Fixes for GitHub issue #65.

Minor wording changes to clarify meaning.

06-Multivariate-Kalman-Filters.ipynb

@@ -369,9 +369,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAADlCAYAAAB3YbDsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef5568128>"
+       "<matplotlib.figure.Figure at 0x4b2b198>"
       ]
      },
      "metadata": {},
@@ -862,9 +862,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef83d8860>"
+       "<matplotlib.figure.Figure at 0x879d7f0>"
       ]
      },
      "metadata": {},
@@ -1027,9 +1027,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef8364da0>"
+       "<matplotlib.figure.Figure at 0x87b1198>"
       ]
      },
      "metadata": {},
@@ -1368,9 +1368,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef9419da0>"
+       "<matplotlib.figure.Figure at 0x88bc240>"
       ]
      },
      "metadata": {},
@@ -1378,9 +1378,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef95211d0>"
+       "<matplotlib.figure.Figure at 0x9950f98>"
       ]
      },
      "metadata": {},
@@ -1429,9 +1429,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef9627e48>"
+       "<matplotlib.figure.Figure at 0x7d5fc50>"
       ]
      },
      "metadata": {},
@@ -1527,9 +1527,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef83f5fd0>"
+       "<matplotlib.figure.Figure at 0x7b45eb8>"
       ]
      },
      "metadata": {},
@@ -1576,9 +1576,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef7aa5d30>"
+       "<matplotlib.figure.Figure at 0x7d00cf8>"
       ]
      },
      "metadata": {},
@@ -1640,9 +1640,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef9577278>"
+       "<matplotlib.figure.Figure at 0x9a1a0b8>"
       ]
      },
      "metadata": {},
@@ -1707,7 +1707,7 @@
     "\n",
     "$K$ is the *Kalman gain*, and it is a real number between 0 and 1. Ensure you understand how it selects a mean somewhere between the prediction and measurement. The Kalman gain is a *percentage* or *ratio* - if K is .9 it takes 90% of the measurement and 10% of the prediction. \n",
     "\n",
-    "For the multivariate Kalman filter $\\mathbf{K}$ is a vector, not a scalar. Here is the equation again: $\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of expressing division. Division is not defined for matrices, but it is useful to think of it in this way. So we can read the equation for $\\textbf{K}$ as meaning\n",
+    "For the multivariate Kalman filter $\\mathbf{K}$ is a vector, not a scalar. Here is the equation again: $\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of finding the reciprocal. Division is not defined for matrices, but it is useful to think of it in this way. So we can read the equation for $\\textbf{K}$ as meaning\n",
     "\n",
     "$$\\begin{aligned} \\mathbf{K} &\\approx \\frac{\\mathbf{\\bar{P}}\\mathbf{H}^\\mathsf{T}}{\\mathbf{S}} \\\\\n",
     "\\mathbf{K} &\\approx \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf{H}^\\mathsf{T}\n",
@@ -1765,7 +1765,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 28,
    "metadata": {
     "collapsed": false
    },
@@ -1785,16 +1785,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cefb0cc978>"
+       "<matplotlib.figure.Figure at 0x9a6e390>"
       ]
      },
      "metadata": {},
@@ -1802,9 +1802,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cef95a4b00>"
+       "<matplotlib.figure.Figure at 0x9a8a8d0>"
       ]
      },
      "metadata": {},
@@ -1912,7 +1912,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "metadata": {
     "collapsed": false
    },
@@ -1932,7 +1932,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 31,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -1940,9 +1940,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99d2048>"
+       "<matplotlib.figure.Figure at 0x8830c88>"
       ]
      },
      "metadata": {},
@@ -2023,16 +2023,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 32,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9acecc0>"
+       "<matplotlib.figure.Figure at 0x997d978>"
       ]
      },
      "metadata": {},
@@ -2052,16 +2052,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 33,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9aced30>"
+       "<matplotlib.figure.Figure at 0x997af60>"
       ]
      },
      "metadata": {},
@@ -2102,7 +2102,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 34,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -2110,9 +2110,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9aa8668>"
+       "<matplotlib.figure.Figure at 0x880b860>"
       ]
      },
      "metadata": {},
@@ -2120,9 +2120,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b47390>"
+       "<matplotlib.figure.Figure at 0x9aaa470>"
       ]
      },
      "metadata": {},
@@ -2162,7 +2162,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 35,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -2170,9 +2170,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b51e80>"
+       "<matplotlib.figure.Figure at 0x9eb76a0>"
       ]
      },
      "metadata": {},
@@ -2193,16 +2193,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 36,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88b2518>"
+       "<matplotlib.figure.Figure at 0x880f5f8>"
       ]
      },
      "metadata": {},
@@ -2224,16 +2224,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 37,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a74048>"
+       "<matplotlib.figure.Figure at 0x997dd68>"
       ]
      },
      "metadata": {},
@@ -2271,7 +2271,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 38,
    "metadata": {
     "collapsed": false
    },
@@ -2280,7 +2280,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99b3cc0>"
+       "<matplotlib.figure.Figure at 0x9a706d8>"
       ]
      },
      "metadata": {},
@@ -2290,7 +2290,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99554a8>"
+       "<matplotlib.figure.Figure at 0x9994e80>"
       ]
      },
      "metadata": {},
@@ -2325,7 +2325,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 39,
    "metadata": {
     "collapsed": false
    },
@@ -2334,7 +2334,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8845f98>"
+       "<matplotlib.figure.Figure at 0x9a6ac88>"
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      },
      "metadata": {},
@@ -2344,7 +2344,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99dcb00>"
+       "<matplotlib.figure.Figure at 0xaa252b0>"
       ]
      },
      "metadata": {},
@@ -2369,7 +2369,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 40,
    "metadata": {
     "collapsed": false
    },
@@ -2378,7 +2378,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b8ea90>"
+       "<matplotlib.figure.Figure at 0x88122e8>"
       ]
      },
      "metadata": {},
@@ -2403,7 +2403,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 41,
    "metadata": {
     "collapsed": false
    },
@@ -2412,7 +2412,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ae79e8>"
+       "<matplotlib.figure.Figure at 0x99152e8>"
       ]
      },
      "metadata": {},
@@ -2441,7 +2441,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 42,
    "metadata": {
     "collapsed": false
    },
@@ -2450,7 +2450,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9aa55f8>"
+       "<matplotlib.figure.Figure at 0x9a1fc88>"
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      },
      "metadata": {},
@@ -2460,7 +2460,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ddda20>"
+       "<matplotlib.figure.Figure at 0x9aebda0>"
       ]
      },
      "metadata": {},
@@ -2543,7 +2543,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 43,
    "metadata": {
     "collapsed": false
    },
@@ -2552,7 +2552,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8878438>"
+       "<matplotlib.figure.Figure at 0x9eae978>"
       ]
      },
      "metadata": {},
@@ -2603,7 +2603,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 44,
    "metadata": {
     "collapsed": false
    },
@@ -2680,16 +2680,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 45,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAADTCAYAAABDa58YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9e53a90>"
+       "<matplotlib.figure.Figure at 0x88bb748>"
       ]
      },
      "metadata": {},
@@ -2731,16 +2731,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 46,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9e112b0>"
+       "<matplotlib.figure.Figure at 0x9971358>"
       ]
      },
      "metadata": {},
@@ -2774,16 +2774,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 47,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt0AAADaCAYAAAB6rf5jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt0AAADaCAYAAAB6rf5jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xaa6d198>"
+       "<matplotlib.figure.Figure at 0x9963ef0>"
       ]
      },
      "metadata": {},
@@ -2815,7 +2815,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 48,
    "metadata": {
     "collapsed": true
    },
@@ -2833,16 +2833,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 49,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt0AAADaCAYAAAB6rf5jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdcU9f7wPFPBnsJCgqKuPeqihscte466q+4rVqr/X5t\ntcNqa4faurq01tbW8aXu3da6S9UqWicuHHXi3qAoAiEkub8/kEgEHJAQ0Of9euVFcnJyzxNuAs89\n99xzVIqiKAghhBBCCCFsRm3vAIQQQgghhHjWSdIthBBCCCGEjUnSLYQQQgghhI1J0i2EEEIIIYSN\nSdIthBBCCCGEjUnSLYQQQgghhI1J0i2EEEIIIYSNPXHSHRkZSceOHSlRogRqtZq5c+dmqjNmzBiK\nFy+Oq6srzZs359ixY1YNVgghhBBCiILoiZPuxMREatSowdSpU3FxcUGlUlk8/+WXXzJ58mR++OEH\n9u7di5+fHy+99BL37t2zetBCCCGEEEIUJKqcrEjp4eHBjz/+SN++fQFQFIWAgACGDh3KRx99BIBO\np8PPz49vvvmGQYMGWTdqIYQQQgghChCrjOk+e/Ys169fp1WrVuYyZ2dnQkND2bFjhzWaEEIIIYQQ\nosCyStJ97do1AIoWLWpR7ufnZ35OCCGEEEKI55XW1g08PPb7zp07tm5SCCGEEEIIm/Ly8nqq+lbp\n6S5WrBgA169ftyi/fv26+TkhhBBCCCGeV1ZJukuXLk2xYsWIiIgwl+l0OrZv306jRo2s0YQQQggh\nhBAF1hMPL0lMTOTUqVMAmEwmzp8/z8GDBylcuDCBgYG88847TJgwgUqVKlG+fHnGjRuHh4cHPXv2\nzHabT9stL6wrKioKgLp169o5kueb7If8Q/ZF/iD7If+QfZE/yH7IP3IzTPqJk+69e/fSokULIG2c\n9ujRoxk9ejT9+vUjPDycESNGkJyczJAhQ7h9+zYNGjQgIiICNze3HAcnhBBCCCHEs+CJk+5mzZph\nMpkeWSc9ERdCCCGEEEI8YJUx3UIIIYQQQojsSdIthBBCCCGEjUnSLYQQQgghhI3ZfHEcIYQQQois\nmEwm9Hq9vcPI94KCgoC06ZiF7Tg6OqJW264/WpJuIYQQQuQ5k8lESkoKzs7OmVavFpacnZ3tHcIz\nT1EUdDodTk5ONku8ZXiJEEIIIfKcXq+XhFvkGyqVCmdnZ5ueeZGkWwghhBB2IQm3yE9s/XmUpFsI\nIYQQQggbk6RbCCGEEEIIG5OkWwghhBBCCBuTpFsIIYQQIg+cO3cOtVrN3LlzzWVz5sxBrVZz4cIF\nO0Ym8oIk3UIIIYQQVpKeRGd1e/vtt1GpVI+9YG/RokVMnTo1jyIWeUXm6RZCCCGEsLKxY8dStmxZ\ni7KKFSvy66+/otU+Ov1atGgRR48eZdiwYbYMUeQxSbqFEEIIIaysdevW1KtXL8evt8X0dcnJybi4\nuFh9u+LJyPASIYQQQog8kNWY7oc1a9aMdevWmeum39IpisK0adOoXr06Li4uFC1alIEDBxIXF2ex\nnVKlStG2bVs2bdpE/fr1cXFx4auvvrLZexOPZ9WebqPRyJgxY1i4cCFXr17F39+fXr16MWbMGDQa\njTWbEvmI0Whk+fLlHD16lICAAHr16oWnp6e9wxJCCCHsJj4+ntjY2Cyfe1Qv9ieffMKIESO4dOkS\n3333Xabn//Of/xAeHk6/fv0YOnQoFy5cYNq0aezZs4e9e/fi5ORkbuP06dO8+uqrDBo0iDfeeIOS\nJUta582JHLFq0v3ll18yffp05s2bR/Xq1Tl06BD9+vXDycmJTz75xJpNiXzCaDTSpUsXVq9ebS6b\nMmUK27Zto2jRonaMTAghhLCfNm3aWDxWqVRER0c/9nUtW7YkICCA+Ph4evbsafHcjh07mDlzJvPn\nz6dXr14WbYWEhDBv3jzeeOMNIK1H/MyZM6xatYoOHTpY4R2J3LJq0r1jxw46duxI+/btAShZsiQd\nOnRgz5491mxG5CPh4eGsXr0aHx8f3njjDf744w+OHz/OiBEjHnn6TAghhHga63YtZsPupZnK29Tv\nRrsGPXJd39qmTZtG5cqVLcqcnZ1ztc1ly5bh7u5Oq1atLHrRK1asiJ+fH3///bc56QYIDAyUhDsf\nsWrSHRISwvTp0zlx4gQVK1bk2LFj/P3334waNcqazYh8ZP/+/QCMGDGCkSNH8vLLL9OkSRMOHDhg\n58iEEEII+wkODs50IeW5c+dytc2TJ09y7969bM8k37x50+JxmTJlctWesC6rJt0jR47k7t27VKlS\nBY1Gg8Fg4JNPPuHNN9/Msn5UVJQ1mxc5lJv9oNfrAVi+fDkVK1Zk6dK0XgVHR0fZv09Jfl/5h+yL\n/EH2Q/5hi30RFBSU657f543JZKJw4cLm/7UP8/b2tngsM5U8vYSEBI4cOZLt8+XLl8/xtq2adC9Z\nsoT58+ezePFiqlatyoEDBxg2bBilSpViwIAB1mxK5BOdO3dmxYoV7Nu3jy5dupjL+/TpY8eohBBC\nPGvaNejxVMNCnrZ+fpLdhZZly5Zl48aN1K9fHzc3tzyOSuSWVZPuDz74gBEjRhAWFgZA1apVOX/+\nPBMnTswy6a5bt641mxdPKb3nIrf74Z9//mHo0KEcO3YMf39/Ro8eTefOna0R4nPBWvtB5J7si/xB\n9kP+Yct9odPprL7NZ4Wbmxu3b9/OVN69e3d++uknPv/8c7788kuL54xGIwkJCRQqVCivwnwmeXh4\nPPLzfufOnRxv26pJd3JyssVckgBqtRpFUazZjMhnqlWrxubNm+0dhhBCCPFMCA4OZtmyZbzzzjvU\nq1cPtVpN9+7dCQkJYciQIXz99ddER0fTqlUrnJycOH36NL/++itffPEFffv2tXf4IhtWTbpffvll\nJk2aROnSpalSpQoHDhxgypQpvPbaa9ZsRgghhBAi33ra1SQfrv/f//6Xw4cPs2DBAqZNmwak9XJD\n2qwotWvX5ueff+aTTz5Bq9USFBREt27daNGiRY5jELanUqzYDX3v3j0+/fRTfv/9d27cuIG/vz89\nevTgs88+w9HREbDslvfy8rJW0yIH5BRu/iD7If+QfZE/yH7IP2w9vEQupBT5zeM+l7nJY63a0+3u\n7s6UKVOYMmWKNTcrhBBCCCFEgaZ+fBUhhBBCCCFEbkjSLYQQQgghhI1J0i2EEEIIIYSNSdIthBBC\nCCGEjUnSLYQQQgghhI1J0i2EEEIIIYSNSdIthBBCCCGEjUnSLYQQQgghhI1J0i2EEEIIIYSNSdIt\nhBBCCCGEjUnSLYQQQgghhI1J0i2EEEIIIYSNSdIthBBCCGElc+bMQa1Wm28ODg6UKFGC/v37c/ny\nZfr162fxfHa35s2bm7e5fv16WrRogb+/P66urpQqVYrOnTuzePFiO75T8bS09g5ACCGEEOJZM3bs\nWMqWLYtOp2Pnzp3MmTOH7du3s2DBAlq1amWud+zYMSZMmMBbb71FgwYNzOVFixYFYPLkyQwfPpwm\nTZowYsQIPDw8iImJITIyktmzZ9OjR488f28iZ6yadF+9epUPP/yQ9evXk5CQQJkyZfjpp58IDQ21\nZjNCCCGEEPla69atqVevHgADBgygSJEifPnll1y4cIGePXua623ZsoUJEybQpEkTwsLCLLZhMBj4\n/PPPad68OZs2bcrUxs2bN237JoRVWW14SXx8PI0bN0alUrFu3TqOHz/ODz/8gJ+fn7WaEEIIIYQo\nkJo0aQJATEzME78mNjaWu3fvml/7MF9fX6vEJvKG1Xq6v/rqK4oXL86cOXPMZUFBQdbavBBCCCFE\ngXXu3DkAvL29n/g1fn5+uLi4sHr1aoYNG4aPj4+NohN5wWpJ98qVK2nbti3dunVjy5YtBAQEMHDg\nQIYMGWKtJoQQQgjxnBrzP4XPw22z7c8GwJjXVVbdZnx8PLGxseh0Onbv3s3YsWNxdnamQ4cOT7wN\ntVrNyJEjGTNmDCVLlqRx48Y0adLEYuiKKDisNrwkJiaG6dOnU65cOSIiIhg2bBgffvghP/74o7Wa\nEEIIIYQoENq0aYOfnx8lS5bk1VdfxcPDg1WrVhEQEPBU2/nss8+YN28eNWrUYPPmzYwePZoGDRpQ\nsWJFdu/ebaPohS1YrafbZDJRr149xo8fD0DNmjU5deoUP/74Y7a93VFRUdZqXuSC7If8QfZD/iH7\nIn+Q/ZB/2GJfBAUF4ezsbPXt5hfTpk2jcuXKxMfHM2fOHCIjI3P8fnv37k3v3r1JSkoiKiqKxYsX\nM2vWLNq3b8/x48cpUqSIlaN/fiUkJHDkyJFsny9fvnyOt221pDsgIIAqVapYlFWqVIkLFy5Yqwkh\nhBBCPKfGvK5izOv2juLJBQcHm4eAdO7cmaZNm9KjRw9OnDiBq6trjrbp6upKaGgooaGh+Pn58cUX\nX7B+/Xr69OljzdCFjVgt6W7cuDHHjx+3KDt58iSlSpXK9jV169a1VvMiB9J7LmQ/2Jfsh/xD9kX+\nIPsh/7DlvtDpdFbfZn6lVquZNGkSISEhTJs2jZEjR+Z6m8HBwUDadM3Cejw8PB75eb9z506Ot221\nMd3vvvsuu3btYsKECZw+fZrly5czbdo0uZBSCCGEEM+9xo0b07BhQ7777jtSUlKe6DXJycn8888/\nWT63bt06IG1UgSgYrNbTXbduXVauXMmoUaP44osvCAoKYty4cfznP/+xVhNCCCGEEAXW8OHD6dq1\nK+Hh4U+UHyUmJhISEkJwcDBt27alZMmSJCQksHHjRtauXUuDBg2eajYUYV9WXZGyXbt2tGvXzpqb\nFEIIIYQoUFSqrKcf7Ny5M+XKleObb75h8ODBqNXqR9b39vZm9uzZrF27lnnz5nHt2Line truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt0AAADaCAYAAAB6rf5jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlYVNUbwPHvnQGGfRHEHRTFfS1ATcA0d82lzL1c0rLS\nNFssc/fnli2WmZqWuGdqpZmamiaaK+7mDu64ACIiOzP39wcyOg6Ywoygvp/nmQfmzJ1zzsydO/Pe\nc997rqKqqooQQgghhBDCajQF3QEhhBBCCCGedBJ0CyGEEEIIYWUSdAshhBBCCGFlEnQLIYQQQghh\nZRJ0CyGEEEIIYWUSdAshhBBCCGFlEnQLIYQQQghhZRYNuvV6PSNGjMDPzw8HBwf8/PwYMWIEer3e\nks0IIYQQQgjxWLGxZGWTJ0/mu+++Y/78+dSoUYODBw/Sq1cvdDodw4cPt2RTQgghhBBCPDYsGnRv\n376dtm3b0rp1awB8fHxo06YNu3fvtmQzQgghhBBCPFYsml4SEhLCpk2bOHHiBABHjx5l8+bNtGrV\nypLNCCGEEEII8Vix6Ej30KFDuXnzJlWrVkWr1ZKZmcnw4cPp37+/JZsRQgghhBDisWLRoPunn35i\nwYIFLFmyhGrVqrF//34GDRpE2bJl6dOnDwAJCQmWbFIIIYQQQohHzs3N7aGWV1RVVS3VeJkyZfjo\no48YOHCgsWz8+PGEhYVx6tQpQIJuIYQQQgjx+HvYoNuiOd0pKSloNKZVajQaLBjXCyGEEEII8dix\naHrJiy++yKRJkyhXrhxVq1Zl//79fPXVV/Ts2TPH5R92D0FYVkREBAABAQEF3JOnm6yHwkPWReEg\n66HwkHVROMh6KDzyk7Fh0aB72rRpjBgxgrfffptr165RokQJ3njjDUaOHGnJZoQQQgghhHisWDTo\ndnZ25quvvuKrr76yZLVCCCGEEEI81iya0y2EEEIIIYQwJ0G3EEIIIYQQViZBtxBCCCGEEFZm0Zxu\nSzMYDKSnpxd0N55Yvr6+AKSmphZwTx4PdnZ2ZlNiCiGEEEI8iEIbdBsMBtLS0rC3t0dRlILuzhPJ\n3t6+oLvw2FBVldTUVHQ6nQTeQgghhHhohTZ6SE9Pl4BbFBqKomBvby9HXoQQQgiRJ4U26AYk4BaF\ninwehRBCCJFXhTroFkIIIYQQ4kkgQbcQQgghhBBWJkG3EEIIIYQQViZBdyFy9uxZNBoN8+bNM5aF\nhYWh0Wg4f/58AfZMCCGEEELkhwTdj1h2EJ3TbeDAgSiK8p8n7C1evJivv/76EfVYCCGEEELkV6Gd\np/tJN2bMGMqXL29SVqlSJVasWIGNzf1Xy+LFi/n3338ZNGiQNbsohBBCCCEsRILuAtK8eXOCgoLy\n/HxrTF+XkpKCg4ODxesVQgghhHjaSXpJIZJTTve9nn/+edasWWNcNvuWTVVVpk2bRo0aNXBwcKBY\nsWL07duXuLg4k3rKli1Ly5Yt+euvv6hbty4ODg589tlnVnttQgghhBBPM4sG3ZcvX6Znz554e3vj\n4OBAtWrVCA8Pt2QTT4wbN24QGxtrcst2v1Hs4cOHU7t2bby8vFi4cKHxlu2tt97i/fffp379+nzz\nzTe88cYbLF++nEaNGpGWlmbSxunTp3nllVdo1KgR06ZNo379+tZ5sUIIIYQQTzmLpZfcuHGDBg0a\nEBoaypo1ayhatChRUVF4e3tbqoknSosWLUzuK4rCoUOH/vN5TZo0oWTJkty4cYNu3bqZPLZ9+3a+\n//57FixYQPfu3U3aCgkJYf78+fTr1w/IGhGPjIxk1apVtGnTxgKvSAghhBBC5MZiQfdnn31GqVKl\nCAsLM5b5+vpaqvr/tGbnEtbtWmpW3qJuZ1rV65rv5S1t2rRpVKlSxaTM3t4+X3X+/PPPODs706xZ\nM5OR80qVKuHt7c3mzZuNQTdAmTJlJOAWQgghhHgELBZ0//bbb7Rs2ZLOnTvz999/U7JkSfr27cs7\n77xjqSaeKIGBgWYnUp49ezZfdZ48eZJbt25RrFixHB+PiYkxue/n55ev9oQQQgghxIOxWNAdFRXF\nd999x5AhQxg2bBj79+9n4MCBALkG3hEREbnW5+vrm++R36eNwWDA09OTpUvNR/ABPDw8TO7LTCUP\nLzExkSNHjlil7vttD+LRknVROMh6KDxkXRQOsh4Knr+/f56fa7Gg22AwEBQUxPjx4wGoVasWp06d\nYvr06Y9ktLtVva4PlRbysMsXJrmdaFm+fHk2btxI3bp1cXJyesS9EkIIIYQQubFY0F2yZEmqVq1q\nUla5cuX7Xr48ICAg18dSU1Mt1bUnjpOTE/Hx8WblXbp0YcaMGYwdO5bJkyebPKbX60lMTMTd3f1R\ndfOJ5OLict/PbV5kj1xYul7x8GRdFA6yHgoPWReFg6yHwiMhISHPz7VY0N2gQQOOHz9uUnby5EnK\nli1rqSbEbYGBgfz8888MHjyYoKAgNBoNXbp0ISQkhHfeeYcpU6Zw6NAhmjVrhk6n4/Tp06xYsYJx\n48bx2muvFXT3hRBCCCGeOhYLut977z2ee+45JkyYQKdOndi/fz/Tpk1j4sSJlmriifGwV5O8d/m3\n336bw4cPs3DhQqZNmwZkjXJD1qwozzzzDDNnzmT48OHY2Njg6+tL586dady4cZ77IIQQQggh8k5R\nVVW1VGVr1qxh2LBhnDhxAl9fXwYMGMCAAQNMlrl7WN7NzS3XulJTU+VESlHoWONzKYcNCw9ZF4WD\nrIfCQ9ZF4SDrofB40Dg2JxYb6QZo1aoVrVq1smSVQgghhBBCPPYsehl4IYQQQgghhDkJuoUQQggh\nhLAyCbqFEEIIIYSwMgm6hRBCCCGEsDIJuoUQQgghhLAyCbqFEEIIIYSwMgm6hRBCCCGEsDIJuoUQ\nQgghhLAyCbqFEEIIIYSwMgm6hRBCCCGEsDIJuoUQQgghhLAyCbqFEEIIIYSwMgm6H7GwsDA0Go3x\nZmtrS+nSpenduzeXLl2iV69eJo/ndmvUqJGxzrVr19K4cWNKlCiBo6MjZcuWpX379ixZsqQAX6kQ\nQgghhMhmU9AdeFqNGTOG8uXLk5qayo4dOwgLC2Pbtm0sXLiQZs2aGZc7evQoEyZMYMCAAdSrV89Y\nXqxYMQC+/PJLPvjgA4KDg/noo49wcXEhKiqK8PBw5syZQ9euXR/5axNCCCGEEKasFnRPnDiRTz/9\nlHfeeYdp06ZZq5nHVvPmzQkKCgKgT58+eHl5MXnyZM6fP0+3bt2My/39999MmDCB4OBgOnXqZFJH\nZmYmY8eOpVGjRvz1119mbcTExFj3RQghhBBCiAdilfSSnTt3Mnv2bGrWrImiKNZo4okTHBwMQFRU\n1AM/JzY2lps3bxqfe6+iRYtapG9CCCGEECJ/LB50JyQk0KNHD+bOnYuHh4elq39inT17FuCh3jNv\nb28cHBz4/fffuX79upV6JoQQQggh8svi6SVvvPEGr7zyCg0bNkRVVUtXn6vRP6iM/dE6dY/sA6Nf\nt+yI/Y0bN4iNjSU1NZVdu3YxZswY7O3tadOmzQPXodFoGDp0KKNHj8bHx4cGDRoQHBxskroihBBC\nCCEKnkWD7tmzZxMVFcXixYsBJLXkPlq0aGFyv1y5cixevJiSJUs+VD0jR47Ez8+P7777jk2bNrFh\nwwZGjRqFv78/8+fPp27dupbsthBCCCGEyAOLBd0nTpzg008/Zdu2bWi1WgBUVb3vaHdERESuj/n6\n+mJvb2+p7hU606ZNo0qVKty4cYOwsDDCw8Pz/Hp79OhBjx49SE5OJiIigiVLljB79mxat27N8ePH\n8fLysnDvn16JiYkcOXLEKnXfb3sQj5asi8JB1kPhIeuicJD1UPD8/f3z/FyLBd07duwgNjaWatWq\nGcv0ej1bt25l1qxZJCUlYWtra6nmzIx+XWH061ar3uICAwONKSDt27enYcOGdO3alRMnTuDo6Jin\nOh0dHQkNDSU0NBRvb2/GjRvH2rVrefXVVy3ZdSGEEEII8ZAsFnR36NDBJI9YVVV69+5NxYoVGTZs\nWI4Bd0BAQK71paamWqprhZ5Go2HSpEmEhIQwbdo0hg4dmu86AwMDAbh8+XK+6xJ3uLi43Pdz+7AS\nExOZPHkycXFxNG/enHbt2klaVgHKHkWy5DoWD0/WQ+Eh66JwkPVQeCQkJOT5uRYLut3c3HBzczMp\nc3R0xMPDg6pVq1qqmSdWgwYNqF+/PlOnTmXw4MHodLr/fE5KSgr79u2jQYMGZo+tWbMGgMqVK1u8\nr8Iyrl69SmhoKCdPngRg5syZdO7cmcWLF6PRyMVihRBCiCeJVX/ZFUWRUbuH8MEHH3D16lV+/PHB\npmFJSkoiJCSEunXrMnr0aH788Ue+/vprXnzxRWbOnEm9evUeajYU8Wh98MEHnDx5El9fX7p27Yqr\nqytLly5l4cKFBd01IYQQQliYVS8Dv3nzZmtW/9jKbUekffv2VKhQgc8//5w333zTONqZ2/IeHh7M\nmTOHP/74g/nz53PlyhUURaFChQqMGjWKDz/8UEZMC7Hsw4WjR4+mevXqVK1alREjRhAREcFrr71W\nwL0TQgghhCVZNegW5nr16kWvXr1yfExRFGOqQbbnn38evV6f4/JarZY+ffrQp08fS3dTPAKenp4A\nbNmyhaJFi7Jp0yYAihQpUpDdEkIIIYQVyDCoEAVkyJAhAISFhdGmTRs2b96Mu7u77EQJIYQQTyAJ\nuoUoIC+99BJLliyhXLlyuLi4EBISwpYtW/Dx8SnorgkhhBDCwiS9RIgC1KVLFypUqADIVFBCiPwz\nGAwAcj6PEIWQbJVCCCHEY+769eu8/PLLODg44ODgQNeuXfM1n7AQwvJkpFsIIYR4jLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8811048>"
+       "<matplotlib.figure.Figure at 0x9a6b7b8>"
       ]
      },
      "metadata": {},

07-Kalman-Filter-Math.ipynb

@@ -1254,7 +1254,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x5b4cef0>"
+       "<matplotlib.figure.Figure at 0x58e8ef0>"
       ]
      },
      "metadata": {},
@@ -1288,7 +1288,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x844b048>"
+       "<matplotlib.figure.Figure at 0x8308dd8>"
       ]
      },
      "metadata": {},
@@ -1369,7 +1369,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86337f0>"
+       "<matplotlib.figure.Figure at 0x83c20b8>"
       ]
      },
      "metadata": {},
@@ -1524,7 +1524,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa787198>"
+       "<matplotlib.figure.Figure at 0xa7382e8>"
       ]
      },
      "metadata": {},
@@ -1618,7 +1618,7 @@
     "\\end{aligned}\n",
     "$$\n",
     "\n",
-    "As above, all of the matrices become scalars. $H$ defines how we convert from a position to a measurement. Both are positions, so there is no conversion, and thus $H=1$. Let's substitute in our known values and convert to scalar in one step. One final thing you need to know - division is scalar's analogous operation for matrix inversion, so we will convert the matrix inversion to division.\n",
+    "As above, all of the matrices become scalars. $H$ defines how we convert from a position to a measurement. Both are positions, so there is no conversion, and thus $H=1$. Let's substitute in our known values and convert to scalar in one step. The inverse of a 1$\\times$1 matrix is the reciprocal of the value so we will convert the matrix inversion to division.\n",
     "\n",
     "$$\n",
     "\\begin{aligned}\n",
@@ -1774,7 +1774,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa5ca5c0>"
+       "<matplotlib.figure.Figure at 0xa5bf9e8>"
       ]
      },
      "metadata": {},

08-Designing-Kalman-Filters.ipynb

@@ -3785,7 +3785,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin blue line, and a Kalman filter with R=10 as a thick red line. These R values are chosen merely to show the effect of measurement noise on the output, they are not intended to imply a correct design.\n",
+    "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin green line, and a Kalman filter with R=10 as a thick blue line. These R values are chosen merely to show the effect of measurement noise on the output, they are not intended to imply a correct design.\n",
     "\n",
     "We can see that neither filter does very well. At first both track the measurements well, but as time continues they both diverge. This happens because the state model for air drag is nonlinear and the Kalman filter assumes that it is linear. If you recall our discussion about nonlinearity in the g-h filter chapter we showed why a g-h filter will always lag behind the acceleration of the system. We see the same thing here - the acceleration is negative, so the Kalman filter consistently overshoots the ball position. There is no way for the filter to catch up so long as the acceleration continues, so the filter will continue to diverge.\n",
     "\n",