Fixed bug, some clean up.

I was plotting velocity, not position of filter in one plot.

Also, wrote a initialize_filter function so all plot start
with the filter initialized to the same value.

15_Adaptive_Filtering/Adaptive_Filtering.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:4194c0e0a4f144a3a622c419fc2d60daaf82f71101e32e53b614d64e571f872d"
+  "signature": "sha256:9db8ce6c5109bbbdc28040752dc575e21e34a00bf0cd0ba8ac47e8b7cf7b2a20"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -262,7 +262,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f7ee9cb3240>"
+        "<IPython.core.display.HTML at 0x7f2c1fcf0208>"
        ]
       }
      ],
@@ -280,6 +280,8 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
+      "**author's note: this chapter is in heavy development - read it if you want, but there are bugs in the sw, a lot of stuff if being revised, text may not match the plots, etc**\n",
+      "\n",
       "So far we have considered the problem of tracking objects that are well behaved in relation to our process model. For example, we can use a constant velocity model track an object moving in a straight line. So long as the object moves in a straight line at a reasonably constant speed, or varies it's track and/or velocity very slowly this filter will perform very well. Suppose instead that we are trying to track a manuevering target, by which I mean an object with control inputs, such as a car along a road, an aircraft in flight, and so on. In these situations the filters perform quite poorly. Alternatively, consider a situation such as tracking a sailboat in the ocean. Even if we model the control inputs we have no way to model the wind or the ocean currents. \n",
       "\n",
       "A first order approach to this problem is just to make the process noise $\\mathbf{Q}$ larger to account for the unpredictability of the system dynamics. While this can *work* in the sense of providing a non-diverging filter, the result is typically far from optimal. The larger $\\mathbf{Q}$ results in the filter giving more emphasis to the noise in the measurements. We will see an example of this shortly.\n",
@@ -442,7 +444,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd826828>"
+        "<matplotlib.figure.Figure at 0x7f2c02e6a5f8>"
        ]
       }
      ],
@@ -471,9 +473,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd5304a8>"
+        "<matplotlib.figure.Figure at 0x7f2c02e59748>"
        ]
       }
      ],
@@ -504,7 +506,16 @@
       "                    [0,  1]], dtype=float)\n",
       "cvfilter.H = array([[1, 0]], dtype=float)\n",
       "\n",
-      "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)"
+      "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
+      "\n",
+      "\n",
+      "def initialize_filter(kf):\n",
+      "    \"\"\" helper function - we will be reinitialing the filter\n",
+      "    many times.\n",
+      "    \"\"\"\n",
+      "    \n",
+      "    kf.x.fill(0)\n",
+      "    kf.P = np.eye(kf.x.shape[0]) * .1"
      ],
      "language": "python",
      "metadata": {},
@@ -546,7 +557,7 @@
       "kxs, _, _, _ = cvfilter.batch_filter(z_xs)\n",
       "t = np.arange(0, len(z_xs) * dt, dt)\n",
       "plt.plot(t, xs)\n",
-      "plt.plot(t, kxs[:,1], ls=':')\n",
+      "plt.plot(t, kxs[:,0], ls=':')\n",
       "plt.xlabel('time (sec)')\n",
       "plt.show()"
      ],
@@ -556,9 +567,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd5632b0>"
+        "<matplotlib.figure.Figure at 0x7f2c02c45a58>"
        ]
       }
      ],
@@ -576,7 +587,7 @@
      "collapsed": false,
      "input": [
       "# reinitialize filter\n",
-      "cvfilter.x = array([0., 0.])\n",
+      "initialize_filter(cvfilter)\n",
       "\n",
       "pos2, zs2 = generate_data(120, noise_factor)\n",
       "xs2 = pos2[:,0]\n",
@@ -596,9 +607,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd530438>"
+        "<matplotlib.figure.Figure at 0x7f2c02d79128>"
        ]
       }
      ],
@@ -615,10 +626,11 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
+      "# reinitialize filter\n",
+      "initialize_filter(cvfilter)\n",
       "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=2.0) # var was 0.02\n",
       "\n",
       "# recompute track\n",
-      "cvfilter.x = array([0., 0.])\n",
       "kxs2, _, _, _ = cvfilter.batch_filter(z_xs2)\n",
       "\n",
       "plt.plot(t, xs2, label='track')\n",
@@ -633,9 +645,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd5307f0>"
+        "<matplotlib.figure.Figure at 0x7f2c02d5e9b0>"
        ]
       }
      ],
@@ -652,6 +664,8 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
+      "# reinitialize filter\n",
+      "initialize_filter(cvfilter)\n",
       "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=20.0) # var was 0.02\n",
       "\n",
       "# recompute track\n",
@@ -670,9 +684,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd2f86d8>"
+        "<matplotlib.figure.Figure at 0x7f2c02da3160>"
        ]
       }
      ],
@@ -722,9 +736,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxkAAAGdCAYAAAB+Xb4YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd262710>"
+        "<matplotlib.figure.Figure at 0x7f2c02e2d0b8>"
        ]
       }
      ],
@@ -775,7 +789,7 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAxYAAAGaCAYAAACSU9UtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ec91c4550>"
+        "<matplotlib.figure.Figure at 0x7f2c02b50eb8>"
        ]
       }
      ],
@@ -797,7 +811,7 @@
       "z_xs2 = zs2[:,0]\n",
       "\n",
       "# reinitialize filter\n",
-      "cvfilter.x = array([0., 0.])\n",
+      "initialize_filter(cvfilter)\n",
       "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
       "xs = []\n",
       "res = []\n",
@@ -824,13 +838,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ebfeab630>"
+        "<matplotlib.figure.Figure at 0x7f2c02c55208>"
        ]
       }
      ],
-     "prompt_number": 19
+     "prompt_number": 14
     },
     {
      "cell_type": "markdown",
@@ -892,7 +906,9 @@
       "from filterpy.common import dot3\n",
       "from numpy.linalg import inv\n",
       "\n",
-      "cvfilter.x = array([0., 0.])\n",
+      "# reinitialize filter\n",
+      "initialize_filter(cvfilter)\n",
+      "\n",
       "cvfilter.R = np.eye(1)*0.2\n",
       "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
       "epss = []\n",
@@ -915,13 +931,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd2d3588>"
+        "<matplotlib.figure.Figure at 0x7f2c02be97b8>"
        ]
       }
      ],
-     "prompt_number": 20
+     "prompt_number": 15
     },
     {
      "cell_type": "markdown",
@@ -941,7 +957,8 @@
       "from filterpy.common import dot3\n",
       "from numpy.linalg import inv\n",
       "\n",
-      "cvfilter.x = array([0., 0.])\n",
+      "# reinitialize filter\n",
+      "initialize_filter(cvfilter)\n",
       "cvfilter.R = np.eye(1)*0.2\n",
       "\n",
       "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
@@ -981,13 +998,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ebfde1240>"
+        "<matplotlib.figure.Figure at 0x7f2bfaf266a0>"
        ]
       }
      ],
-     "prompt_number": 24
+     "prompt_number": 16
     },
     {
      "cell_type": "markdown",
@@ -1029,7 +1046,13 @@
       "\n",
       "\n",
       "def zarchan_adaptive_filter(Q_scale_factor, std_scale):\n",
-      "    cvfilter.x = array([0., 0.])\n",
+      "    pos2, zs2 = generate_data(120, noise_factor=0.2)\n",
+      "    xs2 = pos2[:,0]\n",
+      "    z_xs2 = zs2[:,0]\n",
+      "\n",
+      "    # reinitialize filter\n",
+      "    initialize_filter(cvfilter)\n",
+      "\n",
       "    cvfilter.R = np.eye(1)*0.2\n",
       "\n",
       "    phi = 0.02\n",
@@ -1069,6 +1092,7 @@
       "    plt.xlabel('time (sec)')\n",
       "    plt.title('velocity')\n",
       "    plt.show()\n",
+      "\n",
       "    \n",
       "zarchan_adaptive_filter(1000, 2)"
      ],
@@ -1078,13 +1102,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd55a748>"
+        "<matplotlib.figure.Figure at 0x7f2bfaebdcc0>"
        ]
       }
      ],
-     "prompt_number": 65
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -1106,21 +1130,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ec91cb630>"
+        "<matplotlib.figure.Figure at 0x7f2bfb18b6d8>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd2b8048>"
+        "<matplotlib.figure.Figure at 0x7f2bfb18b4e0>"
        ]
       }
      ],
-     "prompt_number": 63
+     "prompt_number": 18
     },
     {
      "cell_type": "markdown",
@@ -1142,21 +1166,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd4fd668>"
+        "<matplotlib.figure.Figure at 0x7f2c02e07dd8>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd4fdeb8>"
+        "<matplotlib.figure.Figure at 0x7f2c02e07128>"
        ]
       }
      ],
-     "prompt_number": 66
+     "prompt_number": 19
     },
     {
      "cell_type": "markdown",
@@ -1183,45 +1207,45 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ebfdb44e0>"
+        "<matplotlib.figure.Figure at 0x7f2bfaddca20>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ec91d2400>"
+        "<matplotlib.figure.Figure at 0x7f2bfaddc780>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ebfccf390>"
+        "<matplotlib.figure.Figure at 0x7f2bfb155a20>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd2d8e10>"
+        "<matplotlib.figure.Figure at 0x7f2c02e046d8>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ecd2d8048>"
+        "<matplotlib.figure.Figure at 0x7f2c02c41f28>"
        ]
       }
      ],
-     "prompt_number": 68
+     "prompt_number": 20
     },
     {
      "cell_type": "markdown",
@@ -1365,13 +1389,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7ec9170be0>"
+        "<matplotlib.figure.Figure at 0x7f2bf9490240>"
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 21
     },
     {
      "cell_type": "markdown",
@@ -1441,7 +1465,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 17
+     "prompt_number": 21
     },
     {
      "cell_type": "heading",