Added animation of multivariate tracking.

Chapter06_Multivariate_Kalman_Filter/Multivariate_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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@@ -257,13 +257,13 @@
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@@ -391,11 +391,11 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f1d42a7f0>"
+        "<matplotlib.figure.Figure at 0x7ff131bb32e8>"
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@@ -443,7 +443,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
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+     "prompt_number": 3
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      "cell_type": "markdown",
@@ -465,7 +465,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
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+     "prompt_number": 4
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      "cell_type": "markdown",
@@ -483,7 +483,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
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@@ -502,7 +502,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
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     {
      "cell_type": "markdown",
@@ -528,7 +528,7 @@
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@@ -559,11 +559,11 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc2e9ac8>"
+        "<matplotlib.figure.Figure at 0x7ff1107cb710>"
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 8
     },
     {
      "cell_type": "markdown",
@@ -613,11 +613,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc2aa080>"
+        "<matplotlib.figure.Figure at 0x7ff1108b5a90>"
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 9
     },
     {
      "cell_type": "markdown",
@@ -711,11 +711,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc0637b8>"
+        "<matplotlib.figure.Figure at 0x7ff110a479b0>"
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 10
     },
     {
      "cell_type": "markdown",
@@ -738,11 +738,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc1e1fd0>"
+        "<matplotlib.figure.Figure at 0x7ff1107f6d68>"
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 11
     },
     {
      "cell_type": "markdown",
@@ -765,11 +765,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc169898>"
+        "<matplotlib.figure.Figure at 0x7ff1107a5c50>"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 12
     },
     {
      "cell_type": "markdown",
@@ -796,11 +796,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc20f828>"
+        "<matplotlib.figure.Figure at 0x7ff1108c8b38>"
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -861,11 +861,11 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc063fd0>"
+        "<matplotlib.figure.Figure at 0x7ff11084a358>"
        ]
       }
      ],
-     "prompt_number": 15
+     "prompt_number": 14
     },
     {
      "cell_type": "heading",
@@ -991,7 +991,7 @@
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 15
     },
     {
      "cell_type": "markdown",
@@ -1020,7 +1020,7 @@
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 16
     },
     {
      "cell_type": "markdown",
@@ -1049,7 +1049,7 @@
        ]
       }
      ],
-     "prompt_number": 18
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -1093,7 +1093,7 @@
        ]
       }
      ],
-     "prompt_number": 19
+     "prompt_number": 18
     },
     {
      "cell_type": "markdown",
@@ -1126,7 +1126,7 @@
        ]
       }
      ],
-     "prompt_number": 20
+     "prompt_number": 19
     },
     {
      "cell_type": "markdown",
@@ -1161,7 +1161,7 @@
        ]
       }
      ],
-     "prompt_number": 21
+     "prompt_number": 20
     },
     {
      "cell_type": "markdown",
@@ -1314,7 +1314,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 22
+     "prompt_number": 21
     },
     {
      "cell_type": "markdown",
@@ -1338,7 +1338,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 23
+     "prompt_number": 22
     },
     {
      "cell_type": "heading",
@@ -1680,7 +1680,7 @@
        ]
       }
      ],
-     "prompt_number": 24
+     "prompt_number": 23
     },
     {
      "cell_type": "heading",
@@ -1769,7 +1769,7 @@
        ]
       }
      ],
-     "prompt_number": 25
+     "prompt_number": 24
     },
     {
      "cell_type": "markdown",
@@ -1794,7 +1794,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 28
+     "prompt_number": 25
     },
     {
      "cell_type": "markdown",
@@ -1889,7 +1889,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 36
+     "prompt_number": 26
     },
     {
      "cell_type": "markdown",
@@ -1962,7 +1962,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 37
+     "prompt_number": 27
     },
     {
      "cell_type": "markdown",
@@ -1983,9 +1983,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc1ecf60>"
+        "<matplotlib.figure.Figure at 0x7ff110673cf8>"
        ]
       },
       {
@@ -1993,11 +1993,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc0af550>"
+        "<matplotlib.figure.Figure at 0x7ff131bb32e8>"
        ]
       }
      ],
-     "prompt_number": 39
+     "prompt_number": 28
     },
     {
      "cell_type": "markdown",
@@ -2007,8 +2007,13 @@
       "\n",
       "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n",
       "\n",
-      "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that.\n",
-      "\n",
+      "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that."
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
       "In the previous chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filter with this code merely by altering are assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter."
      ]
     },
@@ -2068,7 +2073,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 40
+     "prompt_number": 29
     },
     {
      "cell_type": "markdown",
@@ -2097,7 +2102,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 41
+     "prompt_number": 30
     },
     {
      "cell_type": "markdown",
@@ -2155,9 +2160,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efbffb978>"
+        "<matplotlib.figure.Figure at 0x7ff11065dac8>"
        ]
       },
       {
@@ -2165,11 +2170,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efbfb8d68>"
+        "<matplotlib.figure.Figure at 0x7ff110945b38>"
        ]
       }
      ],
-     "prompt_number": 42
+     "prompt_number": 31
     },
     {
      "cell_type": "markdown",
@@ -2331,7 +2336,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 43
+     "prompt_number": 32
     },
     {
      "cell_type": "markdown",
@@ -2397,13 +2402,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc12d8d0>"
+        "<matplotlib.figure.Figure at 0x7ff1108ba6a0>"
        ]
       }
      ],
-     "prompt_number": 45
+     "prompt_number": 33
     },
     {
      "cell_type": "markdown",
@@ -2457,21 +2462,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc126278>"
+        "<matplotlib.figure.Figure at 0x7ff11082ce80>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc31bef0>"
+        "<matplotlib.figure.Figure at 0x7ff110a321d0>"
        ]
       }
      ],
-     "prompt_number": 46
+     "prompt_number": 34
     },
     {
      "cell_type": "markdown",
@@ -2580,13 +2585,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc126160>"
+        "<matplotlib.figure.Figure at 0x7ff1107f8748>"
        ]
       }
      ],
-     "prompt_number": 47
+     "prompt_number": 35
     },
     {
      "cell_type": "markdown",
@@ -2652,11 +2657,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc1354e0>"
+        "<matplotlib.figure.Figure at 0x7ff1107d3c18>"
        ]
       }
      ],
-     "prompt_number": 48
+     "prompt_number": 36
     },
     {
      "cell_type": "markdown",
@@ -2681,11 +2686,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc257668>"
+        "<matplotlib.figure.Figure at 0x7ff1108560b8>"
        ]
       }
      ],
-     "prompt_number": 49
+     "prompt_number": 37
     },
     {
      "cell_type": "markdown",
@@ -2745,7 +2750,17 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ff1108b9f98>"
+       ]
+      }
+     ],
+     "prompt_number": 38
     },
     {
      "cell_type": "markdown",
@@ -2764,7 +2779,17 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ff1107c7b00>"
+       ]
+      }
+     ],
+     "prompt_number": 39
     },
     {
      "cell_type": "markdown",
@@ -2788,7 +2813,17 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ff11072f1d0>"
+       ]
+      }
+     ],
+     "prompt_number": 40
     },
     {
      "cell_type": "markdown",
@@ -2809,7 +2844,17 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ff110a75dd8>"
+       ]
+      }
+     ],
+     "prompt_number": 41
     },
     {
      "cell_type": "markdown",
@@ -2875,21 +2920,29 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efc0ff780>"
+        "<matplotlib.figure.Figure at 0x7ff11092be80>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7efa69aa20>"
+        "<matplotlib.figure.Figure at 0x7ff110886208>"
        ]
       }
      ],
-     "prompt_number": 50
+     "prompt_number": 42
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "If you are viewing this in IPython Notebook or on the web, here is an animation of the filter filtering the data. I've tuned the filter parameters such that it is easy to see a change in $\\mathbf{P}$ as the filter progresses.\n",
+      "<img src='track1.gif'>"
+     ]
     },
     {
      "cell_type": "markdown",
@@ -2946,7 +2999,17 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAGDCAYAAADOPB2zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ff10ee2b3c8>"
+       ]
+      }
+     ],
+     "prompt_number": 43
     },
     {
      "cell_type": "markdown",

Chapter06_Multivariate_Kalman_Filter/animations.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:f0b53bc4a8dfc9063521f2cf75e9cf39f93cd7c877479e9bfd623e3b385146f2"
+  "signature": "sha256:85d4be8ca8ef18fbc963a1985da4ce5a2a0c556da762a2d3ebd4ddf2b7e255ba"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -127,12 +127,12 @@
         "    div.output_subarea.output_text.output_pyout {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    div.output_subarea.output_stream.output_stdout.output_text {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    code{\n",
         "      font-size: 70%;\n",
@@ -243,24 +243,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 2,
+       "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f1407a69c18>"
+        "<IPython.core.display.HTML at 0x7f3e158449e8>"
        ]
       }
      ],
-     "prompt_number": 2
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from filterpy.common import Q_DWPA"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 3
+     "prompt_number": 1
     },
     {
      "cell_type": "code",
@@ -364,7 +353,7 @@
       "\n",
       "fig = plt.figure()\n",
       "#ax = fig.add_subplot(111, projection='3d')\n",
-      "animate('ellipse.gif', ellipse_animate, 30, 125)    "
+      "animate('ellipse.gif', ellipse_animate, 30, 125)"
      ],
      "language": "python",
      "metadata": {},
@@ -386,10 +375,11 @@
       "import matplotlib.pyplot as plt\n",
       "from matplotlib import cm\n",
       "from mpl_toolkits.mplot3d import Axes3D\n",
-      "\n",
+      "from gif_animate import animate\n",
+      "import numpy.random as random\n",
       "from DogSensor import DogSensor\n",
       "import stats\n",
-      "\n",
+      "from filterpy.common import Q_DWPA\n",
       "from filterpy.kalman import KalmanFilter\n",
       "\n",
       "def dog_tracking_filter(R,Q=0,cov=1.):\n",
@@ -402,66 +392,65 @@
       "    dog_filter.R *= R                 # measurement uncertainty\n",
       "    dog_filter.P *= cov               # covariance matrix \n",
       "    if np.isscalar(Q):\n",
-      "        dog_filter.Q = Q_DWPA(2, sigma=Q)\n",
+      "        dog_filter.Q = Q_DWPA(2, var=Q)\n",
       "    else:\n",
       "        dog_filter.Q = Q\n",
       "    return dog_filter\n",
       "\n",
-      "def plot_track_ellipses(noise, count, R, Q=0, P=20., plot_P=True, title='Kalman Filter'):\n",
-      "    dog = DogSensor(velocity=1, noise=noise)\n",
-      "    f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
       "\n",
-      "    ps = []\n",
-      "    zs = []\n",
-      "    cov = []\n",
-      "    for t in range (count):\n",
-      "        z = dog.sense()\n",
-      "        f.update (z)\n",
-      "        ps.append (f.x[0,0])\n",
-      "        cov.append(f.P)\n",
-      "        zs.append(z)\n",
-      "        f.predict()\n",
-      "\n",
-      "    p0, = plt.plot([0,count],[0,count],'g', label='actual')\n",
-      "    p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed', label='measurement')\n",
-      "    p2, = plt.plot(range(1,count+1),ps, c='b', label='filter')\n",
-      "    plt.legend(loc='best')\n",
-      "    plt.title(title)\n",
-      "\n",
-      "    for i,p in enumerate(cov):\n",
-      "        stats.plot_covariance_ellipse ((i+1, ps[i]), cov=p, axis_equal=False, \n",
+      "R = 5\n",
+      "Q = .01\n",
+      "noise = 2.\n",
+      "P=20.\n",
+      "dog = DogSensor(velocity=1, noise=noise)\n",
+      "f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
+      "random.seed(200)\n",
+      "zs = []\n",
+      "xs = []\n",
+      "def animate_track(frame):\n",
+      "    if frame > 30: return\n",
+      "    \n",
+      "    plt.gca().set_xlim(-100,100)\n",
+      "    if frame == 0:\n",
+      "        stats.plot_covariance_ellipse ((0, f.x[0,0]), cov=f.P, axis_equal=True, \n",
       "                                       facecolor='g', edgecolor=None, alpha=0.2)\n",
+      "        xs.append (f.x[0,0])\n",
+      "        \n",
+      "    z = dog.sense()\n",
+      "    zs.append(z)\n",
+      "    f.update(z)\n",
+      "    xs.append (f.x[0,0])\n",
+      "    \n",
+      "    stats.plot_covariance_ellipse ((frame+1, f.x[0,0]), cov=f.P, axis_equal=True, \n",
+      "                                       facecolor='g', edgecolor=None, alpha=0.5,\n",
+      "                                       xlim=(-5,30), ylim=(-5,30))\n",
+      "    \n",
+      "    plt.plot(zs, c='r', linestyle='dashed')\n",
+      "    plt.plot(xs, c='b')\n",
+      "    f.predict()\n",
       "\n",
-      "        if i == len(cov)-1:\n",
-      "            s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n",
-      "            plt.text (20,10,s,fontsize=18)\n",
-      "            s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n",
-      "            plt.text (20,5,s,fontsize=18)\n",
-      "    #plt.xlim((-10,30))\n",
-      "    #plt.ylim((-10,40))\n",
-      "    plt.show()\n",
-      "\n",
-      "\n",
-      "plot_track_ellipses (noise=5, R=5, Q=.2, count=20, title='R = 5')\n",
-      "plot_track_ellipses (noise=5, R=.5, Q=.2, count=20, title='R = 0.5')"
+      "animate('track1.gif', animate_track, 37, 200, figsize=(10.5, 10.5))"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
-       "ename": "TypeError",
-       "evalue": "Q_DWPA() got an unexpected keyword argument 'sigma'",
-       "output_type": "pyerr",
-       "traceback": [
-        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-        "\u001b[1;32m<ipython-input-5-852864bed579>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     60\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     61\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 62\u001b[1;33m \u001b[0mplot_track_ellipses\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnoise\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mR\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m.2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcount\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m20\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'R = 5'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     63\u001b[0m \u001b[0mplot_track_ellipses\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnoise\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mR\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m.2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcount\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m20\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'R = 0.5'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-        "\u001b[1;32m<ipython-input-5-852864bed579>\u001b[0m in \u001b[0;36mplot_track_ellipses\u001b[1;34m(noise, count, R, Q, P, plot_P, title)\u001b[0m\n\u001b[0;32m     27\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mplot_track_ellipses\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnoise\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcount\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mP\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m20.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mplot_P\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'Kalman Filter'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     28\u001b[0m     \u001b[0mdog\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mDogSensor\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvelocity\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnoise\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnoise\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 29\u001b[1;33m     \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdog_tracking_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mR\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mQ\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcov\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mP\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     30\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     31\u001b[0m     \u001b[0mps\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-        "\u001b[1;32m<ipython-input-5-852864bed579>\u001b[0m in \u001b[0;36mdog_tracking_filter\u001b[1;34m(R, Q, cov)\u001b[0m\n\u001b[0;32m     20\u001b[0m     \u001b[0mdog_filter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mP\u001b[0m \u001b[1;33m*=\u001b[0m \u001b[0mcov\u001b[0m               \u001b[1;31m# covariance matrix\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     21\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0misscalar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 22\u001b[1;33m         \u001b[0mdog_filter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mQ\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mQ_DWPA\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mQ\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     23\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     24\u001b[0m         \u001b[0mdog_filter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mQ\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-        "\u001b[1;31mTypeError\u001b[0m: Q_DWPA() got an unexpected keyword argument 'sigma'"
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAm8AAAJxCAYAAAAU6lVjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f3df4261d30>"
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<img src='track1.gif'>"
+     ]
     },
     {
      "cell_type": "markdown",

README.md

@@ -1,6 +1,6 @@
 Introductory textbook for Kalman filters and Bayesian filters. All code is written in Python, and the book itself is written in Ipython Notebook so that you can run and modify the code in the book in place, seeing the results inside the book. What better way to learn?
 
-![alt tag](https://raw.githubusercontent.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/Chapter05_Kalman_Filters/dog_track.gif)
+![alt tag](https://raw.githubusercontent.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/Chapter06_Multivariate_Kalman_Filter/track1.gif)
 
 
 Reading Online

code/stats.py

@@ -226,7 +226,7 @@ def is_inside_ellipse(x,y, ex, ey, orientation, width, height):
 def plot_covariance_ellipse(mean, cov=None, variance = 1.0,
              ellipse=None, title=None, axis_equal=True,
              facecolor='none', edgecolor='#004080',
-             alpha=1.0):
+             alpha=1.0, xlim=None, ylim=None):
     """ plots the covariance ellipse where
 
     mean is a (x,y) tuple for the mean of the covariance (center of ellipse)
@@ -277,6 +277,11 @@ def plot_covariance_ellipse(mean, cov=None, variance = 1.0,
                     lw=2)
         ax.add_patch(e)
     plt.scatter(mean[0], mean[1], marker='+') # mark the center
+    if xlim is not None:
+        ax.set_xlim(xlim)
+
+    if ylim is not None:
+        ax.set_ylim(ylim)
 
 
 def _to_cov(x,n):