkqSemLSKigDSpJ6woCSJHWOXXySpM6atICySUKS1ElWUJLUE5NWQRlQktQTBpQkqZMMKElS50xiF59NEpKkTrKCkqSemLQKyoCSpJ4woCRJnWRASZI6adICyiYJSVInWUFJUg9MYpu5ASVJPWFASZI6adICymtQkqROsoKSpJ6YtArKgJKknjCgJEmdYxefJKmzJi2gbJKQJHWSFZQk9cSkVVAGlCbaVlt5EmGhHnjggeUewsQwoCRJnWRASZI6ZxK7+Dy/IUnqJCsoSeqJSaugDChJ6gkDSpLUSQaUJKmTJi2gbJKQJHWSFZQk9cAktpkbUJLUEwaUJKmTDChJUidNWkDZJCFJIsleSb6U5MokVyR5fTt/5yQXJrm6/b5TOz9JzkyyLsk3kzxrYF+r2/WvTrJ63DEZUJLUE1ONEuN8DeE+4I1V9QvAAcAJSZ4OnAR8sar2Bb7YTgMcDuzbfh0PfLAd487AKcBzgecAp0yF2qgMKEnqgYWE0zABVVU3VtXX2tt3AVcCewCrgHPa1c4BjmhvrwI+Uo1LgR2T7A4cClxYVRur6jbgQuCwcY7Za1CS1BOb6xpUkicBzwQuA3arqhuhCbEkj21X2wNYP7DZhnbebPNHZkBJ0mTYJcnagek1VbVm+kpJdgD+Fvi9qrpzjlCcaUHNMX9kBpQk9cQCK6hbq2rFPPt/GE04fayqPtPOvinJ7m31tDtwczt/A7DXwOZ7Aje0818wbf7F4wzYa1CS1BNLeQ0qzUpnAVdW1bsGFp0PTHXirQbOG5h/TNvNdwBwR3sq8ALghUl2apsjXtjOG5kVlCT1xBJfg/oV4L8B30ryjXbeHwJnAJ9KcizwQ+Dl7bLPAy8C1gH3AK8CqKqNSf4M+Gq73qlVtXGcARlQktQDS/1efFX1L8x8/QjgoBnWL+CEWfb1YeDDCx2Tp/gkSZ1kBSVJPTFpb3VkQElSTxhQkqROMqAkSZ00aQFlk4QkqZOsoCSpB/zId0lSZxlQkqROmrSAGusaVJLjkpyd5Ih2emU7fdJ820qSxrPEH1jYOeM2SaykedPA/dvpfdrpsT6USpKk6cY6xVdVrwReOTB9NnD2YgxIkjSzvlZC4/IalCT1QJ9P1Y3LgJKknjCgJEmdNGkB5TtJSJI6aaiASvKSJJXk0jnWeUqSTUluSPKoxRuiJAkmr8182FN8lwAFPDPJ9lW1aYZ1PgRsB7yhqu5crAFKkhp9DZpxDVVBVdVtwBXAtsCK6cuTHAP8OvCPVXXuoo5QkrSg6qmvwTbKNahL2u/PG5yZZGfgncAm4DVz7SDJ8UnWJll7yy23jDRQSdJkGSWgvtx+f/60+e8AdgVOq6rvz7WDqlpTVSuqasWuu+46wl1LkiatghqlzfwhFVSSlcBvAVcBb1/EcUmSpulr0Ixr6ICqquuTXAvsneTJwHqaxogAr6mqny7RGCVJGFDz+TKwN81pvr2A/YCPVdVFiz0wSdKDTVpAjfpC3anTfEcDJwO3A29c1BFJksToFdRUQB3efj+xqm5axPFIkmbQ52aHcY0UUFX1vSQ3AbsBlwFrlmRUkqSHMKDmkGSH9ub9wKur6oHFH5IkaSYG1NxOpqme3l1V31iC8UiSZjFpATV0k0SSA4ETgWtogkqSpCUzZwWVZD/gDcDjgEOBe4FXVNXdm2FskqQBk1ZBzXeK71DgWOAumg6+k6tq7ZKPSpL0IHbxTVNV7wLetZnGIkmagwElSeqkSQsoP/JdktRJVlCS1BOTVkEZUJLUEwaUJKlz7OKTJHXWpAWUTRKSpE6ygpKknpi0CsqAkqSeMKAkSZ0ziU0SXoOSJHWSFZQk9cSkVVAGlCT1hAElSeokA0qS1EmTFlA2SUiSOskKSpJ6YBLbzA0oSeoJA0qS1EkGlCSpkyYtoGySkCR1khWUJPXEpFVQBpQk9cAkdvF5ik+SemIqpMb5GnL/hyW5Ksm6JCct8eHMywpKknpiKSuoJFsDfwEcAmwAvprk/Kr6zpLd6TysoCRJAM8B1lXVNVX1U+CTwKrlHNCyVVCXX375rUl+sFz3P4RdgFuXexA952O4cD6GC9f1x/CJw6x0+eWXX7DVVlvtsoD72T7J2oHpNVW1ZmB6D2D9wPQG4LkLuL8FW7aAqqpdl+u+h5FkbVWtWO5x9JmP4cL5GC7clvIYVtVhS3wXM50/rCW+zzl5ik+SBE3FtNfA9J7ADcs0FsCAkiQ1vgrsm2TvJNsCRwHnL+eA7OKb3Zr5V9E8fAwXzsdw4XwMh1BV9yX5XeACYGvgw1V1xXKOKVXLeopRkqQZeYpP6qAkxyU5O8kR7fTKdnrZXzwpbS4GlNRNK4HVwP7t9D7t9FJ3ckmd4Sk+SVukJMfRBP1nq+qzSVYCxwHfraozlnd0GoYVlKQtlVVoz1lBacGSvAQ4D7isqg6YZZ2nAN8ENgJPq6o7N+MQJfWQFZQWwyU0rzh/ZpLtZ1nnQ8B2wBsMJ0nDMKBaSU5LUkkunGFZknysXf75JA9bjjF2VVXdBlwBbAs85C1lkhwD/Drwj1V17mYenqSeMqB+5nTgZuDgJAdPW/Y+4GiaSuGlVXXv5h5cD1zSfn/e4MwkOwPvBDYBr9ncg+oTnyRJD2ZAtarqLuBP28nTp+YnORU4AbgceHFV/XgZhtcHX26/P3/a/HcAuwKnVdX3N++QescnSdIAmyQGJNkG+BbwNODlNG8//x7gSuDXqqrLb9m/rJLsQfNmkzdV1ePaeStpgut7wH9qP2NGc0jyGpoPjVtbVb/czjsVOJnmSdKBXsObmc06Wx4DapqBX/JbgccAPwBWVtX1yzqwHkhyDbA38PM0nyvzdWA/4KCqumg5x9YXPkkaX5KdgH8H7gUeXVWbZljnIprroUd5PbT7PMU3TVWdT3PBfxfgFuAcnDycAAACUklEQVRgw2log6f53kQTTh8znIZXVfcBb24nPwi8G7gOOMRwmpvNOlseA2qaJK+j+ccKsD3gKYDhTTVKHE1zSup24I3LN5x+8knSgtisswUxoAYkWU1zOuV64HPAo4BTlnVQ/TL1z+Fw4OHAW6rqpmUcTy/5JGlBbNbZgngNqpXkSOBvaJ71/yrwHzQX97cB9quq7y3j8HojyY+A3YDLgOdX1QPLPKReaZ8k/TXNJ5l+DfgN4C+q6neXdWA9YbPOlsUKCmhbej8B3AMcVlVXVtV64P00AeUbSw4hyQ7tzfuBVxtOo2mfJJ1F02F2CM3LGzYBv912n2ke7anQa4Hdkjy5fb3Yh4AArzGc+mXiAyrJAcBn28lVVbV2YPHpwB3Ake2zMM3tZJrq6cyq+sZyD6ZPfJK0qGzW2UJM9Cm+JM8A/hn4OeBlVXXeDOu8BTiNOV5bIUhyIM1HRf+Q5jTK3cs8pN5onyT9E00QHV5VXxpYtjNwDfBo4Fer6l+WZ5T9keRY4K+ALwAvAH5C85onr4f2zEQHlBYmyX7AG4DHAYfSvP7k16ZVoZqDT5IWX3s69KqBWb9TVR9arvFofAaUxpbkRODPgbuAtcDJVfWvyzsqyWadLYUBJWmL0jbrrKN5HdkKr4f218Q3SUja4tiss4WwgpK0xbBZZ8uyzXIPQJIWYpZmnVcYTv3nKT5JfXcocCzwazRvt3WInaRbBk/xSZI6yQpKktRJBpQkqZMMKElSJxlQkqROMqAkSZ1kQEmSOsmAkiR1kgElSeokA0qS1En/D9VVp/WVt1ChAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The Position of an object can be influenced by a force (e.g. wind), which leads to an acceleration disturbance (noise). This process noise has to be modeled with the process noise covariance matrix Q.\n",
    "\n",
    "$$Q = \\begin{bmatrix}\n",
    "    \\sigma_{x}^2 & 0 & \\sigma_{x \\dot x} & 0 & \\sigma_{x \\ddot x} & 0 \\\\\n",
    "    0 & \\sigma_{y}^2 & 0 & \\sigma_{y \\dot y} & 0 & \\sigma_{y \\ddot y} \\\\\n",
    "    \\sigma_{\\dot x x} & 0 & \\sigma_{\\dot x}^2 & 0 & \\sigma_{\\dot x \\ddot x} & 0 \\\\\n",
    "    0 & \\sigma_{\\dot y y} & 0 & \\sigma_{\\dot y}^2 & 0 & \\sigma_{\\dot y \\ddot y} \\\\\n",
    "    \\sigma_{\\ddot x x} & 0 & \\sigma_{\\ddot x \\dot x} & 0 & \\sigma_{\\ddot x}^2 & 0 \\\\\n",
    "    0 & \\sigma_{\\ddot y y} & 0 & \\sigma_{\\ddot y \\dot y} & 0 & \\sigma_{\\ddot y}^2\n",
    "   \\end{bmatrix} \\cdot \\sigma_{j}$$\n",
    "\n",
    "To easily calcualte Q, one can ask the question: How the noise effects my state vector? For example, how the jerk change the position over one timestep dt. With $\\sigma_{j}$ as the magnitude of the standard deviation of the jerk, which distrubs the car. We do not assume cross correlation, which means if a jerk will act in x direction of the movement, it will not push in y direction at the same time.\n",
    "\n",
    "We can construct the values with the help of a matrix $G$, which is an \"actor\" to the state vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import Symbol, Matrix\n",
    "from sympy.interactive import printing\n",
    "printing.init_printing(use_latex=True)\n",
    "dts = Symbol('\\Delta t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{\\Delta t^{3}}{6}\\\\\\frac{\\Delta t^{2}}{2}\\\\\\Delta t\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡        3⎤\n",
       "⎢\\Delta t ⎥\n",
       "⎢─────────⎥\n",
       "⎢    6    ⎥\n",
       "⎢         ⎥\n",
       "⎢        2⎥\n",
       "⎢\\Delta t ⎥\n",
       "⎢─────────⎥\n",
       "⎢    2    ⎥\n",
       "⎢         ⎥\n",
       "⎣\\Delta t ⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gs = Matrix([dts**3/6, dts**2/2, dts])\n",
    "Gs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{\\Delta t^{6}}{36} & \\frac{\\Delta t^{5}}{12} & \\frac{\\Delta t^{4}}{6}\\\\\\frac{\\Delta t^{5}}{12} & \\frac{\\Delta t^{4}}{4} & \\frac{\\Delta t^{3}}{2}\\\\\\frac{\\Delta t^{4}}{6} & \\frac{\\Delta t^{3}}{2} & \\Delta t^{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡        6          5          4⎤\n",
       "⎢\\Delta t   \\Delta t   \\Delta t ⎥\n",
       "⎢─────────  ─────────  ─────────⎥\n",
       "⎢    36         12         6    ⎥\n",
       "⎢                               ⎥\n",
       "⎢        5          4          3⎥\n",
       "⎢\\Delta t   \\Delta t   \\Delta t ⎥\n",
       "⎢─────────  ─────────  ─────────⎥\n",
       "⎢    12         4          2    ⎥\n",
       "⎢                               ⎥\n",
       "⎢        4          3           ⎥\n",
       "⎢\\Delta t   \\Delta t           2⎥\n",
       "⎢─────────  ─────────  \\Delta t ⎥\n",
       "⎣    6          2               ⎦"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gs*Gs.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.77777778e-10 0.00000000e+00 8.33333333e-09 0.00000000e+00\n",
      "  1.66666667e-07 0.00000000e+00]\n",
      " [0.00000000e+00 2.77777778e-10 0.00000000e+00 8.33333333e-09\n",
      "  0.00000000e+00 1.66666667e-07]\n",
      " [8.33333333e-09 0.00000000e+00 2.50000000e-07 0.00000000e+00\n",
      "  5.00000000e-06 0.00000000e+00]\n",
      " [0.00000000e+00 8.33333333e-09 0.00000000e+00 2.50000000e-07\n",
      "  0.00000000e+00 5.00000000e-06]\n",
      " [1.66666667e-07 0.00000000e+00 5.00000000e-06 0.00000000e+00\n",
      "  1.00000000e-04 0.00000000e+00]\n",
      " [0.00000000e+00 1.66666667e-07 0.00000000e+00 5.00000000e-06\n",
      "  0.00000000e+00 1.00000000e-04]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "sj = 0.1\n",
    "\n",
    "Q = np.matrix([[(dt**6)/36, 0, (dt**5)/12, 0, (dt**4)/6, 0],\n",
    "               [0, (dt**6)/36, 0, (dt**5)/12, 0, (dt**4)/6],\n",
    "               [(dt**5)/12, 0, (dt**4)/4, 0, (dt**3)/2, 0],\n",
    "               [0, (dt**5)/12, 0, (dt**4)/4, 0, (dt**3)/2],\n",
    "               [(dt**4)/6, 0, (dt**3)/2, 0, (dt**2),0],\n",
    "               [0, (dt**4)/6, 0, (dt**3)/2, 0, (dt**2)]]) *sj**2\n",
    "\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dXg6skHQt8KPUNsCfAH8j6VKyy37np0CrS02W98zQ0FCsWbOmL/s2MxstktY2uD8EwOTJk+OYY47peB8PPfRQ032MRb7EZ2ZmheRLfGZmBdDDQRJjlgPKzKwAHFB5DigzswJwQOU5oMzMCsABldfSIAlJp0oKSQ82WOdoSXskPSPpwHrrmZmZtaLVHtRqsnHrx0maFBF7aqxzCzARuDQiXuhWgWZmZdfq12YMmpZ6UBGxE1gHTAByY+0lnQt8GPhuRNzZ1QrNzAZAD58kMWa18zmo1enfD1TOlHQIcAOwB7iwS3WZmQ0UB1ReOwH1QPr3g1XzrwemAddFxJNdqcrMbMA4oPLaGcWX60FJmgt8HFhP+gbGRtJ3lFwAMH369DZ2bWZWbmUOmk613IOKiK3AJuBQSe+WdADZwAgBF6ZvVWzWxvKIGIqIoWnTpnVctJmZlV+7n4N6AJhJdpnvCLLvqb8jIu7rdmFmZoOi7JfqOtVuQK0m+36Pc4ATgF1kj1A3M7MRcEDldRJQAKekfy+LiGe7WI+Z2UByQOW1FVAR8WNJzwKHAg8By3tSlZnZgHFA5bX1fVCSJqeX+4BPRcQb3S/JzMys/Ut8V5H1npZFxCM9qMfMbCC5B5XXckBJOhG4DNhIFlRmZtYFHsVXW8OAkjQHuBR4JzAfeB04KyJeGoXazMwGhgMqr1kPaj6wGHiRbATfVRGxpudVmZkNGAdUXsOAiogbgRtHqRYzM7M3+Rt1zcwKwD2oPAeUmVkBOKDyHFBmZn3mUXy1OaDMzArAAZXngDIzKwAHVF5bjzoyMzMbLe5BmZkVgHtQeQ4oM7MCcEDlOaDMzPrMo/hqc0CZmRWAAyrPgyTMzKyQ3IMyMysA96DyHFBmZgXggMpzQJmZ9ZkHSdTmgDIbw3bv3t3vErpq8uTJ/S6hbxxQeR4kYWZmheQelJlZAbgHleeAMjMrAAdUngPKzKwAHFB5Digzsz7zKL7aHFBmZgXggMrzKD4zMysk96DMzArAPag8B5SZWQE4oPIcUGZmBeCAynNAmZn1mUfx1eZBEmZmVkjuQZmZFYB7UHkOKDOzAnBA5TmgzMwKwAGVN6KAkjQVmApsj4jt3SnJzGzwOKDyRjpI4mLgifSvmZl1YHgUX6c/ZeVRfGZmJSdpgaT1kjZIuqLG8omS7kzLH5I0o2LZlWn+eknzm7UpaWZq4yepzQkVy35P0uOS1kn6RrO6RxRQEXF1RCgirh5JO2Zmg65XPShJ44CbgFOA2cDZkmZXrbYY2BkRRwHLgKVp29nAImAOsAC4WdK4Jm0uBZZFxCxgZ2obSbOAK4H/EhFzgD9u9p64B2VmVgA9vMR3PLAhIjZGxGvACmBh1ToLga+n13cDJylreCGwIiJejYhNwIbUXs020zYnpjZIbZ6WXv8hcFNE7ASIiOeaFe6AMjMrgBEG1FRJayp+Lqho+jBgc8X0ljSPWutExF7geWBKg23rzZ8C7EptVO/raOBoST+Q9KCkBc3eEw8zNzMrgBEOdtgeEUP1mq4xL1pcp978Wp2bRutDljezgBOAw4HVko6JiF01toE6O6lJ0nWSQtL3aiyTpDvS8lWSDmi1XTMz66ktwBEV04cDz9RbR9J44CBgR4Nt683fDhyc2qje1xbgnoh4PV0uXE8WWHW1c4lvCfAcME/SvKplXwbOAVYDH42I19to18xsoPV4mPkPgVlpdN0EskEPK6vWWQmcl16fAdwXEZHmL0qj/GaSBcrD9dpM29yf2iC1eU96/S3gw+l4p5Jd8tvYqPCWAyoiXgQ+nyaXDM+XdA1wEbAW+EhEvNJqm2ZmlulVQKX7QRcD95J9bvWuiFgn6RpJp6bVbgWmSNoAXAZckbZdB9wFPA78b+CiiNhXr83U1uXAZamtKalt0ro/l/Q4WYj9aUT8vOF7kgVea1K37THgPcCZZDe/vpQK/FCzp0mkG3cXAEyfPv0/Pf300y3v28zydu/e3e8Sumry5Mn9LqHrJK1tcH8IgHe84x1x5plndryPm2++uek+xqK2RvGl1Lw8TX6VbLz8U8DJrTzqKCKWR8RQRAxNmzat3VrNzEqrh5f4xqy2h5lHxEpgHdkz+LYB8yJia7cLMzOzwdb2MHNJl5B9qhhgEvBCVysyMxtAZe4JdaqtHpSk88juOW0Fvg0cCHyuB3WZmQ2MHo/iG7Pa+RzU6WSjMXYAJ5ON3NsDfFLS0b0pz8xsMDig8loKqPS5p28CLwMLIuKJiNgMfIXsMuEXe1eimVn5OaDymgaUpPeTfcAKYGFErKlYvITsmU2nS5rbg/rMzAaCAyqvYUBJOhZYBUwEzoqI+yuXR8QO0mPZgRt6UqGZmQ2khqP4IuIx4JAm6yyh4skSZmbWvjL3hDrlp5mbmfVZ2S/VdcoBZWZWAA6oPAeUmVkBOKDy/I26ZmZWSO5BmZkVgHtQeQ4oM7MCcEDlOaDMzPrMo/hqc0CZmRWAAyrPgyTMzKyQ3IMyMysA96DyHFBmZgXggMpzQJmZFYADKs8BZWbWZx7FV5sDysysABxQeR7FZ2ZmheQelJlZAbgHleeAMhvDJk+e3O8Sumr37t39LqFvHFB5DigzswJwQOU5oMzM+syj+GrzIAkzMysk96DMzArAPag8B5SZWQE4oPIcUGZmBeCAynNAmZkVgAMqzwFlZtZnHsVXm0fxmZlZIbkHZWZWAO5B5TmgzMwKwAGV54AyMysAB1SeA8rMrAAcUHkeJGFmZoXkHpSZWZ95mHltDigzswJwQOU5oMzMCsABlTeigJI0FZgKbI+I7d0pycxs8Dig8kY6SOJi4In0r5mZWdf4Ep+ZWQG4B5U3ooCKiKuBq7tSiZnZgPIovtrcgzIzKwAHVJ4DysysABxQeQ4oM7MCcEDltTSKT9KpkkLSgw3WOVrSHknPSDqweyWamdkgarUHtRoI4DhJkyJiT411bgEmApdGxAvdKtDMbBC4B5XXUg8qInYC64AJwFD1cknnAh8GvhsRd9ZrR9IFktZIWrNt27YOSzYzK5fhUXyd/pRVOx/UXZ3+/UDlTEmHADcAe4ALGzUQEcsjYigihqZNm9ZWoWZmZdbLgJK0QNJ6SRskXVFj+URJd6blD0maUbHsyjR/vaT5zdqUNDO18ZPU5oSqfZ2RbhnlOjvV2gmoB9K/H6yafz0wDbguIp5soz0zM0t6FVCSxgE3AacAs4GzJc2uWm0xsDMijgKWAUvTtrOBRcAcYAFws6RxTdpcCiyLiFnAztT2cC1vBy4BHmrlPRlRD0rSXODjwPrhAzIzs0I5HtgQERsj4jVgBbCwap2FwNfT67uBk5Ql30JgRUS8GhGbgA2pvZptpm1OTG2Q2jytYj9/TtapqTWOIaflgIqIrcAm4FBJ75Z0ANnACAEXpiLNzKwDPbzEdxiwuWJ6S5pXc52I2As8D0xpsG29+VOAXamN/fYl6TjgiIj4p1beD2j/c1APADPJLvMdQdbtuyMi7muzHTMzqzDCwQ5TJa2pmF4eEcuHm66xflTvvs469ebX6tzUXV/SW8guHZ5fY3ld7QbUauA84BzgBGAX8CdttmFmZhW6MBpve0TUG3SwhaxDMexw4Jk662yRNB44CNjRZNta87cDB0san3pRw/PfDhwDfD8d5zuBlZJOjYjKYN1Pu1+3MXwf6hTgrcCVEfFsm22YmVmVHl7i+yEwK42um0A26GFl1ToryTofAGcA90VEpPmL0ii/mcAs4OF6baZt7k9tkNq8JyKej4ipETEjImYADwINwwna7EFFxI8lPQscSjYKY3mTTczMrI8iYq+ki4F7gXHA1yJinaRrgDURsRK4Fbhd0gayntOitO06SXcBjwN7gYsiYh9ArTbTLi8HVki6FvhRarsjbQWUpMnp5T7gUxHxRqc7NjOzX+jlB24jYhWwqmren1W83gOcWWfbLwBfaKXNNH8j2Si/RvWc0Erd7d6Duoqs97QsIh5pc1szM6ujlwE1VrUcUJJOBC4DNpIFlZmZdYkDKq9hQEmaA1xKNuJiPvA6cFZEvDQKtZmZDYQujOIrpWY9qPlkj6l4kWwE31XNRl2YmVn7HFB5DQMqIm4EbhylWszMzN7kb9Q1MysA96DyHFBmZgXggMpzQJmZ9ZkHSdTmgDIzKwAHVF67z+IzMzMbFe5BmZkVgHtQeQ4oM7MCcEDlOaDMzArAAZXngDIz6zOP4qvNAWVmVgAOqDyP4jMzs0JyD8rq2r17d79L6KrJkyc3X2mMKdtf3dk3hg+msp3LbnBAmZkVgAMqzwFlZlYADqg8B5SZWZ95FF9tHiRhZmaF5B6UmVkBuAeV54AyMysAB1SeA8rMrAAcUHkOKDOzAnBA5XmQhJmZFZJ7UGZmfeZh5rU5oMzMCsABleeAMjMrAAdUngPKzKwAHFB5DigzswJwQOV5FJ+ZmRVSRwEl6ROSbpN0Wpqem6av6G55ZmblNzyKr9Ofsuq0BzUXOA94b5o+Kk0v6EZRZmaDxgGV19E9qIg4Hzi/Yvo24LZuFGRmNojKHDSd8iAJM7MCcEDleZCEmZkVkntQZmYF4B5UngPKzKzPyj7YoVMtX+KTdJ2kkPS9Gssk6Y60fJWkA7pbpplZuXkUX14796CWAM8B8yTNq1r2ZeAcYDXw0Yh4vUv1mZkNBAdUXssBFREvAp9Pk0uG50u6BrgIWAt8JCJe6WqFZmY2kNq9B7Uc+CNgSNIZwGHAVcATwIKIeKHRxpIuAC4AmD59evvVmpmVVJl7Qp1qa5h5ROwFLk+TXwWWAU8BJ0fE9ha2Xx4RQxExNG3atHZrNTMrLV/iy2t7FF9ErJS0DphDuicVEVu7XpmZ2YAoe9B0qu2AknQJWTgBTAIaXtYzM7PmHFB5bV3ik3Qe8CVgK/Bt4EDgcz2oy8xsoPgSX147n4M6HbgV2AGcTDZybw/wSUlH96Y8MzMbVC0FVPrc0zeBl8lG6z0REZuBr5BdJvxi70o0Mys/96DymgaUpPcD30qTCyNiTcXiJcDzwOmS5vagPjOzgeCAymsYUJKOBVYBE4GzIuL+yuURsQNYmiZv6EmFZmYlN5JwKnNANRzFFxGPAYc0WWcJFU+WMDOz9pU5aDrl74MyM7NC8tdtmJkVgHtQee5BmZkVQC/vQUlaIGm9pA2SrqixfKKkO9PyhyTNqFh2ZZq/XtL8Zm1Kmpna+Elqc0Kaf5mkxyU9Kun/SDqyWd0OKDOzAuhVQEkaB9wEnALMBs6WNLtqtcXAzog4iuwZq0vTtrOBRWRPD1oA3CxpXJM2lwLLImIWsDO1DfAjYCgifgO4G7i+2XvigDIz67Mej+I7HtgQERsj4jVgBbCwap2FwNfT67uBk5Q1vBBYERGvRsQmYENqr2abaZsTUxukNk8DiIj7I+LlNP9B4PBmhTugzMwKoIcBdRiwuWJ6S5pXc530rRXPA1MabFtv/hRgV2qj3r4g61V9p1nhHiRhZjb2TZVU+RCF5RGxPL2ulWBRNV1vnXrza3VuGq3/ix1JHwOGgN+use5+HFBmZgUwwlF82yNiqM6yLcARFdOHA8/UWWeLpPHAQWTPXW20ba3524GDJY1Pvaj99qXssXn/A/jtiHi12UH5Ep+ZWQH08BLfD4FZaXTdBLJBDyur1lkJnJdenwHcFxGR5i9Ko/xmArOAh+u1mba5P7VBavOedHzHAf8TODUinmvlPXEPysysAEbYg6orIvZKuhi4FxgHfC0i1km6BlgTESvJvqnidkkbyHpOi9K26yTdBTwO7AUuioh9qd5cm2mXlwMrJF1LNnLv1jT/L4DJwD+kY/1pRJzaqHYHlJlZn7X6eaZORcQqsueqVs77s4rXe4Az62z7BeALrbSZ5m8kG+VXPX9eu3X7Ep+ZmRWSe1BmZgXQyx7UWOWAMjMrAAdUngPKzKwAHFB5DigzswJwQOU5oKyuyZMn97uErtq9e3e/S+i67GMn5eFf0lbJAWVm1me9HmY+VjmgzMwKwAGV54AyMysAB1SeA8rMrAAcUHkOKDOzAnBA5flRR2ZmVkjuQZmZ9ZlH8dXmgDIzKwAHVJ4DysysABxQeQ4oM7MCcEDleZCEmZkVkntQZmYF4B5UngPKzKzPPIqvNgczPwfBAAAJYElEQVSUmVkBOKDyHFBmZgXggMrzIAkzMyukjgJK0ick3SbptDQ9N01f0d3yzMwGw/B9qE5+yqrTHtRc4DzgvWn6qDS9oBtFmZkNGgdUXkf3oCLifOD8iunbgNu6UZCZ2aApe9B0yoMkzMwKwAGV54AyMysAB1SeR/GZmVkhuQdlZlYA7kHltdSDknSqpJD0YIN1jpa0R9Izkg7sXolmZuXnUXx5rfagVgMBHCdpUkTsqbHOLcBE4NKIeKFbBZqZlV3Zg6ZTLfWgImInsA6YAAxVL5d0LvBh4LsRcWdXKzQzGwDuQeW1M0hidfr3A5UzJR0C3ADsAS5s1ICkCyStkbRm27ZtbRVqZmaDpZ2AeiD9+8Gq+dcD04DrIuLJRg1ExPKIGIqIoWnTprWxazOzcnMPKq+dUXy5HpSkucDHgfXA0i7WZWY2UMocNJ1qOaAiYqukTcBMSe8GNpMNjBBwYUS81qMazcxKzwGV1+7noB4AZpJd5jsCmAPcERH3dbswM7NBUfZLdZ1q90kSw5f5zgGuAnYBf9LViszMzGi/BzUcUKekfy+LiGe7WI+Z2UByDyqvrYCKiB9LehY4FHgIWN6TqszMBowDKq+tgJI0Ob3cB3wqIt7ofklmZoPHAZXX7iW+q8h6T8si4pEe1GNmNnA8SKK2lgNK0onAZcBGsqAyM7MucUDlNQwoSXOAS4F3AvOB14GzIuKlUajNzMwGWLMe1HxgMfAi2Qi+qyJiTc+rMjMbMO5B5TUMqIi4EbhxlGoxMxtYDqg8f6OumVkBOKDyHFBmZn3mUXy1tfuoIzMzs1HhHpSZWQG4B5XngDIzKwAHVJ4DysysABxQeQ4oM7MCcEDlOaDMzPrMo/hq8yg+M7OSk7RA0npJGyRdUWP5REl3puUPSZpRsezKNH+9pPnN2pQ0M7Xxk9TmhGb7qMcBZWZWAMO9qE5+mrQ7DriJ7ItmZwNnS5pdtdpiYGdEHAUsA5ambWcDi4A5wALgZknjmrS5lOwbL2YBO1PbdffRiAPKzKwAehVQwPHAhojYGBGvASuAhVXrLAS+nl7fDZykrOGFwIqIeDUiNgEbUns120zbnJjaILV5WpN91OWAMjMrgB4G1GHA5orpLWlezXUiYi/wPDClwbb15k8BdqU2qvdVbx919W2QxNq1a7dLenoUdjUV2D4K+xlNZTsmH0/xle2YRvN4jmy2wtq1a++VNHUE+5gkqfKbJpZHxPL0ulaCRdV0vXXqza/VuWm0fqt17KdvARUR00ZjP5LWRMTQaOxrtJTtmHw8xVe2Yyra8UTEgh42vwU4omL6cOCZOutskTQeOAjY0WTbWvO3AwdLGp96SZXr19tHXb7EZ2ZWbj8EZqXRdRPIBj2srFpnJXBeen0GcF9ERJq/KI3AmwnMAh6u12ba5v7UBqnNe5rsoy5/DsrMrMQiYq+ki4F7gXHA1yJinaRrgDURsRK4Fbhd0gayXs2itO06SXcBjwN7gYsiYh9ArTbTLi8HVki6FvhRapt6+2hETQJszJN0QcW12FIo2zH5eIqvbMdUtuMpq9IHlJmZjU2+B2V9J2mqpPeMcBST9YCkT0i6TdJpaXpums49jcCs2xxQVgQXA0+kf61Y5pLd2H5vmj4qTfdy1JkZ4IAy64my9Aoj4vyIUERcnaZvS9Mn9LeyzrhHOLY4oApM0qmSQtKDDdY5WtIeSc9IOnA06+uWiLi68pdgSbhXWEzuEY4hHmZebKvJPml9nKRJEbGnxjq3ABOBSyPihVGtzmyMiYjzgfMrpm8DbutPNdZMqXpQkq5LPY7v1VgmSXek5askHdCPGtsRETuBdcAEIPepd0nnAh8GvhsRd45yedZASXuFZqOqVAEFLAGeA+ZJmle17MvAOWS9ko9GxOujXVyHVqd/P1A5U9IhwA3AHuDC0S7KzKzXShVQEfEi8Pk0uWR4fvrE9EXAWuAjEfFKH8rr1APp3w9Wzb8emAZcFxFPjm5JnStbL7eMfI6sKEr3Qd30EMLHgPcAZ5I94v1LZDesPxQRY+qJzJIOI3vI4rMR8c40by5ZcP0Y+I30fSxjgqS3k32nzDuAkyPiXyqWfYXsD4nVwPwx9odEafgcWVGUqgcFb37PyOVp8qtk39z4FNl/tDEVTgARsRXYBBwq6d3pL9ZbyB5df+FYCicoXy+3jCMty3SOynh+BknpelDDJP072dcUPwd8cCxdBqsm6TayobD/lexx9dcBd0TEx/pZV6fK1MuV9MvAz4HXgYNqjbSUdB/ZYJZFY2UwS1nOUVnPz8CIiNL9AJeQDc8Osm9tnNbvmkZ4PIvTsawCXgZ2Aof2u64RHtOp6Zi2AW+Q9RIP63ddHR7LY+lY5tZYdm5adm+/6xzUc1TW8zMIP6W7xCfpPLK/9LYC3wYOBD7X16JGbngk3ynAW4ErI+LZPtYzYpE94n8d2TebbgPmRXY5cywq5UjLEp2jUp6fQVCqgJJ0Otl3juwATia7Xr4H+KSko/tZ20hExI+B4UB6CBjzXxMg6RKyS7AAk4Cx/CHjUo20HFaic1TK8zMIShNQ6XNP3yS7BLYgIp6IiM3AV8iemPHFftY3EpImp5f7gE9FxBv9rGekStjLzf2FnkZafhxYDyztR1EjUbJzVLrzMyhKMUhC0vuBfyELolMi4v6KZYcAG4GDgN+KiH/tT5Wdk7QU+AywLCIu63c9I5F6uf8A7AJ+C9hNNlx+PDAn9RbHHEkbgZnArwKbyb5JdA5wUkTc18/a2lXGc1Sm8zNIxnwPStKxZIMHJgJnVYYTQETs4Bd/Id0wyuWNmKQTgcvIQvaqPpczImXu5bL/ZaRPk/3yu2Os/fIr8TkqxfkZNKXoQZWNpDnApcA7gflkQ2Q/FBFr+lrYCAxAL3cx8LfAd4ATgFeB94ylwSxlPkdlOD+DaMz3oEpqPtnQ8g+RXT8/eYyHU6l7ucmYHmk5AOdoTJ+fQeUelFmXSPoZcCjZSMsPjvXBLGXj8zP2uAdl1gVlG2lZNj4/Y5MDyqw7riL76/yvI+KRfhdjOT4/Y5Av8ZmNUBppeS/wU7Kny7/U55Ksgs/P2OWvfDfrQJ2Rlmf5l18x+PyUgy/xmXWmVCMtS8jnpwR8ic/MzArJPSgzMyskB5SZmRWSA8rMzArJAWVmZoXkgDIzs0JyQJmZWSE5oMzMrJAcUGZmVkgOKDMzK6T/DyU3Dbf/jJMbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,5.5])\n",
    "plt.ylim([5.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Identity Matrix $I$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0. 0. 0.]\n",
      " [0. 1. 0. 0. 0. 0.]\n",
      " [0. 0. 1. 0. 0. 0.]\n",
      " [0. 0. 0. 1. 0. 0.]\n",
      " [0. 0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 0. 1.]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(n)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurements\n",
    "\n",
    "Typical update rates:\n",
    "\n",
    "* Acceleration from IMU with `10Hz`\n",
    "* Position from GPS with `1Hz`\n",
    "\n",
    "Which means, that every 10th of an acceleration measurement, there is a new position measurement from GPS. The Kalman Filter can perfectly handle this unsynchronous measurement incoming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "m = 500 # Measurements\n",
    "\n",
    "sp= 1.0 # Sigma for position\n",
    "px= 0.0 # x Position\n",
    "py= 0.0 # y Position\n",
    "\n",
    "mpx = np.array(px+sp*np.random.randn(m))\n",
    "mpy = np.array(py+sp*np.random.randn(m))\n",
    "\n",
    "# Generate GPS Trigger\n",
    "GPS=np.ndarray(m,dtype='bool')\n",
    "GPS[0]=True\n",
    "# Less new position updates\n",
    "for i in range(1,m):\n",
    "    if i%10==0:\n",
    "        GPS[i]=True\n",
    "    else:\n",
    "        mpx[i]=mpx[i-1]\n",
    "        mpy[i]=mpy[i-1]\n",
    "        GPS[i]=False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Accelerations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Acceleration\n",
    "sa= 0.1 # Sigma for acceleration\n",
    "ax= 0.0 # in X\n",
    "ay= 0.0 # in Y\n",
    "\n",
    "mx = np.array(ax+sa*np.random.randn(m))\n",
    "my = np.array(ay+sa*np.random.randn(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 500)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mpx,mpy,mx,my))\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_m():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.subplot(211)\n",
    "    plt.step(range(m),mpx, label='$x$')\n",
    "    plt.step(range(m),mpy, label='$y$')\n",
    "    plt.ylabel(r'Position $m$')\n",
    "    plt.title('Measurements')\n",
    "    plt.ylim([-10, 10])\n",
    "    plt.legend(loc='best',prop={'size':18})\n",
    "\n",
    "    plt.subplot(212)\n",
    "    plt.step(range(m),mx, label='$a_x$')\n",
    "    plt.step(range(m),my, label='$a_y$')\n",
    "    plt.ylabel(r'Acceleration $m/s^2$')\n",
    "    plt.ylim([-1, 1])\n",
    "    plt.legend(loc='best',prop={'size':18})\n",
    "\n",
    "    plt.savefig('Kalman-Filter-CA-Measurements.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_m()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "xt = []\n",
    "yt = []\n",
    "dxt= []\n",
    "dyt= []\n",
    "ddxt=[]\n",
    "ddyt=[]\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "Kddy=[]\n",
    "\n",
    "\n",
    "def savestates(x, Z, P, K):\n",
    "    xt.append(float(x[0]))\n",
    "    yt.append(float(x[1]))\n",
    "    dxt.append(float(x[2]))\n",
    "    dyt.append(float(x[3]))\n",
    "    ddxt.append(float(x[4]))\n",
    "    ddyt.append(float(x[5]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))\n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Pddy.append(float(P[5,5]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))\n",
    "    Kddy.append(float(K[5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Kalman Filter\n",
    "\n",
    "![Kalman Filter](https://raw.github.com/balzer82/Kalman/master/Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "for filterstep in range(m):\n",
    "    \n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    x = A*x\n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = A*P*A.T + Q    \n",
    "    \n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # if there is a GPS Measurement\n",
    "    if GPS[filterstep]:\n",
    "        # Compute the Kalman Gain\n",
    "        S = H*P*H.T + R\n",
    "        K = (P*H.T) * np.linalg.pinv(S)\n",
    "    \n",
    "        \n",
    "        # Update the estimate via z\n",
    "        Z = measurements[:,filterstep].reshape(H.shape[0],1)\n",
    "        y = Z - (H*x)                            # Innovation or Residual\n",
    "        x = x + (K*y)\n",
    "        \n",
    "        # Update the error covariance\n",
    "        P = (I - (K*H))*P\n",
    "\n",
    "   \n",
    "    \n",
    "    # Save states for Plotting\n",
    "    savestates(x, Z, P, K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Thats it.\n",
    "\n",
    "![Job done](http://www.troll.me/images/the-chuck-norris/job-done.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Let's take a look at the filter performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Uncertainty $P$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_P():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.subplot(211)\n",
    "    plt.plot(range(len(measurements[0])),Px, label='$x$')\n",
    "    plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
    "    plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.subplot(212)\n",
    "    plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n",
    "    plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_P()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_P2():\n",
    "    fig = plt.figure(figsize=(6, 6))\n",
    "    im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "    plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
    "    ylocs, ylabels = plt.yticks()\n",
    "    # set the locations of the yticks\n",
    "    plt.yticks(np.arange(7))\n",
    "    # set the locations and labels of the yticks\n",
    "    plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "    xlocs, xlabels = plt.xticks()\n",
    "    # set the locations of the yticks\n",
    "    plt.xticks(np.arange(7))\n",
    "    # set the locations and labels of the yticks\n",
    "    plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "    plt.xlim([-0.5,5.5])\n",
    "    plt.ylim([5.5, -0.5])\n",
    "\n",
    "    from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "    divider = make_axes_locatable(plt.gca())\n",
    "    cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "    plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('Kalman-Filter-CA-CovarianceMatrix.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_P2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_K():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "    plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "    plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "    plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "    plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
    "    plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "    plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_K()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_x():\n",
    "    \n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "\n",
    "    plt.subplot(311)\n",
    "    plt.step(range(len(measurements[0])),ddxt, label='$\\ddot x$')\n",
    "    plt.step(range(len(measurements[0])),ddyt, label='$\\ddot y$')\n",
    "\n",
    "    plt.title('Estimate (Elements from State Vector $x$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel(r'Acceleration $m/s^2$')\n",
    "    plt.ylim([-.1,.1])\n",
    "\n",
    "    plt.subplot(312)\n",
    "    plt.step(range(len(measurements[0])),dxt, label='$\\dot x$')\n",
    "    plt.step(range(len(measurements[0])),dyt, label='$\\dot y$')\n",
    "\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel(r'Velocity $m/s$')\n",
    "    plt.ylim([-1,1])\n",
    "\n",
    "    plt.subplot(313)\n",
    "    plt.step(range(len(measurements[0])),xt, label='$x$')\n",
    "    plt.step(range(len(measurements[0])),yt, label='$y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel(r'Position $m$')\n",
    "    plt.ylim([-1,1])\n",
    "\n",
    "    plt.savefig('Kalman-Filter-CA-StateEstimated.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_x()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_xy():\n",
    "\n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "    plt.plot(xt,yt, label='State',alpha=0.5)\n",
    "    plt.scatter(xt[0],yt[0], s=100, label='Start', c='g')\n",
    "    plt.scatter(xt[-1],yt[-1], s=100, label='Goal', c='r')\n",
    "\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.title('Position')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlim([-5, 5])\n",
    "    plt.ylim([-5, 5])\n",
    "    plt.savefig('Kalman-Filter-CA-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_xy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![Nice](http://www.troll.me/images/stifler-thumbs-up/nice.jpg)\n",
    "\n",
    "It works pretty well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As you can see, good idea to measure the position as well as the acceleration to try to estimate the position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your drifted 11m from origin.\n"
     ]
    }
   ],
   "source": [
    "dist=np.cumsum(np.sqrt(np.diff(xt)**2 + np.diff(yt)**2))\n",
    "print('Your drifted %dm from origin.' % dist[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "To use this notebook as a presentation type:\n",
    "\n",
    "`jupyter-nbconvert --to slides Kalman-Filter-CA-2.ipynb --reveal-prefix=reveal.js --post serve` \n",
    "\n",
    "Questions? [@Balzer82](https://twitter.com/balzer82)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}