Changes to condense material.

Lots of small changes to try to get page count down. I'm not liking
this.

01_g-h_filter.ipynb

@@ -324,7 +324,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e162e8>"
+       "<matplotlib.figure.Figure at 0x6e97400>"
       ]
      },
      "metadata": {},
@@ -359,7 +359,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e16be0>"
+       "<matplotlib.figure.Figure at 0x6ee2860>"
       ]
      },
      "metadata": {},
@@ -391,7 +391,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7637780>"
+       "<matplotlib.figure.Figure at 0x76b0cf8>"
       ]
      },
      "metadata": {},
@@ -411,9 +411,9 @@
     "\n",
     "> So two sensors, even if one is less accurate than the other, is better than one.\n",
     "\n",
-    "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight will play a large role later, so don't forget it.\n",
+    "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight of using all measurements regardless of accuracy will play a large role later, so don't forget it.\n",
     "\n",
-    "So, what if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's just write a simulation for now."
+    "What if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's just write a simulation for now."
    ]
   },
   {
@@ -427,7 +427,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Average of measurements is 165.0636\n"
+      "Average of measurements is 164.9647\n"
      ]
     }
    ],
@@ -458,7 +458,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Average of measurements is 165.0104\n"
+      "Average of measurements is 165.0147\n"
      ]
     }
    ],
@@ -491,7 +491,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x4faa240>"
+       "<matplotlib.figure.Figure at 0x502b390>"
       ]
      },
      "metadata": {},
@@ -529,7 +529,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x4faa3c8>"
+       "<matplotlib.figure.Figure at 0x7772198>"
       ]
      },
      "metadata": {},
@@ -558,7 +558,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x77dee10>"
+       "<matplotlib.figure.Figure at 0x784dd68>"
       ]
      },
      "metadata": {},
@@ -589,7 +589,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x786f128>"
+       "<matplotlib.figure.Figure at 0x77f4550>"
       ]
      },
      "metadata": {},
@@ -621,7 +621,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x77deb70>"
+       "<matplotlib.figure.Figure at 0x784a400>"
       ]
      },
      "metadata": {},
@@ -656,7 +656,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e32710>"
+       "<matplotlib.figure.Figure at 0x6f5b828>"
       ]
      },
      "metadata": {},
@@ -685,7 +685,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7812a58>"
+       "<matplotlib.figure.Figure at 0x76e7240>"
       ]
      },
      "metadata": {},
@@ -700,7 +700,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here the measurement is in blue, the previous estimate (output of the filter) is black, and the estimate is red. So we have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right?. If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n",
+    "We have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right? If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n",
     "\n",
     "> The key insight to this entire book is in the next paragraph. Read it carefully!\n",
     "\n",
@@ -711,9 +711,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should like between 159 (the prediction) and 164.2 (the measurement).\n",
+    "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should lie between 159 (the prediction) and 164.2 (the measurement).\n",
     "\n",
-    "Should it be half way? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when A was much more accurate than B - we scaled the answer to be closer to A than B. Let's look at that in a chart."
+    "Should it be half way? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when scale A was much more accurate than scale B - we scaled the answer to be closer to A than B. Let's look at that in a chart."
    ]
   },
   {
@@ -727,7 +727,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7682a90>"
+       "<matplotlib.figure.Figure at 0x770e1d0>"
       ]
      },
      "metadata": {},
@@ -758,7 +758,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 49,
    "metadata": {
     "collapsed": false
    },
@@ -783,9 +783,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7739cc0>"
+       "<matplotlib.figure.Figure at 0x7b0c9b0>"
       ]
      },
      "metadata": {},
@@ -801,7 +801,7 @@
     "time_step = 1 # day\n",
     "scale_factor = 4/10\n",
     "\n",
-    "def predict_using_gain_guess(weight, gain_rate): \n",
+    "def predict_using_gain_guess(weight, gain_rate, do_print=True): \n",
     "    # store the filtered results\n",
     "    estimates = []\n",
     "    predictions = []\n",
@@ -818,16 +818,18 @@
     "        # save for plotting\n",
     "        estimates.append(weight)\n",
     "        predictions.append(prediction)\n",
-    "        print('previous: {:.2f}, prediction: {:.2f} estimate {:.2f}'.format(\n",
-    "              estimates[-2], prediction, weight))\n",
+    "        if do_print:\n",
+    "            print('previous: {:.2f}, prediction: {:.2f} estimate {:.2f}'.format(\n",
+    "                  estimates[-2], prediction, weight))\n",
     "\n",
     "    # plot results\n",
     "    n = len(weights)\n",
     " \n",
-    "    book_plots.plot_filter(range(n+1), estimates)\n",
-    "    book_plots.plot_measurements(range(1, n+1), weights, c='b', label='Scale')\n",
-    "    book_plots.plot_track([1, n],[160, 160+n], c='k', label='Actual Weight')\n",
-    "    book_plots.plot_track(range(1, n+1), predictions, c='r', label='Predictions')\n",
+    "    xs = list(range(n+1))\n",
+    "    book_plots.plot_filter(xs, estimates, marker='o')\n",
+    "    book_plots.plot_measurements(xs[1:], weights, c='b', label='Scale')\n",
+    "    book_plots.plot_track([1, n], [160, 160+n], c='k', label='Actual Weight')\n",
+    "    book_plots.plot_track(xs[1:], predictions, c='r', label='Predictions', marker='v')\n",
     "    book_plots.show_legend()\n",
     "    plt.xlabel('day')\n",
     "    plt.ylabel('weight (lbs)')\n",
@@ -851,34 +853,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 50,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "previous: 160.00, prediction: 160.00 estimate 159.20\n",
-      "previous: 159.20, prediction: 159.20 estimate 161.20\n",
-      "previous: 161.20, prediction: 161.20 estimate 160.84\n",
-      "previous: 160.84, prediction: 160.84 estimate 160.46\n",
-      "previous: 160.46, prediction: 160.46 estimate 161.12\n",
-      "previous: 161.12, prediction: 161.12 estimate 162.51\n",
-      "previous: 162.51, prediction: 162.51 estimate 165.35\n",
-      "previous: 165.35, prediction: 165.35 estimate 166.17\n",
-      "previous: 166.17, prediction: 166.17 estimate 166.26\n",
-      "previous: 166.26, prediction: 166.26 estimate 168.16\n",
-      "previous: 168.16, prediction: 168.16 estimate 169.37\n",
-      "previous: 169.37, prediction: 169.37 estimate 170.66\n"
-     ]
-    },
     {
      "data": {
-      "image/png": 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+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b26b38>"
+       "<matplotlib.figure.Figure at 0x7783470>"
       ]
      },
      "metadata": {},
@@ -886,7 +870,7 @@
     }
    ],
    "source": [
-    "predict_using_gain_guess (weight=initial_guess, gain_rate=0)"
+    "predict_using_gain_guess (weight=initial_guess, gain_rate=0, do_print=False)"
    ]
   },
   {
@@ -903,7 +887,7 @@
     "\n",
     "On the next day we measure 164.2, which implies a weight gain of 4.4 lbs (since 164.2 - 159.8 = 4.4), not 1. Can we use this information somehow? It seems plausible. After all, the weight measurement itself is based on a real world measurement of our weight, so there is useful information. Our estimate of our weight gain may not be perfect, but it is surely better than just guessing our gain is 1 lb. Data is better than a guess, even if it is noisy.\n",
     "\n",
-    "So, should we just set the new gain/day to 4.4 lbs?  Hmm, sounds like our same problem again. Yesterday we though the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n",
+    "So, should we just set the new gain/day to 4.4 lbs? Yesterday we though the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Hmm, sounds like our same problem again. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n",
     "\n",
     "$$new gain = old gain + \\frac{1}{3}\\frac{measurement - predicted~weight}{1~ day}\n",
     "$$"
@@ -920,7 +904,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7760fd0>"
+       "<matplotlib.figure.Figure at 0x6f314a8>"
       ]
      },
      "metadata": {},
@@ -1011,16 +995,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 52,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6edf898>"
+       "<matplotlib.figure.Figure at 0x8e95780>"
       ]
      },
      "metadata": {},
@@ -1035,13 +1020,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Now let's explore a few different problem domains to better understand this. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23km at time t and moving at 60 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of 500 meters. So at t+1 sec the measurement could be anywhere from 22.5 km to 23 km. But the train is moving at 60 kph, which is 16.6 meters/second. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.0166 km because a train cannot slow down very much at all in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n",
+    "Now let's explore a few different problem domains to better understand this. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23km at time t and moving at 60 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of 500 meters. So at t+1 sec the measurement could be anywhere from 22.5 km to 23 km. But the train is moving at 60 kph, which is 16.6 meters/second. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.0166 km because a train cannot slow down very much in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n",
     "\n",
     "Now consider the problem of tracking a thrown ball. We know that a ballistic object moves in a parabola in a vacuum when in a gravitational field. But a ball thrown on the surface of the Earth is influenced by air drag, so it does not travel in a perfect parabola. Baseball pitchers take advantage of this fact when they throw curve balls. Let's say that we are tracking the ball inside a stadium using computer vision. The accuracy of the computer vision tracking might be modest, but predicting the ball's future positions by assuming that it is moving on a parabola is not extremely accurate either. In this case we'd probably design a filter that gave roughly equal weight to the measurement and the prediction.\n",
     "\n",
     "Now consider trying to track a child's balloon in a hurricane. We have no legitimate model that would allow us to predict the balloon's behavior except over very brief time scales (we know the balloon cannot go 10 miles in 1 second, for example). In this case we would design a filter that emphasized the measurements over the predictions.\n",
     "\n",
-    "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution (in a least squares sense). In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself."
+    "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself."
    ]
   },
   {
@@ -1112,9 +1097,9 @@
    "outputs": [
     {
      "data": {
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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7667b00>"
+       "<matplotlib.figure.Figure at 0x77bd2e8>"
       ]
      },
      "metadata": {},
@@ -1199,16 +1184,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 53,
    "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 0x76a9ba8>"
+       "<matplotlib.figure.Figure at 0x9554748>"
       ]
      },
      "metadata": {},
@@ -1266,9 +1251,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x776e9b0>"
+       "<matplotlib.figure.Figure at 0x78580b8>"
       ]
      },
      "metadata": {},
@@ -1329,9 +1314,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x787fb00>"
+       "<matplotlib.figure.Figure at 0x7a26d68>"
       ]
      },
      "metadata": {},
@@ -1394,9 +1379,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8e46400>"
+       "<matplotlib.figure.Figure at 0x7a4b080>"
       ]
      },
      "metadata": {},
@@ -1466,34 +1451,15 @@
    "cell_type": "code",
    "execution_count": 29,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x94de0b8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x8e46668>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0wAAAEjCAYAAAABoIERAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x77ef1d0>"
+       "<matplotlib.figure.Figure at 0x7ab9748>"
       ]
      },
      "metadata": {},
@@ -1501,14 +1467,20 @@
     }
    ],
    "source": [
-    "zs = gen_data(x0=5, dx=5, count=100, noise_factor=50)\n",
+    "np.random.seed(100)\n",
+    "zs = gen_data(x0=5, dx=5, count=50, noise_factor=50)\n",
     "data1 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.1, h=0.01)\n",
-    "data2 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.5, h=0.01)\n",
-    "data3 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.9, h=0.01)\n",
+    "data2 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.4, h=0.01)\n",
+    "data3 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.8, h=0.01)\n",
     "\n",
-    "plot_g_h_results(zs, data1, 'g = 0.1')\n",
-    "plot_g_h_results(zs, data2, 'g = 0.5')\n",
-    "plot_g_h_results(zs, data3, 'g = 0.9')"
+    "with book_format.figsize(y=6):\n",
+    "    book_plots.plot_measurements(zs, lw=1, color='k')\n",
+    "    book_plots.plot_filter(data1, label='g = 0.1', marker='+', lw=2, ms=15)\n",
+    "    book_plots.plot_filter(data2, label='g = 0.4', marker='v', lw=2, ms=10)\n",
+    "    book_plots.plot_filter(data3, label='g = 0.8', lw=2)\n",
+    "    book_plots.show_legend()\n",
+    "    plt.xlim([20,40])\n",
+    "    plt.ylim([0, 250])"
    ]
   },
   {
@@ -1527,29 +1499,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7779b00>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7779dd8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x75f8550>"
+       "<matplotlib.figure.Figure at 0x7ad7b38>"
       ]
      },
      "metadata": {},
@@ -1558,16 +1510,20 @@
    ],
    "source": [
     "zs = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n",
-    "for i in range(100):\n",
+    "for i in range(50):\n",
     "    zs.append(14)\n",
     "\n",
     "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.1, h=0.01)\n",
     "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.5, h=0.01)\n",
     "data3 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.9, h=0.01)\n",
     "\n",
-    "plot_g_h_results(zs, data1, 'g = 0.1')\n",
-    "plot_g_h_results(zs, data2, 'g = 0.5')\n",
-    "plot_g_h_results(zs, data3, 'g = 0.9')"
+    "with book_format.figsize(y=5):\n",
+    "    book_plots.plot_measurements(zs)\n",
+    "    book_plots.plot_filter(data1, label='g = 0.1', marker='+', lw=2, ms=10)\n",
+    "    book_plots.plot_filter(data2, label='g = 0.5', marker='v', lw=2)\n",
+    "    book_plots.plot_filter(data3, label='g = 0.9', lw=2)\n",
+    "    book_plots.show_legend()\n",
+    "    plt.ylim([6, 20])"
    ]
   },
   {
@@ -1588,19 +1544,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x75f8b70>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7779d68>"
+       "<matplotlib.figure.Figure at 0x7a2b2e8>"
       ]
      },
      "metadata": {},
@@ -1610,11 +1556,14 @@
    "source": [
     "zs = [5,6,7,8,9,9,9,9,9,10,11,12,13,14,15,16,16,16,16,16,16,16,16,16,16,16]\n",
     "    \n",
-    "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.302, h=0.054)\n",
-    "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.546, h=0.205)\n",
+    "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.302, h=.054)\n",
+    "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.546, h=.205)\n",
     "\n",
-    "plot_g_h_results(zs, data1, 'g = 0.302, h = 0.054')\n",
-    "plot_g_h_results(zs, data2, 'g = 0.546, h = 0.205')"
+    "with book_format.figsize(y=5):\n",
+    "    book_plots.plot_measurements(zs)\n",
+    "    book_plots.plot_filter(data2, label='g = 0.546\\nh = 0.205', marker='o', lw=2)\n",
+    "    book_plots.plot_filter(data1, label='g = 0.302\\nh = 0.054', marker='v', lw=2)\n",
+    "    book_plots.show_legend()"
    ]
   },
   {
@@ -1642,29 +1591,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0cAAAEjCAYAAAD5QHrmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b7eb70>"
-      ]
-     },
-     "metadata": {},
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-     "data": {
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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b7ec18>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x77103c8>"
+       "<matplotlib.figure.Figure at 0x7772c88>"
       ]
      },
      "metadata": {},
@@ -1678,11 +1607,13 @@
     "data2 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.05)\n",
     "data3 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.5)\n",
     "\n",
-    "plot_g_h_results(zs, data1, 'dx=0, h = 0.05')\n",
-    "plt.ylim([-1, 5])\n",
-    "plot_g_h_results(zs, data2, 'dx=2, h = 0.05')\n",
-    "plt.ylim([-1, 5])\n",
-    "plot_g_h_results(zs, data3, 'dx=2, h = 0.5')"
+    "\n",
+    "with book_format.figsize(y=5):\n",
+    "    book_plots.plot_measurements(zs)\n",
+    "    book_plots.plot_filter(data1, label='dx=0, h = 0.05', lw=2)\n",
+    "    book_plots.plot_filter(data2, label='dx=2, h = 0.05', marker='v', lw=2)\n",
+    "    book_plots.plot_filter(data3, label='dx=2, h = 0.5',  marker='o', lw=2)\n",
+    "    book_plots.show_legend()"
    ]
   },
   {
@@ -1695,7 +1626,7 @@
     "\n",
     "If you really want to test yourself, read the next paragraph and try to predict the results before you move the sliders. \n",
     "\n",
-    "Some things to try include setting $g$  and $h$ to their miminum values. See how perfectly the filter tracks the data! But now adjust $\\dot{x}$ to larger or smaller than 5. The filter should diverge from the data and never reacquire it. Start adding back either $g$ or $h$ and see how the filter snaps back to the data. See what the difference in the line is when you add only $g$ vs only $h$. Can you explain the reason for the difference? Then try setting $g$ greater than 1. Can you explain the results? Put $g$ back to a reasonable value (such as 0.1), and then make $h$ very large. Can you explain these results? Finally, set both $g$ and $h$ to their largest values. \n",
+    "Some things to try include setting $g$  and $h$ to their miminum values. See how perfectly the filter tracks the data! This is only because we are perfectly predicting the weight gain. Adjust $\\dot{x}$ to larger or smaller than 5. The filter should diverge from the data and never reacquire it. Start adding back either $g$ or $h$ and see how the filter snaps back to the data. See what the difference in the line is when you add only $g$ vs only $h$. Can you explain the reason for the difference? Then try setting $g$ greater than 1. Can you explain the results? Put $g$ back to a reasonable value (such as 0.1), and then make $h$ very large. Can you explain these results? Finally, set both $g$ and $h$ to their largest values. \n",
     "\n",
     "If you want to explore with this more, change the value of the array `zs` to the values used in any of the charts above and rerun the cell to see the result."
    ]
@@ -1707,16 +1638,6 @@
     "collapsed": false
    },
    "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x8b6b8d0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/plain": [
@@ -1726,6 +1647,16 @@
      "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x77bb4a8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
@@ -1786,9 +1717,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7845e80>"
+       "<matplotlib.figure.Figure at 0x7b28438>"
       ]
      },
      "metadata": {},
@@ -1839,9 +1770,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9504f28>"
+       "<matplotlib.figure.Figure at 0x7ac3eb8>"
       ]
      },
      "metadata": {},
@@ -1870,9 +1801,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x781c518>"
+       "<matplotlib.figure.Figure at 0x7693550>"
       ]
      },
      "metadata": {},
@@ -1903,9 +1834,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x776ea90>"
+       "<matplotlib.figure.Figure at 0x7a705c0>"
       ]
      },
      "metadata": {},
@@ -1953,9 +1884,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6eb71d0>"
+       "<matplotlib.figure.Figure at 0x8ba99e8>"
       ]
      },
      "metadata": {},
@@ -1984,9 +1915,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7645128>"
+       "<matplotlib.figure.Figure at 0x787ce48>"
       ]
      },
      "metadata": {},

04_Gaussians.ipynb

@@ -109,7 +109,7 @@
        "        color: #1d3b84;\n",
        "        font-size: 16pt;\n",
        "        margin-bottom: 0em;\n",
-       "        margin-top: 1.5em;\n",
+       "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "        white-space: nowrap;\n",
        "    }\n",
@@ -133,6 +133,11 @@
        "        overflow-y: scroll;\n",
        "        max-height: 50000px;\n",
        "    }\n",
+       "    div.output_wrapper{\n",
+       "        margin-top:0.2em;\n",
+       "        margin-bottom:0.2em;\n",
+       "}\n",
+       "\n",
        "    code{\n",
        "      font-size: 70%;\n",
        "    }\n",
@@ -253,6 +258,8 @@
    "source": [
     "#format the book\n",
     "%matplotlib inline\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2 \n",
     "from __future__ import division, print_function\n",
     "from book_format import load_style, set_figsize, figsize\n",
     "load_style()"
@@ -271,6 +278,7 @@
    "source": [
     "The last chapter ended by discussing some of the drawbacks of the Discrete Bayesian filter. For many tracking and filtering problems our desire is to have a filter that is *unimodal* and *continuous*. That is, we want to model our system using floating point math (continuous) and to have only one belief represented (unimodal). For example, we want to say an aircraft is at (12.34, -95.54, 2389.5) where that is latitude, longitude, and altitude. We do not want our filter to tell us \"it *might be* at (1.65, -78.01, 2100.45) or it *might be* at (34.36, -98.23, 2543.79).\" That doesn't match our physical intuition of how the world works, and as we discussed, it can be prohibitively expensive to compute the multimodal case. \n",
     "\n",
+    "\n",
     ">So we desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is very computationally efficient to calculate. As you might guess from the chapter name, Gaussian distributions provide all of these features."
    ]
   },
@@ -282,23 +290,26 @@
     "\n",
     "### Random Variables\n",
     "\n",
-    "To understand Gaussians we first need to understand a few simple mathematical definitions and computations.\n",
-    "\n",
     "To understand Gaussians we first need to understand a few simple mathematical computations. We start with a *random variable* x. Maybe x is the height of the students in a class in meters. We call $x$ *random* because the height of one student does not depend on the height of another student - each is independent. For a specific classrom perhaps the heights are\n",
     "\n",
     "$$x= [1.8, 2.0, 1.7, 1.9, 1.6]$$\n",
     "\n",
     "Another example of a random variable would be the result of a coin toss. Each coin toss is independent from all other tosses. Rolling a die would be another example of a random variable.\n",
     "\n",
-    "The coin toss and die roll are examples of *discrete random variables*. That is, the outcome of any given event comes from a discrete set of values. The roll of a six sided die can never produce a value of 7 or 3.24, for example. In contrast, the student heights are continuous; they can take on any value (within biological limits, naturally). For example, heights of 1.7, 1.71, 1.711, 1.7111, 1.71111,.... are all possible. Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, or 27 discrete choices. Nonetheless the heights can vary between any arbitrary real value between those ranges, and so it is continuous. \n",
-    "\n",
+    "The coin toss and die roll are examples of *discrete random variables*. That is, the outcome of any given event comes from a discrete set of values. The roll of a six sided die can never produce a value of 7 or 3.24, for example. In contrast, the student heights are continuous; they can take on any value (within biological limits, naturally). For example, heights of 1.7, 1.71, 1.711, 1.7111, 1.71111,.... are all possible. Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, or 27 discrete choices. Nonetheless the heights can vary between any arbitrary real value between those ranges, and so it is continuous. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "### The Mean of a Random Variable\n",
     "\n",
-    "We want to know the *average* height of the students. Another word for *average* is the *mean*.  We compute the mean by summing the values and dividing by the number of values. In this case we have\n",
+    "We want to know the *average* height of the students. We all know how to find the average, but let me belabor the point so I can introduce more formal notation and terminology. Another word for *average* is the *mean*.  We compute the mean by summing the values and dividing by the number of values. In this case we have\n",
     "\n",
     "$$mean = (1.8 + 2.0 + 1.7 + 1.9 + 1.6)/5 = 1.8$$\n",
     "\n",
-    "In statistics we normally use the symbol $\\mu$ to denote the mean, so we could write \n",
+    "In statistics we use the symbol $\\mu$ to denote the mean, so we could write \n",
     "\n",
     "$$\\mu_x = 1.8$$\n",
     "\n",
@@ -306,7 +317,7 @@
     "\n",
     "$$ \\mu_x = \\frac{1}{n}\\sum^n_{i=1} x_i$$\n",
     "\n",
-    "NumPy has the function `numpy.mean()` which computes the mean for you."
+    "NumPy has the function `numpy.mean()` which computes the mean. We will put the heights of the students in the list `x`."
    ]
   },
   {
@@ -380,7 +391,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n",
+    "All three classes have the same mean height of 1.8 meters. So the mean tells us something about the data, but it does not tell the whole story. We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n",
     "\n",
     "Statistics has formalized this concept of measuring variation into the notion of *standard deviation* and *variance*:\n",
     "\n",
@@ -404,8 +415,6 @@
     "\\sigma_x&= 0.1414\n",
     "\\end{aligned}$$\n",
     "\n",
-    "We use the symbol $\\sigma$ to denote the standard deviation.\n",
-    "\n",
     "We can verify this computation with the NumPy method `std()` which computes the standard deviation."
    ]
   },
@@ -432,7 +441,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "What does this number *mean* (no pun intended)? *How much* in \"how much do the heights vary\" is not a mathematical term. We will be able to define it much more precisely once we introduce the concept of a Gaussian in the next section. For now I'll say that for many things in nature, including the height of people, 68% of all values lie within one standard deviation of the mean. In other words we can conclude that for a random class 68% of the students will have heights between 1.66 (1.8-0.1414) meters and 1.94 (1.8+0.1414) meters. \n",
+    "What does the standard deviation *signify*? It tells us \"how much\" the heights vary amongst themseves. *How much* is not a mathematical term. We will be able to define it much more precisely once we introduce the concept of a Gaussian in the next section. For now I'll say that for many things in nature, including the height of people, 68% of all values lie within one standard deviation of the mean. In other words we can conclude that for a random class 68% of the students will have heights between 1.66 (1.8-0.1414) meters and 1.94 (1.8+0.1414) meters. \n",
     "\n",
     "We can look at this in a plot:"
    ]
@@ -446,9 +455,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAC1CAYAAAA9WRuxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e2ce48>"
+       "<matplotlib.figure.Figure at 0x71ea3c8>"
       ]
      },
      "metadata": {},
@@ -457,31 +466,18 @@
    ],
    "source": [
     "import matplotlib.pyplot as plt\n",
-    "\n",
-    "def plot_height_std(x, lw=10):\n",
-    "    m = np.mean(x)\n",
-    "    s = np.std(x)\n",
-    "\n",
-    "    for i, height in enumerate(x):\n",
-    "        plt.plot([i+1, i+1], [0, height], color='k', lw=lw)\n",
-    "    plt.xlim(0,len(x)+1)\n",
-    "    plt.axhline(m-s, ls='--')\n",
-    "    plt.axhline(m+s, ls='--')\n",
-    "    plt.fill_between((0, len(x)+1), m-s, m+s, \n",
-    "                     facecolor='yellow', alpha=0.4)\n",
-    "    plt.xlabel('student')\n",
-    "    plt.ylabel('height (m)')\n",
-    "    plt.show()\n",
+    "from gaussian_internal import plot_height_std\n",
     "    \n",
     "x= [1.8, 2.0, 1.7, 1.9, 1.6]\n",
-    "plot_height_std(x)"
+    "with figsize(y=2):\n",
+    "    plot_height_std(x)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "For only 5 students we obviously will not get exactly 68% within one standard deviation (normally denoted as $1\\sigma$), but we do see that 3 out of 5 students are within $1\\sigma$, or 60%, which is as close as you can get to 68% with only 5 samples. I haven't yet introduced enough math or Python for you to fully understand the next bit of code, but let's look at the results for a class with 100 students."
+    "For only 5 students we obviously will not get exactly 68% within one standard deviation (denoted as $1\\sigma$), but we do see that 3 out of 5 students are within $1\\sigma$, or 60%, which is as close as you can get to 68% with only 5 samples. I haven't yet introduced enough math or Python for you to fully understand the next bit of code, but let's look at the results for a class with 100 students."
    ]
   },
   {
@@ -493,9 +489,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAADxCAYAAACkjiOMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x5123358>"
+       "<matplotlib.figure.Figure at 0x7b0d470>"
       ]
      },
      "metadata": {},
@@ -505,14 +501,16 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "mean of x = 1.815\n",
-      "std of x = 0.144\n"
+      "mean of x = 1.787\n",
+      "std of x = 0.152\n"
      ]
     }
    ],
    "source": [
     "from numpy.random import randn\n",
     "x = [1.8 + .1414*randn() for i in range(100)]\n",
+    "\n",
+    "set_figsize(y=3.)\n",
     "plot_height_std(x, lw=2)\n",
     "\n",
     "print('mean of x = {:.3f}'.format(np.mean(x)))\n",
@@ -538,10 +536,7 @@
     "$$ \n",
     "\\begin{aligned}\n",
     "\\sigma_y &=\\sqrt{\\frac{(2.2-1.8)^2 + (1.5-1.8)^2 + (2.3-1.8)^2 + (1.7-1.8)^2 + (1.3-1.8)^2} {5}} \\\\\n",
-    "&= \\sqrt{\\frac{0.4^2 + (-0.3)^2 + 0.5^2 + (-0.1)^2 + (-0.5)^2}{5}} \\\\\n",
-    "&= \\sqrt{\\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5}} \\\\\n",
-    "&= \\sqrt{0.152} \\\\\n",
-    "\\sigma_y&= 0.39 \\ m\n",
+    "&= \\sqrt{0.152} = 0.39 \\ m\n",
     "\\end{aligned}$$\n",
     "\n",
     "We will verify that with NumPy with"
@@ -660,9 +655,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhkAAADPCAYAAABY4sOQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nACALkQEAZCEyAIAs/g+bDfLifky6YQAAAABJRU5ErkJggg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAACxCAYAAAALSUEOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ndAAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x772ea58>"
+       "<matplotlib.figure.Figure at 0x83f0be0>"
       ]
      },
      "metadata": {},
@@ -670,7 +665,7 @@
     }
    ],
    "source": [
-    "with figsize(8, 3):\n",
+    "with figsize(y=2.5):\n",
     "    x = [3, -3, 3, -3]\n",
     "    m = np.average(x)\n",
     "    for i in range(len(x)):\n",
@@ -691,9 +686,9 @@
     "\n",
     "This is clearly incorrect, as there is more than 0 variance in the data. \n",
     "\n",
-    "Maybe we can use the absolute value? We can see by inspection that the result is $12/4=3$ which is certainly correct - each value varies by 3 from the mean. But what if we change $x=[6, -2, -3, 1]$? In this case we get $12/4=3$. $x$ is clearly more spread out than in the last example, but we get the same variance, so this cannot be correct. If we use the correct formula we get a variance of 3.5, which correctly reflects the larger variatin in $x$.\n",
+    "Maybe we can use the absolute value? We can see by inspection that the result is $12/4=3$ which is certainly correct - each value varies by 3 from the mean. But what if we change $x=[6, -2, -3, 1]$? In this case we get $12/4=3$. $x$ is clearly more spread out than in the last example, but we get the same variance, so this cannot be correct. If we use the correct formula we get a variance of 3.5, which reflects the larger variation in $x$.\n",
     "\n",
-    "This is clearly not a proof of correctness; indeed, Gauss recognized that is is somewhat arbitrary. If the variable is distributed normally we can prove that the variance is computed by this function. If there are outliers, meaning values that are not normally distributed, than squaring the difference gives disproportinate weight to that term. For example, let's see what happens if we have $x = [1,-1,1,-2,3,2,100]$. I'll use NumPy's `var()` method to compute the variance for me."
+    "This is not a proof of correctness. Indeed, Carl Friedrich Gauss the inventor of the technique recognized that is is somewhat arbitrary. If there are outliers, then squaring the difference gives disproportionate weight to that term. For example, let's see what happens if we have $x = [1,-1,1,-2,3,2,100]$. I'll use NumPy's `var()` method to compute the variance for me."
    ]
   },
   {
@@ -720,7 +715,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Is this *correct*? You tell me. Without the outlier of 100 we get $\\sigma^2=2.89$, which accurately reflects how $x$ absent the outlier is varying. The one outlier swamps the computation. I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem. For Kalman filters, which assume Gaussian distributions, we can prove that squaring the terms produces optimal results. More about that soon."
+    "Is this *correct*? You tell me. Without the outlier of 100 we get $\\sigma^2=2.89$, which accurately reflects how $x$ is varying absent the outlier. The one outlier swamps the computation. I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem. For Kalman filters, which assume Gaussian distributions, we can prove that this computation produces optimal results. More about that soon."
    ]
   },
   {
@@ -743,7 +738,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Before we go into the math, lets just look at a graph of a Gaussian distribution to get a sense of what we are talking about."
+    "Let's look at a graph of a Gaussian distribution to get a sense of what we are talking about."
    ]
   },
   {
@@ -755,9 +750,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e12fd0>"
+       "<matplotlib.figure.Figure at 0x83f00f0>"
       ]
      },
      "metadata": {},
@@ -774,11 +769,35 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Probably this is immediately recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions most observations are distributed in such a manner. In fact, this is the bell curve the student heights given earlier. \n",
+    "Probably this is immediately recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions many observations are distributed in such a manner. In fact, this is the bell curve for the student heights given earlier. \n",
     "\n",
     "This curve is not unique to heights - a vast amount of natural phenomena exhibits this sort of distribution, including the sensors that we use in filtering problems. As we will see, it also has all the attributes that we are looking for - it represents a unimodal belief or value as a probability, it is continuous, and it is computationally efficient. We will soon discover that it also other desirable qualities that we do not yet recognize we need.\n",
     "\n",
-    "To further motivate you, recall the shapes of the probability distributions in the *Discrete Bayes* chapter. They were not perfect bell curves, but they were shaped somewhat like this - a tall center bar surrounded with shorter bars which get shorter the further away they are from the tall bar. We will be using Gaussians to replace the discrete probabilities used in that chapter!"
+    "To further motivate you, recall the shapes of the probability distributions in the *Discrete Bayes* chapter. They were not perfect bell curves, but they were shaped somewhat like this, as in the plot below. We will be using Gaussians to replace the discrete probabilities used in that chapter!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7b2b1d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import book_plots\n",
+    "with figsize(y=1.5):\n",
+    "    book_plots.bar_plot([ 0.,0., 0., 0.1, 0.15, 0.5, 0.2, .15, 0, 0])"
    ]
   },
   {
@@ -797,16 +816,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAukAAADxCAYAAAB23inUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7792908>"
+       "<matplotlib.figure.Figure at 0x827da90>"
       ]
      },
      "metadata": {},
@@ -814,7 +833,8 @@
     }
    ],
    "source": [
-    "plot_gaussian(mean=120, variance=17**2, xlabel='speed(kph)')"
+    "with figsize(y=3.):\n",
+    "    plot_gaussian(mean=120, variance=17**2, xlabel='speed(kph)')"
    ]
   },
   {
@@ -872,7 +892,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -880,9 +900,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuAAAADxCAYAAACKywIeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6ebd4a8>"
+       "<matplotlib.figure.Figure at 0x82f06d8>"
       ]
      },
      "metadata": {},
@@ -918,7 +938,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -970,7 +990,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
@@ -998,7 +1018,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1006,9 +1026,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8023908>"
+       "<matplotlib.figure.Figure at 0x84aad68>"
       ]
      },
      "metadata": {},
@@ -1047,16 +1067,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAr8AAADTCAYAAACIsHvmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x75e3eb8>"
+       "<matplotlib.figure.Figure at 0x8355208>"
       ]
      },
      "metadata": {},
@@ -1065,8 +1085,8 @@
    ],
    "source": [
     "from gaussian_internal import display_stddev_plot\n",
-    "display_stddev_plot()\n",
-    "plt.show()"
+    "with figsize(y=3):\n",
+    "    display_stddev_plot()"
    ]
   },
   {
@@ -1092,7 +1112,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
@@ -1101,7 +1121,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAADaCAYAAAB3s44kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9244898>"
+       "<matplotlib.figure.Figure at 0x9580470>"
       ]
      },
      "metadata": {},
@@ -1134,186 +1154,6 @@
     "<img src='animations/04_gaussian_animate.gif'>"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Plotting Exponentials (Optional)\n",
-    "\n",
-    "Where does the shape of the Gaussian come from? Recall the equation for the Gaussian:\n",
-    "\n",
-    "$$ f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 }$$\n",
-    "\n",
-    "$\\mu$ and $\\sigma$ are constants, so a simplified form of this equation is\n",
-    "\n",
-    "$$ \n",
-    "f(x, \\mu, \\sigma) = c_1 * e^{-c_2{(x-\\mu)^2} }\n",
-    "$$\n",
-    "\n",
-    "Let's just simplify it further by assuming the constants are one(not true for Gaussians, but the general shape will be the same) and the mean is zero.\n",
-    "\n",
-    "$$ \n",
-    "f(x)=e^{-x^2}\n",
-    "$$\n",
-    "\n",
-    "Raising a value to a negative power is the same as the reciprocal of the value raised to a positive power. I.e.\n",
-    "\n",
-    "$$e^{-x^2} = \\frac{1}{e^{x^2}}$$\n",
-    "\n",
-    "\n",
-    "Let's plot this in stages. Here is $e^{x^2}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x921dfd0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "x = np.arange(0, 3, 0.01)\n",
-    "plt.plot(x, np.exp(x**2))\n",
-    "plt.title('exp(x^2)')\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As x gets larger the value of $e^{x^2}$ grows exponentially (hence the name *exponential function*). If we take the reciprocal of a rapidly increasing number the result should approach, but never reach 0."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAADnCAYAAABbsTOlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x9440240>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.plot(x, 1/np.exp(x**2))\n",
-    "plt.title('exp(1/x^2)')\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We know that $1/e^x = e^{-x}$, so we can equivalently calculate"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x942e710>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.plot(x, np.exp(-x**2))\n",
-    "plt.title('exp(-x^2)')\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The final piece of the puzzle is to plot the values for -x as well."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x9389da0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "x = np.arange(-3, 3, 0.01)\n",
-    "plt.plot(x, np.exp(-x**2))\n",
-    "plt.title('exp(-x^2)')\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And with this we have the shape of the Gaussian. The Gaussian equation has different constants, and hence a somewhat different shape, but both are 'bell curves', as seen below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x768a6d8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "x = np.arange(-3, 3, 0.01)\n",
-    "plt.plot(x, np.exp(-x**2))\n",
-    "plot_gaussian(mean=0, variance=0.16, xlim=(-3,3))"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1350,7 +1190,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -1379,7 +1219,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
@@ -1412,7 +1252,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
@@ -1421,9 +1261,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 1.05751477 -1.71810667 -1.04164275  3.77628444  1.95256769  0.85021954\n",
-      "  3.05092585  1.81631717 -0.83092277  1.62226327 -0.91105988 -0.75027954\n",
-      "  2.92276957  5.99617367  4.84176047]\n"
+      "[ 1.11423749  4.39157757  4.1503389  -4.72602688  0.87441394  3.02216612\n",
+      "  1.68783969  2.62305797 -1.97748458  3.13669459  5.76477214  6.2583519\n",
+      "  1.6562668  -2.1690448  -1.78347529]\n"
      ]
     }
    ],
@@ -1440,7 +1280,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
@@ -1467,7 +1307,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
@@ -1515,7 +1355,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 25,
    "metadata": {
     "collapsed": false
    },
@@ -1524,7 +1364,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e75f28>"
+       "<matplotlib.figure.Figure at 0x9503eb8>"
       ]
      },
      "metadata": {},
@@ -1553,7 +1393,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false
    },
@@ -1574,16 +1414,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 27,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAADaCAYAAAAMl0zoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd8FVX6/z83DUIg9B5AekcJwbrr4u7XXdFdFtf2tbt+\n19XV39p72bgrunYMggpiAaWDoCIoiBQBgQRISALpIY000ntu+/1x78ydcmbmzNy5LTnvfbnkzpw5\n55kzZ8555jnPeY7F6XQ6wWAwGAwGg8FgMPxOWKAFYDAYDAaDwWAwuitMGWcwGAwGg8FgMAIEU8YZ\nDAaDwWAwGIwAwZRxBoPBYDAYDAYjQDBlnMFgMBgMBoPBCBBMGWcwGAwGg8FgMAIEU8YZDAaDwWAw\nGIwAoaqMHzhwAAsWLEBcXBzCwsKwatUq0fnGxkY8+OCDGDVqFHr16oUpU6bgvffe86nADAaDwWAw\nGAxGVyFC7WRLSwtmzZqFu+++G3fddRcsFovo/KOPPor9+/fjyy+/xNixY7F//37cd999GDRoEO64\n4w6fCs5gMBgMBoPBYIQ6FtodOPv06YNly5bhrrvu4o/NnDkTN954IxITE/lj8+bNw6xZs7BkyRLz\npWUwGAwGg8FgMLoQXvmMz58/H9988w1KS0sBAIcPH0ZqaiquueYaU4RjMBgMBoPBYDC6MqpuKlq8\n8cYbuOuuuzB69GhERLiyWrp0Ka699lpThGMwGAwGg8FgMLoyXinjTz75JI4ePYpvv/0WY8aMwf79\n+/HEE09gzJgx+MMf/iBK29DQ4JWgDAaDwWAwGAxGIOnbt6/peRpWxltaWpCUlIStW7fiuuuuAwDM\nmDEDqampePvtt2XKOIPBYDAYDAaDwRBj2Gfc6XTC6XQiLEycRVhYGCjXhDIYDAaDwWAwGN0azdCG\nubm5AACHw4GioiKkpqZi4MCBGDVqFH73u9/h2WefRe/evTF69Gjs378fX3zxBd566y3VQn1h4meE\nPikpKQCAhISEAEvCCGZYO2HQwNoJgwbWThg0+NrVWtUynpycjPj4eMTHx6O9vR2JiYmIj4/nQxmu\nWbMGl1xyCe644w5Mnz4db775JhYtWoSHHnrIp0IzGAwGg8FgMBhdAVXL+Lx58+BwOBTPDx48GCtX\nrjRdKAaDwWAwGAwGozvgVZxxBoPBYDAYDAaDYRymjDMYDAaDwWCEKMfO7MX6PcsCLQbDC5gyzmAw\nGAwGgxGi/Jy2A4czdgdaDIYXMGWcwWAwGAwGI1SxWAItAcNLmDLOYDAYDAaDwWAECKaMMxgMBoPB\nYIQoFjDLeKjDlHEGg8FgMBiMUIXp4iEPU8YZDAaDwWAwGIwAwZRxBoPBYDAYDAYjQDBlnNHtqG+u\nQVFFbqDFYDAYDAbDa5jPeOjDlHFGt2PV9+/inQ1PBVoMwxzO2IX0gmOBFoPBYDAYQQBTxkOfiEAL\nwGD4Hacz0BJ4xfo9H6B/70GYOe7iQIvCYDAYDAbDS1Qt4wcOHMCCBQsQFxeHsLAwrFq1SpYmJycH\nf/nLX9C/f3/ExMRgzpw5yMrK8pnADAaDwWAwGAxGV0FVGW9pacGsWbOQlJSE6OhoWCS7PBUWFuKK\nK67A+PHjsXfvXmRmZuLVV19F7969fSo0g+EVbLcyBoPBYHQVJEPaziPrYXfYAyNLiFNWXYiHkxb6\nvVxVN5X58+dj/vz5AIB77rlHdv6FF17ANddcg7feeos/dsEFF5gqIIPBkONEaLvaMBgMBsMcpD7j\nO4+ux2Uzrka/3gMDJFHoUtNYFZByDS/gdDgc2L59O6ZOnYprrrkGQ4YMwcUXX4yNGzeaKR+DYTpd\nwS7OVHEGg8Gx5/g2fLrjzUCLwQginCG+NipQSD1A/IXhBZxVVVVobm7Ga6+9hkWLFuHNN9/Enj17\ncPvtt6N379649tprFa9NSUkxWiyjG+Dr9tHU1OyXcnyJtbMzpOU3g+5+/ww6ukM72XdiOxrazneL\ne/UVoVx3Tc1NAMT3cOpUGmJ69A2USCFLSU0eAHl7mDhxok/LNayMOxwOAMDChQvx6KOPAgBmzZqF\nlJQULF26VFUZZzACSVdwGWc2DwaDwREoax4jOGChDU0kQFVpWBkfNGgQIiIiMG3aNNHxKVOmYMOG\nDarXJiQkGC2W0YXhvkR93T5+KfoaFQ2h2w5XHwKiIiNDVn5v8Vc7Yejn4aSFePSm/2LciKmBFqVb\ntZPdWatR3xoa99rS1oivDnyKO//waKBFAdA12snhs1tR2ei5h9WHXMbR/n0GB1iy0KNHgQN7z8jb\nQ0NDg0/LNewzHhUVhblz58rCGObk5OhexGm1daKlrdGoKAwNMgqS2cpqAV3BhsAWcDKCler68kCL\n0K2w222orC01fH1jS72J0mhTVJmL5Kx9fi2zO8Jcxo0RqFkGzdCGqampSE1NhcPhQFFREVJTU1FS\nUgIAePrpp7FhwwZ8/PHHyMvLw8cff4wNGzbgoYce0iXEuj3L8NyKu4zfBUOVFd++irzSjECLwTAT\n1tEyghbWOP3Jz6d2wuF0GL7+xZX3+FUhZwsLGQw5qsp4cnIy4uPjER8fj/b2diQmJiI+Ph6JiYkA\ngD//+c9YsWIF3n77bcyaNQvLli3DF198wYdDpKWu6bzxO2Aw9ML8KxkMRhehw9rudR42u9UESRgB\ng41pIY+qz/i8efP4hZpK3H333bj77rtNFYoB1DRUwu6wYUj/kYEWxWdU15djcL/hfi+XLXZhMHwH\nM3x2DRpb6tAjsid6REUHWhSGBuQxjb2IRgjUYmjDPuNm4stbb+toCeqv/rU/LkV2cZrs+Nvrn8Si\n1frcfUKNV1b9wxSrTnfgZO5hFFXk8L+DxWfc6XRiz/FtgRaDwQgKahur0NreHGgxDCDvT15c+Ves\n+mFxAGRhMLRp72xDVd25QIthGkGhjPtSrXjmo9uxZd9KH5bgHUcyf8SRzB9lx4P5A8JMAuI/GIKG\n8c92vIl1ez7QdY3V1olNe1f4SCIXTqcDXx/83KdlMACHw4631z0ZaDEYGrz82d/xyXdvBFoMIg6n\nA1V1ZcRzSh/3jc21vhSJwTDM5n0rsGj1g17nsyt5M5Kz9psgkXcEhTLua2oaKwMtQsBhcWhDF+IH\nC8VHTHX9Ofx8aocPJGKYSXZxmubsgs1hQ3FVnp8kImO1WbFlv7ZhI1hmbQBg9aFFsNttfi2ztSM4\nLePp+cd0z7Y6YHxhKMPDhp8+gtXW6bP8yU4qwfMe+oL2zlZT8tl++Et8d/hLU/LyhqBQxn2uJga5\nImr0lalUsHIw1Ak1n/Gs4lTXH7pnEfx3nyxCgnG2/7ImJGYXzjeUY3/q9kCLoRu7s2uHdaV9yzus\nbconlV5f9lqbwqH071HfXOO7AoJcxwl2hM28W/uM+5ygVxTE8n247T+avtR1TdV4NQh8yu12Gxpb\n6gIthj5CrOP6cNu/ZcdoWrQ/OhW9b9b5hgqfyBHS0PRPPujCqurKUFFbQp1eazF/sBJqH9++ptPa\nQZ3W6UXIRIYLzlARFdnDZ2WEchvPK8sMvFtuEOiIAVPGvzm4Gm+vfypQxQc1Z4pOaKax+XnqVYmd\nR9fjxZV/DbQYugjljouDbgrSD/fp7sRo5CmuzMN/Pn8AAFBYnoXC8iyNK7oHgZpVeHPdE3jti39S\np3fQWpiDYGBjKPPkB7cgszCFKq0v2mZ3m0Xj3FMs/la3QqSal2x+ASdyDgZUBvH41c0s45lnU1Bc\nmeufwoLcEmqkcwoWH/CGULOKM3wDRRu22jwWucUbn8Xijc/6UqKQgeZDhktD21fklJzCpzveVM9T\np6Wb1jIefDpAcPSVwURDi3hhplIb7Op+xxx2hw25pem6rrHarGjr0PZbtjuCw3AWzAR61i0YWnlw\nuKkEiWLJMEAIWjlCtbWJBkaKevfHa9VdBmtfQlWHOmYgAOB49s9IzT3sjVgypLs8rvr+XXy+821T\nyzCT7maB1Qdd5xCoOmxua0SDHyO55FWm4f0tL+m6Zt2PS/HMR7dppvO8sz6sy1Ad1IIFQTtnPuM+\nJNjdEoJZoaltrFY9H8yyK9JNPv782e7NaAW5pRleR75oam0IvR199biMCwYNrxUlnc1D6j98Iueg\nwvRysPUJvpenobmWfx7BPt6QUGpLgerf39v0HBI/u89v5Rm5z6p6fTGufVmXpDYXkmNzgAiGuuoW\nynjQ45d2oH+AKKrIxcsGO8SG5lo8nLTQ0LW+xp+D5cNJC2VTwl0Jfgw3wYL2/pYXcTL3EADX7qwb\nf/pIdD4la79mm1r61UtI/PRvXsuy9+Q3KK0u8DofGqjcVHjLuAurzYpHllyPsupCH0omRmoZDxZX\nOSX8NcCu+OZVvPTJvQH3e9UD7ZMLpGXc4fBfFByfjgmB1/MYWgTBM2LKeIjiTedxMvcw3t34jGY6\nmt0xlTprn4ZxCjHaOlpMz5Oq7whyZYnUhi0WV5eUmvcLDqZ/LzpHoxy3tDeZItvWA5/ix5SvRMcc\nDrtPYkjTKDxOLt6zO63D7Yf6xtrHNK9dtPohxc1e9CD169SrjOeXnUbBOdei3db2Zt0f69X15cgp\nUffrrW2sxrnzZ0XHfK2UZxQmAwAaWgLU5xl5zymvCYQybvejEs5xtGCn7wvxc1UyNy16gt4yfuDA\nASxYsABxcXEICwvDqlWrFNPef//9CAsLwzvvvGO6kP7mg60va7pnmIm/G0JOySmcLc82JS+lFz7Y\nrWb+RG+f2NbRqsuaXllbSnwO/nkC+nyZtYgIj5Ad++nENlhtgd+R9seUr/DsR3eYn7GO0Ia09Sx8\n/arqylBUKd8wSO8HvdRNJUxh+FDqE5I2P48lW14AYGxjnC93JWHpV+p+vR9u+zdeXLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e33208>"
+       "<matplotlib.figure.Figure at 0x84b4470>"
       ]
      },
      "metadata": {},
@@ -1607,7 +1447,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 28,
    "metadata": {
     "collapsed": false
    },
@@ -1627,16 +1467,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAADaCAYAAAAMl0zoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x779ff98>"
+       "<matplotlib.figure.Figure at 0x7b4eba8>"
       ]
      },
      "metadata": {},

05_Kalman_Filters.ipynb

@@ -109,7 +109,7 @@
        "        color: #1d3b84;\n",
        "        font-size: 16pt;\n",
        "        margin-bottom: 0em;\n",
-       "        margin-top: 1.5em;\n",
+       "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "        white-space: nowrap;\n",
        "    }\n",
@@ -133,6 +133,11 @@
        "        overflow-y: scroll;\n",
        "        max-height: 50000px;\n",
        "    }\n",
+       "    div.output_wrapper{\n",
+       "        margin-top:0.2em;\n",
+       "        margin-bottom:0.2em;\n",
+       "}\n",
+       "\n",
        "    code{\n",
        "      font-size: 70%;\n",
        "    }\n",
@@ -253,6 +258,8 @@
    "source": [
     "#format the book\n",
     "%matplotlib inline\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2\n",
     "from __future__ import division, print_function\n",
     "from book_format import load_style, figsize\n",
     "load_style()"
@@ -347,10 +354,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      " 0.3995\t-0.7489\t-0.3729\t-0.2535\t 0.2941\t\n",
-      "-1.7145\t-0.7816\t 1.2143\t 1.2930\t-0.1405\t\n",
-      "-0.6533\t-1.7633\t-0.9005\t-0.2530\t 0.8972\t\n",
-      " 1.0882\t-0.4164\t 1.3602\t-0.5687\t 1.5670\t\n"
+      " 1.1006\t-0.2120\t-0.4838\t 0.3862\t 0.8021\t\n",
+      "-0.2236\t 1.1977\t-1.5618\t 1.5419\t 2.1203\t\n",
+      "-0.2861\t-1.1764\t-0.0429\t 0.5016\t 0.2213\t\n",
+      " 1.0790\t 0.7600\t 1.5109\t-1.0479\t 1.0137\t\n"
      ]
     }
    ],
@@ -386,9 +393,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74669e8>"
+       "<matplotlib.figure.Figure at 0x6bf21d0>"
       ]
      },
      "metadata": {},
@@ -397,10 +404,8 @@
    ],
    "source": [
     "import matplotlib.pyplot as plt\n",
-    "import matplotlib.pylab as pylab\n",
     "import book_plots as bp\n",
     "\n",
-    "\n",
     "dog = DogSensor(measurement_variance=0.0)\n",
     "xs = []\n",
     "for i in range(10):\n",
@@ -408,7 +413,7 @@
     "    xs.append(x)\n",
     "    print(\"%.4f\" % x, end=' '),\n",
     "bp.plot_track(xs, label='dog position')\n",
-    "plt.legend(loc='best')\n",
+    "bp.show_legend()\n",
     "plt.show()"
    ]
   },
@@ -430,9 +435,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7451f98>"
+       "<matplotlib.figure.Figure at 0x6c71a20>"
       ]
      },
      "metadata": {},
@@ -445,18 +450,18 @@
     "                    process_variance=process_var)\n",
     "\n",
     "    xs = []\n",
-    "    for i in range(100):\n",
+    "    for i in range(50):\n",
     "        x = dog.sense_position()\n",
     "        xs.append(x)\n",
     "\n",
-    "    bp.plot_track([0, 99], [1, 100])\n",
+    "    bp.plot_track([0, 49], [1, 50])\n",
     "    bp.plot_measurements(xs, label='Sensor')\n",
     "    plt.xlabel('time')\n",
     "    plt.ylabel('pos')\n",
-    "    plt.ylim([0, 100])\n",
+    "    plt.ylim([0, 50])\n",
     "    plt.title('variance = {}, process variance = {}'.format(\n",
     "              measurement_var, process_var))\n",
-    "    plt.legend(loc='best')\n",
+    "    bp.show_legend()\n",
     "    plt.show()\n",
     "\n",
     "test_sensor(measurement_var=4.0)"
@@ -485,9 +490,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74dc630>"
+       "<matplotlib.figure.Figure at 0x6bf20b8>"
       ]
      },
      "metadata": {},
@@ -507,9 +512,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7bd2be0>"
+       "<matplotlib.figure.Figure at 0x73fcc18>"
       ]
      },
      "metadata": {},
@@ -538,9 +543,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ce00f0>"
+       "<matplotlib.figure.Figure at 0x76a0d30>"
       ]
      },
      "metadata": {},
@@ -571,9 +576,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cef1d0>"
+       "<matplotlib.figure.Figure at 0x76a0668>"
       ]
      },
      "metadata": {},
@@ -609,7 +614,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7dbb7f0>"
+       "<matplotlib.figure.Figure at 0x79db828>"
       ]
      },
      "metadata": {},
@@ -644,9 +649,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cc95f8>"
+       "<matplotlib.figure.Figure at 0x75b6898>"
       ]
      },
      "metadata": {},
@@ -658,7 +663,7 @@
     "                measurement_variance=5, process_variance=0.0)\n",
     "xs = range(100)\n",
     "ys = []\n",
-    "for i in xs:\n",
+    "for _ in xs:\n",
     "    ys.append(dog.sense_position())\n",
     "               \n",
     "bp.plot_track(xs, ys, label='Dog position')\n",
@@ -732,9 +737,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAEWCAYAAADiqu8oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VMXbxvHv7qaQBAg9EEAIXYqUhBaRIogU/SEWqgqI\nCKhIB6PYEZAuKCAWQEBABUWBV0AlIEUhYpAqaKhCAqGElrp73j+igXWTENJ2k9yf68plzsycc57N\nGLLPzpwZk2EYBiIiIiIiIuJUZmcHICIiIiIiIkrOREREREREXIKSMxEREREREReg5ExERERERMQF\nKDkTERERERFxAUrOREREREREXICSMxEREREREReQoeRszpw5BAQE4OXlRVBQEFu3bk2z7YEDB2jT\npg1ly5bFy8uLqlWr8vLLL5OYmGjXbvPmzQQGBqa0+eCDD7L2SkRERERERPKwWyZnK1asYNiwYYwb\nN47w8HCCg4Pp2LEjJ0+eTLW9p6cn/fr1Y+PGjRw+fJiZM2fy8ccf89JLL6W0OXr0KJ06daJFixaE\nh4cTEhLCkCFDWLVqVfa9MhERERERkTzEZBiGkV6Dpk2b0qBBA7uRrRo1avDoo48yYcKEDN1kxIgR\n/Pzzz2zfvh2AsWPH8vXXX/PHH3+ktBkwYAD79+9PaSMiIiIiIlKQpDtylpCQwO7du2nfvr1defv2\n7TOcRP3555+sX7/e7ho7duxI9ZphYWFYrdaMxi4iIiIiIpJvpJucRUdHY7Va8fPzsysvU6YMkZGR\n6V44ODgYLy8vatSoQdOmTXn99ddT6qKiohyu6efnR1JSEtHR0bf5EkRERERERPI+t5y68Oeff87V\nq1cJDw9n9OjRjBkzhsmTJ9/WNWJiYnIoOhERERGRnOfr6+vsECQPSTc5K1WqFBaLhaioKLvyqKgo\nypUrl+6FK1SoAECtWrWwWq089dRTTJw4EYvFQtmyZR1G3qKionBzc6NUqVKZeR0iIiIiIiJ5WrrT\nGj08PAgMDGTDhg125Rs3biQ4ODjDN7FardhsNmw2GwDNmzdn48aNDtds3LgxFoslw9cVERERERHJ\nL245rXHEiBE88cQTNGnShODgYObNm0dkZCSDBg0CICQkhF27dvH9998DsHjxYry8vKhbty4eHh6E\nhYXx0ksv0b17d9zd3QEYNGgQ7733HsOHD+eZZ55h27ZtLFq0iOXLl6cZh4aEnSssLAyAoKAgJ0dS\nsKkfXIf6wjWoH1yH+sI1qB9cgx7Nkcy6ZXLWrVs3zp8/z/jx4zlz5gz16tVj3bp1VKxYEYDIyEgi\nIiJS2ru7uzNx4kSOHDmCYRhUqlSJ559/nuHDh6e0qVy5MuvWrWP48OHMnTuX8uXLM3v2bLp27ZoD\nL1FERERERMT1ZWhBkMGDBzN48OBU6xYsWGB33KNHD3r06HHLa7Zs2ZJff/01I7cXERERERHJ99J9\n5kxERERERERyh5IzERERERERF6DkTERERERExAUoORMREREREXEBSs5ERERERERcgJIzERERERER\nF6DkTERERERExAUoORMREREREXEBSs5ERERERERcgJIzERERERERF6DkTERERERExAUoORMRERER\nEXEBSs5ERERERERcgJIzERERERERF6DkTERERERExAUoORMREREREXEBSs5ERERERERcgJIzERER\nERERF6DkTERERERExAUoORMREREREXEBSs5ERERERERcgJIzERERERERF6DkTERERERExAUoORMR\nEREREXEBSs5ERERERERcgJIzERERERERF6DkTERERERExAUoORMREREREXEBSs5ERERERERcQIaS\nszlz5hAQEICXlxdBQUFs3bo1zbahoaF06dIFf39/fHx8qF+/PgsWLHBoYzabHb4OHz6ctVcjIiIi\nIiKSR90yOVuxYgXDhg1j3LhxhIeHExwcTMeOHTl58mSq7Xfs2EH9+vVZuXIl+/fvZ/DgwTzzzDMs\nW7bMoe2BAweIjIxM+apWrVrWX5GIiGTYvgiDo6cNrl43MAzD2eGIiIgUaG63ajB9+nT69etH//79\nAZg1axbfffcdc+fOZcKECQ7tQ0JC7I4HDRrEpk2bWLlyJT179rSrK126NCVLlsxK/CIikobL1wy2\n74X4ROhyjynVNvcPgzPnk78v5AGlixtU8YeJg6BZ3dTPERERkZyR7shZQkICu3fvpn379nbl7du3\nZ/v27Rm+SUxMDCVKlHAoDwoKwt/fn3bt2hEaGprh64mISOoOnzAImWvQpL9BiQ7QaSS8Mj/1toZh\nEB1z4zguAU5GwebfwLtQ7sQrIiIiN6Q7chYdHY3VasXPz8+uvEyZMkRGRmboBmvWrOHHH3+0S+b8\n/f2ZN28ejRs3Jj4+nsWLF9O2bVs2b95MixYtMvEyRETkhzCD+4Y6lu+LgOhLBqWK2Y+ExVyFxCTH\n9iWKQt0qqd/jnSUGNe+AB4LBzU0jayIiItnpltMas2Lbtm307t2b2bNnExQUlFJeo0YNatSokXLc\nrFkzjh07xpQpU9JMzsLCwnIyVMkg9YNrUD+4DlfqC+8kE8UL1+PiVXeHuoWr/qT1XTF2Zedi3KlR\nvhqXrrpx8aobidbkyRR1K11i9+6/HK5x4Yobr8yvR5LVTGnfBLoGR9OjdRSFC9ly5gXdBlfqh4JO\nfeEa1A/OVb16dWeHIHlUuslZqVKlsFgsREVF2ZVHRUVRrly5dC+8detWOnfuzFtvvcXAgQNvGUiT\nJk1YsWJFBkIWESnYkqzgZnEsd3czeLDpeT79oWxKWYBfLA2qXsWveKJD+9K+iSwZcxAAw4Br8WbO\nx7hjM1IfEfv2l5Ik/ZPAnYvxYP7/+fPlT6UZ0PE0XYOjMWtzFhERkSxJNznz8PAgMDCQDRs28Mgj\nj6SUb9y4kcceeyzN87Zs2cIDDzzAm2++yQsvvJChQMLDw/H390+z/uaRN8l9/34Cp35wLvWD63BG\nXxiGwcpQCJkLH74IrRs5JlGvlDX46xz0fwA6BUOZ4t6AN1AmS/e22Qx6vONYfuGqO9sPV2LC0EqY\nTLk/zVG/E65DfeEa1A+uISYm5taNRFJxy2mNI0aM4IknnqBJkyYEBwczb948IiMjGTRoEJC8OuOu\nXbv4/vvvgeQ9zDp37szzzz9Pz549U55Ns1gslC5dGoCZM2cSEBBA7dq1SUhIYMmSJaxevZpVq1bl\n1OsUEcnTDp8weHoibP09+XjUe7DzIwOz2T4hqlrBxE9zs//+ZrOJz8cbfLAaPtsA12Jv1E15Hqck\nZiIiIvnNLZOzbt26cf78ecaPH8+ZM2eoV68e69ato2LFigBERkYSERGR0n7RokXExcUxZcoUpkyZ\nklJeuXLllHaJiYmMHj2aU6dO4eXlRd26dVm3bh0dOnTI7tcnIpKnGYbB/NUwcjZcj7tRvvsPWLIe\nnuyYe7E0qmnigzEw5TmDactg6mfwUEtoUluJmYiISHYwGS686+jNQ8K+vr5OjEQ0TcI1qB9cR271\nxbEzBrV7JS9zfzOLBcb1hdeecl5i9Pc5AxPgX9oxhth4g9c/hpAnoFiRnItRvxOuQ33hGtQPrkHv\nYSWz9Pi2iIgLq1zOxOTn7Ms6NoPfP3VuYgZQvrQp1cQM4MW5MGUp1O8Dobtd9jNAERERl6LkTETE\nxT33CHRoBj5e8FEIrJkKd1Z23amE638xmP1F8vcno6DdUJi5wsCFJ2qIiIi4hBzd50xERDLOMIxU\nF9YwmUx88pLB1VioVsF1k7J/vfu5/bHNBiNmwR8nYNZwA3dtXi0iIpIqjZyJiLiAsxcN2g6BTb+m\nPrpUtqQpTyRmAF9NhJE94b955r4IsFqdE5OIiEheoORMRMTJDhw1aDYAQn+DR19OXjY/L/P0MDHl\neRNrpkAR7+SyAH9YNQEKeeaNBFNERMQZlJyJiDjRtt8NggfCsTPJxxevwINj4MLlvJ2gAXRsbmLb\nB3BXNfh2MpQursRMREQkPXrmTETESUJ3Gzw4xn5DZ4A7/CC/pDF1q5jYvcBxs2wRERFxpJEzEREn\nOXbGMTEb0AXWTYPiRfNPMpNWYmazGQx/12DHvrw/SigiIpIdlJyJiDhJ384m5o6+cfzmAJg3mgKx\nmqFhGAyZkbyy4/3D4KdwJWgiIiKa1igi4kQDHzKRmGQQGw+je+f/pAySE7MRs2DuquTjq7HQcSR8\nM9ng3sCC8TMQERFJjZIzEREne/7RgpWQmEwmihexHym7HgcPjIINMw1a1C9YPw8REZF/aVqjiEgu\n2HXQ4M9Tmrr3r1efMjFhkH1ZXAIMmZ78LJqIiEhBpORMRCSHHTxm0HEEtBgEvx1W4vGvF58wMXXI\njeM6AfDtlLQXEBEREcnvNK1RRCQHnYwyuH84XLicfNz6OVj9jkHrRkpAAEb0MHE9zuD/diQnZiXy\n0SqVIiIit0sjZyIiOeR8THJidursjbIr12FzuPNickUv94EfZysxExERUXImIpID4uINHhgFh47b\nlz/TBV7t55yYXJXJZMLTI+3EzDA0FVRERAoGJWciIjnA0wM6NLcve6Q1vD8yORmRWzMMg7cXGQye\nogRNREQKBj1zJiKSA0wmE689BbUrG/QdD83rwpLXwGJRYpYRsfEGAybCZxuTj++sDEO7OTUkERGR\nHKfkTEQkBz12r4nqFQyqlCfdqXtir/8EWP79jeORs6HmHQYdmulnKCIi+ZemNYqI5LAGNUwU9VFS\ncTte7gNFvG8c22zQ49XkbQlERETyKyVnIiLZ4PQ5g+ORShyyS50qJpa/Ceab/kpdvgaDJuv5MxER\nyb+UnImIZFFcvMFDL0LTp2H7XiUO2aVjcxNTnrtx3KgmfPaGFlQREZH8S8+ciYhk0Line truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74668d0>"
+       "<matplotlib.figure.Figure at 0x75ca630>"
       ]
      },
      "metadata": {},
@@ -765,9 +770,9 @@
     "plt.plot(xs, ys, label='original')\n",
     "\n",
     "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
-    "plt.plot(xs, ys, label='multiply')\n",
+    "plt.plot(xs, ys, label='multiply', ls='--')\n",
     "\n",
-    "plt.legend(loc='best')\n",
+    "bp.show_legend()\n",
     "plt.show()"
    ]
   },
@@ -793,9 +798,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7491b70>"
+       "<matplotlib.figure.Figure at 0x75cefd0>"
       ]
      },
      "metadata": {},
@@ -816,7 +821,7 @@
     "plt.plot(xs, ys, label='measure 2')\n",
     "\n",
     "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
-    "plt.plot(xs, ys, label='multiply')\n",
+    "plt.plot(xs, ys, label='multiply', ls='--')\n",
     "plt.legend()\n",
     "plt.show()"
    ]
@@ -845,9 +850,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x861a3c8>"
+       "<matplotlib.figure.Figure at 0x7631c88>"
       ]
      },
      "metadata": {},
@@ -868,7 +873,7 @@
     "plt.plot(xs, ys, label='measure 2')\n",
     "\n",
     "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
-    "plt.plot(xs, ys, label='multiply')\n",
+    "plt.plot(xs, ys, label='multiply', ls='--')\n",
     "plt.legend()\n",
     "plt.show()"
    ]
@@ -881,6 +886,8 @@
     "\n",
     "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
     "\n",
+    "Of course, this example is quite exaggerated. The width of the Gaussians is fairly narrow, so this combination of measurements is quite unlikely. It is hard to eyeball this, but the measurements are well over $3\\sigma$ apart, so the probability of this happening is less than 1%. Still, it can happen, and the math is correct. \n",
+    "\n",
     "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
     "\n",
     "$$\n",
@@ -973,26 +980,26 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "time: 0 \tposition = 3.566 \tvariance = 2.500\n",
-      "time: 1 \tposition = 2.147 \tvariance = 1.667\n",
-      "time: 2 \tposition = 2.152 \tvariance = 1.250\n",
-      "time: 3 \tposition = 1.261 \tvariance = 1.000\n",
-      "time: 4 \tposition = 0.745 \tvariance = 0.833\n",
-      "time: 5 \tposition = 0.796 \tvariance = 0.714\n",
-      "time: 6 \tposition = 0.638 \tvariance = 0.625\n",
-      "time: 7 \tposition = 0.722 \tvariance = 0.556\n",
-      "time: 8 \tposition = 0.871 \tvariance = 0.500\n",
-      "time: 9 \tposition = 0.973 \tvariance = 0.455\n",
-      "time: 10 \tposition = 0.898 \tvariance = 0.417\n",
-      "time: 11 \tposition = 0.817 \tvariance = 0.385\n",
-      "time: 12 \tposition = 0.965 \tvariance = 0.357\n",
-      "time: 13 \tposition = 0.445 \tvariance = 0.333\n",
-      "time: 14 \tposition = 0.360 \tvariance = 0.312\n",
-      "time: 15 \tposition = 0.384 \tvariance = 0.294\n",
-      "time: 16 \tposition = 0.470 \tvariance = 0.278\n",
-      "time: 17 \tposition = 0.445 \tvariance = 0.263\n",
-      "time: 18 \tposition = 0.292 \tvariance = 0.250\n",
-      "time: 19 \tposition = 0.457 \tvariance = 0.238\n"
+      "time: 0 \tposition = 1.074 \tvariance = 2.500\n",
+      "time: 1 \tposition = 1.349 \tvariance = 1.667\n",
+      "time: 2 \tposition = 0.307 \tvariance = 1.250\n",
+      "time: 3 \tposition = -0.297 \tvariance = 1.000\n",
+      "time: 4 \tposition = 0.058 \tvariance = 0.833\n",
+      "time: 5 \tposition = 0.634 \tvariance = 0.714\n",
+      "time: 6 \tposition = 0.548 \tvariance = 0.625\n",
+      "time: 7 \tposition = 0.504 \tvariance = 0.556\n",
+      "time: 8 \tposition = 0.402 \tvariance = 0.500\n",
+      "time: 9 \tposition = 0.160 \tvariance = 0.455\n",
+      "time: 10 \tposition = 0.126 \tvariance = 0.417\n",
+      "time: 11 \tposition = 0.393 \tvariance = 0.385\n",
+      "time: 12 \tposition = 0.361 \tvariance = 0.357\n",
+      "time: 13 \tposition = 0.287 \tvariance = 0.333\n",
+      "time: 14 \tposition = 0.103 \tvariance = 0.312\n",
+      "time: 15 \tposition = 0.268 \tvariance = 0.294\n",
+      "time: 16 \tposition = 0.282 \tvariance = 0.278\n",
+      "time: 17 \tposition = 0.253 \tvariance = 0.263\n",
+      "time: 18 \tposition = 0.333 \tvariance = 0.250\n",
+      "time: 19 \tposition = 0.350 \tvariance = 0.238\n"
      ]
     }
    ],
@@ -1091,23 +1098,23 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "PREDICT:     1.0000   502.0000\tUPDATE:     4.0880     9.8047\n",
-      "PREDICT:     5.0880    11.8047\tUPDATE:     4.1639     5.4138\n",
-      "PREDICT:     5.1639     7.4138\tUPDATE:     6.8504     4.2574\n",
-      "PREDICT:     7.8504     6.2574\tUPDATE:    10.4530     3.8490\n",
-      "PREDICT:    11.4530     5.8490\tUPDATE:     9.5694     3.6904\n",
-      "PREDICT:    10.5694     5.6904\tUPDATE:     9.2446     3.6267\n",
-      "PREDICT:    10.2446     5.6267\tUPDATE:    10.7525     3.6007\n",
-      "PREDICT:    11.7525     5.6007\tUPDATE:     8.3439     3.5900\n",
-      "PREDICT:     9.3439     5.5900\tUPDATE:     8.8032     3.5856\n",
-      "PREDICT:     9.8032     5.5856\tUPDATE:     7.2800     3.5838\n"
+      "PREDICT:     1.0000   502.0000\tUPDATE:     5.9374     9.8047\n",
+      "PREDICT:     6.9374    11.8047\tUPDATE:     6.0781     5.4138\n",
+      "PREDICT:     7.0781     7.4138\tUPDATE:     4.6672     4.2574\n",
+      "PREDICT:     5.6672     6.2574\tUPDATE:     5.6747     3.8490\n",
+      "PREDICT:     6.6747     5.8490\tUPDATE:     6.1235     3.6904\n",
+      "PREDICT:     7.1235     5.6904\tUPDATE:     7.2806     3.6267\n",
+      "PREDICT:     8.2806     5.6267\tUPDATE:     8.4183     3.6007\n",
+      "PREDICT:     9.4183     5.6007\tUPDATE:    10.2644     3.5900\n",
+      "PREDICT:    11.2644     5.5900\tUPDATE:    13.1794     3.5856\n",
+      "PREDICT:    14.1794     5.5856\tUPDATE:    12.7885     3.5838\n"
      ]
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c0b048>"
+       "<matplotlib.figure.Figure at 0x7637198>"
       ]
      },
      "metadata": {},
@@ -1143,7 +1150,7 @@
     "    \n",
     "bp.plot_filter(ps)\n",
     "bp.plot_measurements(zs)\n",
-    "plt.legend(loc='best')\n",
+    "bp.show_legend()\n",
     "plt.show()"
    ]
   },
@@ -1233,7 +1240,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance."
+    "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance. The variance is plotted as a lightly shaded yellow area between dotted lines."
    ]
   },
   {
@@ -1245,19 +1252,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86395c0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x869c518>"
+       "<matplotlib.figure.Figure at 0x7637dd8>"
       ]
      },
      "metadata": {},
@@ -1267,16 +1264,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "102.0000 6.3099 4.6267 4.2812 4.1939\n",
-      "4.1708 4.1646 4.1629 4.1624 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n",
-      "4.1623 4.1623 4.1623 4.1623 4.1623\n"
+      "Variance:\n",
+      "\t2.5200 4.0428 3.6649 6.0266 5.8804\n",
+      "\t5.2240 6.3572 6.5137 7.9885 8.0157\n",
+      "\t9.6223 12.5884 13.0473 12.9739 12.8976\n",
+      "\t13.6351 16.7189 18.5777 18.9743 19.9421\n",
+      "\t20.6522 22.9380 24.0564 27.1851 25.4667\n"
      ]
     }
    ],
@@ -1286,33 +1279,31 @@
     "movement = 1\n",
     "movement_variance = 2\n",
     "sensor_variance = 4.5\n",
-    "pos = (0, 100)   # gaussian N(0,100)\n",
+    "pos = (0, 100)   # gaussian N(0, 100)\n",
     "\n",
     "dog = DogSensor(pos[0], velocity=movement, \n",
     "                measurement_variance=sensor_variance, \n",
     "                process_variance=0.5)\n",
     "\n",
-    "zs, ps, vs = [], [], []\n",
-    "for i in range(50):\n",
+    "zs, positions, variance = [], [], []\n",
+    "for i in range(25):\n",
     "    pos = predict(pos[0], pos[1], movement, movement_variance)    \n",
     "    Z = dog.sense_position()\n",
     "    zs.append(Z)\n",
-    "    vs.append(pos[1])\n",
+    "    variance.append(pos[1])\n",
     "    \n",
     "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
-    "    ps.append(pos[0])\n",
+    "    positions.append(pos[0])\n",
     "       \n",
     "bp.plot_measurements(zs)\n",
-    "bp.plot_filter(ps)\n",
-    "plt.legend(loc=2)\n",
+    "bp.plot_filter(positions, vars=variance)\n",
+    "bp.show_legend()\n",
     "plt.show()\n",
     "\n",
-    "plt.plot(vs)\n",
-    "plt.title('Variance')\n",
-    "plt.show()\n",
-    "\n",
-    "for i in range(0, len(vs), 5):\n",
-    "    print('{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(*[v for v in vs[i:i+5]]))"
+    "print('Variance:')\n",
+    "for i in range(0, len(positions), 5):\n",
+    "    print('\\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(\n",
+    "            *[v for v in positions[i:i+5]]))"
    ]
   },
   {
@@ -1588,9 +1579,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9768860>"
+       "<matplotlib.figure.Figure at 0x798c9e8>"
       ]
      },
      "metadata": {},
@@ -1600,7 +1591,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x97e3940>"
+       "<matplotlib.figure.Figure at 0x7aad7b8>"
       ]
      },
      "metadata": {},
@@ -1641,10 +1632,8 @@
     "\n",
     "# plot the filter output and the variance\n",
     "bp.plot_measurements(zs)\n",
-    "bp.plot_filter(estimates)\n",
-    "plt.legend(loc='best')\n",
-    "plt.xlim((0, N))\n",
-    "plt.ylim((0, 30))\n",
+    "bp.plot_filter(estimates, vars=ps)\n",
+    "bp.show_legend()\n",
     "plt.show()\n",
     "plt.plot(ps)\n",
     "plt.title('Variance')\n",
@@ -1656,7 +1645,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
+    "The first plot shows the individual sensor measurements vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
     "\n",
     "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The section **Explaining the Results - Multi-Sensor Fusion** explains why this happens."
    ]
@@ -1736,9 +1725,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEWCAYAAAAuFoLqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X9U1Fd+//HXMECUH5kV4swQxxBtUYhpOAaTKpuyUcFo\nY1WaNESbNubYuj1rPBJ2D43drLDWkq9Z4xc5mrTJHiMHasmPk5PNr2Op1TVB3Abpmh9as2Y19ojO\n+GN1AANoZ+b7R+p8HRkdcAY+w8zzcc6co3fu5/N5j1fgxZ0792Py+Xw+AQAAADBEgtEFAAAAAPGM\nQA4AAAAYiEAOAAAAGIhADgAAABiIQA4AAAAYiEAOAAAAGIhADgAAABhoUIH8+eefV0JCglauXBnQ\nXl1drXHjxiklJUUzZ87UoUOHAp7v6+vTypUrNXbsWKWlpWnhwoXq6OgIv3oAAABghBtwIP/Vr36l\nV199Vffcc49MJpO/ff369dq4caM2b96strY2Wa1WlZSUqLu729+nvLxcb7/9tpqamvTxxx+rs7NT\n8+fPl9frjeyrAQAAAEaYAQVyt9utJ554Qq+99prGjBnjb/f5fKqtrdXq1atVWlqqKVOmqL6+Xl1d\nXdq+fbv/2K1bt2rDhg2aPXu2pk6dqoaGBn322WfauXPn0LwqAAAAYIQYUCBfvny5/uzP/kzf+973\n5PP5/O3Hjh2Ty+XSnDlz/G2jRo1SUVGRWltbJUnt7e26fPlyQB+Hw6G8vDx/HwAAACBeJYbq8Oqr\nr+ro0aP+Ge+rl6s4nU5Jks1mCzjGarXq5MmT/j5ms1mZmZkBfWw2m1wuV3jVAwAAACPcDQP5l19+\nqR//+MdqaWmR2WyW9O0ylatnya/n6uA+UG63e9DHAAAAANHCYrEM+pgbLlnZt2+fzp49qylTpigp\nKUlJSUn66KOP9NJLLyk5OVm33XabJPWb6Xa5XLLb7ZIku90uj8ejc+fOBfRxOp3+PgAAAEC8umEg\nLy0t1RdffKFPP/1Un376qQ4cOKBp06Zp8eLFOnDggHJycmS329Xc3Ow/pre3Vy0tLSosLJQkFRQU\nKCkpKaDPiRMndPjwYX8fAAAAIF7dcMmKxWLpN+2ekpKiMWPG6K677pL07ZaGNTU1ys3NVU5Ojtat\nW6f09HQtWbLEf45ly5apsrJSVqtVGRkZqqioUH5+voqLi294bRhn//79kqRp06YZXEl8YxyiB2MR\nHRiH6MA4RA/GIjqEu+w65Ic6r2UymQLWh1dWVqqnp0crVqzQ+fPnNX36dDU3Nys1NdXfp7a2VomJ\niSorK1NPT4+Ki4vV2Nh4U+vMAQAAgFgy6EC+e/fufm1VVVWqqqq67jHJycmqq6tTXV3dYC8HAAAA\nxLQB36kTAAAAQOQRyAEAAAADEcgBAAAAAxHIAQAAAAMRyAEAAAADEcgBAAAAAxHIAQAAAAMRyAEA\nAAADEcgBAAAAAxHIAQAAAAMRyAEAAAADEcgBAAAAAxHIAQAAAAMRyAEAAAADEcgBAAAAAxHIAQAA\nAAMRyAEAAAADEcgBAAAAAxHIAQAAAAOFDORbtmxRfn6+LBaLLBaLCgsL9eGHH/qfX7p0qRISEgIe\nhYWFAefo6+vTypUrNXbsWKWlpWnhwoXq6OiI/KsBAITUffyo3G17+z26jx81ujQAiEuJoTqMHz9e\nL7zwgnJycuT1erVt2zYtWrRIbW1tys/Pl8lkUklJiRoaGvzHJCcnB5yjvLxc7777rpqampSRkaGK\nigrNnz9f7e3tSkhgkh4AhpPn9Cl1Vq/q135r9SYpe6IBFQFAfAsZyBcsWBDw93Xr1unll1/WJ598\novz8fPl8PiUnJ8tqtQY93u12a+vWrdq2bZtmz54tSWpoaFB2drZ27typOXPmROBlAAAAACPToKan\nPR6Pmpqa1Nvbq6KiIkmSyWRSS0uLbDabJk+erOXLl+vMmTP+Y9rb23X58uWA4O1wOJSXl6fW1tYI\nvQwAAABgZAo5Qy5Jn3/+uWbMmKG+vj6NHj1ab7zxhiZPnixJmjt3rh555BFNmDBBx44d03PPPadZ\ns2apvb1dycnJcjqdMpvNyszMDDinzWaTy+WK/CsCAAAARpABBfLc3Fx99tlncrvdevPNN/X4449r\n9+7dmjZtmsrKyvz9pkyZooKCAmVnZ+uDDz5QaWnpTRe2f//+mz4WkcM4RAfGIXrEwljYu7qCtnd1\ndenICHl9sTAOsYBxiB6MhbFycnLCOn5AS1aSkpI0ceJETZ06VTU1NZo+fbq2bNkStG9WVpYcDoe+\n+uorSZLdbpfH49G5c+cC+jmdTtnt9rCKBwAAAEa6Ac2QX8vj8cjr9QZ97syZM+ro6FBWVpYkqaCg\nQElJSWpubtbixYslSSdOnNDhw4f7bY94tWnTpt1MaYiQK79pMw7GYhyiRyyNhbttrzqDtKenp8sR\n5a8vlsZhJGMcogdjER3cbndYx4cM5M8++6zmz58vh8Ohrq4ubd++XXv27NGOHTt08eJFVVVV6dFH\nH5XdbtfXX3+t1atXy2az+ZerWCwWLVu2TJWVlbJarf5tD/Pz81VcXBxW8QAAAMBIFzKQu1wuPfHE\nE3I6nbJYLMrPz9eOHTtUUlKi3t5effHFF2poaNCFCxeUlZWlWbNm6a233lJqaqr/HLW1tUpMTFRZ\nWZl6enpUXFysxsZGmUymIX1xAAAAQLQLGchfe+216z43atQo7dixI+RFkpOTVVdXp7q6usFVBwAA\nAMQ4bpMJAAAAGIhADgAAABjopnZZAQAYq/v4UXlOnwpoM1uzlJY90aCKAAA3i0AOAAYIN1B7Tp9S\nZ/WqgLZbqzdJ1xwf7Dqe3p6bqBgAMFQI5ABggIEG6qG4TkrF2oheAwAQHtaQAwAAAAYikAMAAAAG\nIpADAAAABmINOQBEELufAAAGi0AOABE0XB/WBADEDgI5AEQJb4JZ7ra9AW3MrgNA7COQA0CU8F74\nnbo3rgloY3YdAGIfgRwAQug+flT2zrOS5J/BHszMdbCZ74HenCfYsYM5HgAQ/QjkABCC5/Qp+V58\nTpLU+b9tg5m5DjbzPdCb8wQ7djDHAwCiH9seAgAAAAZihhwArhJs20KWhwAAhhKBHACuEmzbQpaH\nAACGEoEcAGJEOB8eBQAYh0AOADEinA+PAgCME/JDnVu2bFF+fr4sFossFosKCwv14YcfBvSprq7W\nuHHjlJKSopkzZ+rQoUMBz/f19WnlypUaO3as0tLStHDhQnV0dET2lQDAMLoyG33tgxlpAMBghZwh\nHz9+vF544QXl5OTI6/Vq27ZtWrRokdra2pSfn6/169dr48aNqq+v16RJk7R27VqVlJToyy+/VFpa\nmiSpvLxc7777rpqampSRkaGKigrNnz9f7e3tSkhgoxcAIw/bEQIAIiVkGl6wYIEeeughTZw4Ub//\n+7+vdevWKT09XZ988ol8Pp9qa2u1evVqlZaWasqUKaqvr1dXV5e2b98uSXK73dq6das2bNig2bNn\na+rUqWpoaNBnn32mnTt3DvkLBAAAAKLZoKanPR6Pmpqa1Nvbq6KiIh07dkwul0tz5szx9xk1apSK\niorU2toqSWpvb9fly5cD+jgcDuXl5fn7AAAAAPFqQB/q/PzzzzVjxgz19fVp9OjReuONNzR58mR/\noLbZbAH9rVarTp48KUlyOp0ym83KzMwM6GOz2eRyuSLxGgAAAIARa0CBPDc3V5999pncbrfefPNN\nPf7449q9e/cNjzGZTGEVtn///rCOR2QwDtGBcRg+9q6ufm0ej2dAbYPpG07bUJ2zq6tLR0bI/zW+\nJqID4xA9GAtj5eTkhHX8gJasJCUlaeLEiZo6dapqamo0ffp0bdmyRVlZWZLUb6bb5XLJbrdLkux2\nuzwej86dOxfQx+l0+vsAAKLT2ASf7J1nAx5jE3xGlwUAMeWm9iH3eDzyer2aMGGC7Ha7mpubVVBQ\nIEnq7e1VS0uLNmzYIEkqKChQUlKSmpubtXjxYknSiRMndPjwYRUWFl73GtOmTbuZ0hAhV37TZhyM\nxTgMP3fbXnVe02Y2m/v1C9Y2mL7htA3VOdPT0+W45v+au22vOl98LqDtO9WblH3fd4OeY6jxNREd\nGIfowVhEB7fbHdbxIQP5s88+q/nz58vhcPh3T9mzZ4927Ngh6dstDWtqapSbm6ucnBz/LixLliyR\nJFksFi1btkyVlZWyWq3+bQ/z8/NVXFwcVvEAAADASBcykLtcLj3xxBNyOp2yWCzKz8/Xjh07VFJS\nIkmqrKxUT0+PVqxYofPnz2v69Olqbm5Wamqq/xy1tbVKTExUWVmZenp6VFxcrMbGxrDXmQMAAAAj\nXchA/tprr4U8SVVVlaqqqq77fHJysurq6lRXVze46gAAAIAYx20yAQAAAAMRyAEAAAADEcgBAAAA\nAxHIAQAAAAMRyAEAAAAD3dSNgQBgpOk+flSe06cC2szWLKVlTzSoIgAAvkUgBxAXPKdPqbN6VUDb\nrdWbJAI5AMBgLFkBAAAADEQgBwAAAAxEIAcAAAAMRCAHAAAADEQgBwAAAAxEIAcAAAAMxLaHAIBB\n8SaY5W7bG9DGnu4AcPMI5ACAQfFe+J26N64JaGNPdwC4eSxZAQAAAAxEIAcAAAAMRCAHAAAADEQg\nBwAAAAwUMpA///zzuu+++2SxWGS1WrVgwQIdPHgwoM/SpUuVkJAQ8CgsLAzo09fXp5UrV2rs2LFK\nS0vTwoUL1dHREdlXAwAAAIwwIQP5nj179PTTT2vfvn3atWuXEhMTVVxcrPPnz/v7mEwmlZSUyOl0\n+h8ffvhhwHnKy8v19ttvq6mpSR9//LE6Ozs1f/58eb3eyL8qAAAAYIQIue3hjh07ALine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x982a278>"
+       "<matplotlib.figure.Figure at 0x7aad860>"
       ]
      },
      "metadata": {},
@@ -1802,9 +1791,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEPCAYAAACTNwgMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt4AAAEPCAYAAAB1HsNIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4FFXXwH+z6aRTEiCBhFBCCcVQIghIpIMICggoIq+U\nT0QFG0XhRZQXxK4IKlYERUCkCii9g7TQQgstJJCQhPSe3fn+uNkkm2ySDWyyCdzf88yzuzN37pzZ\nnZ0599xTFFVVVSQSiUQikUgkEkm5orG0ABKJRCKRSCQSyYOAVLwlEolEIpFIJJIKQCreEolEIpFI\nJBJJBSAVb4lEIpFIJBKJpAKQirdEIpFIJBKJRFIBWFtaAGMkJiZaWgSJRCKRSCQSieSucXV1LbJO\nWrwlEolEIpFIJJIKQCreEolEIpFIJBJJBVApXU0KYsxML5HoOXr0KADt2rWzsCSSqoC8XiSmIq8V\niakUe61ERoK3N9StK95bElUFJydIS4PERHBxsaw8FuTMmTNMnDiR7dt/x8oqhqeemsRLL71A9+5P\no9HY3XP/pblLS4u3RCKRSCQSiblJSRGvjo6WlQNAUaBOHfH+5k3LymIBMjMzUVUVVVVp2tST1NRY\nDh78C0XJZvXqD+nZszmKcp6srCgGDRpEeHh4uclS6S3eEolEIpFIJFWOyqR4A/TuDTExYGVlaUkq\nnGHDhvHMM08xZEgHrKxS2bNnMdWq2QOg0QgbtKLksHTpIlJSYvDy8ig3WaTFWyKRSCQSicTcpKaK\nVycny8qhZ+FCWLkSGje2tCQViqrqmDDhKZYv/wmNJhVFIU/pLszo0Y+zcuX7aDQX0Olus379eq5e\nvWpWeaTiLZFIJBKJRGJuXFzg0UfB2hpCQiwnR1oabNgAoaGWk8ECJCcno9PpUNUb9O7dgtWrPyx1\nHysrK6pXd0VRcrhx4wgvvfQiu3fvNqtcUvGWSCQSiUQiMTdt2sCkSbBrF/z3v5aT48IFeOIJGDbM\ncjJYgClTpjBq1NNkZQmfdr1LianY2lpz6NASnn/+ObPKJX28JRKJRCKRlBuqqpKdnY1Op7O0KOWC\nj48PABkZGUU3du4MmzeDszMY214R1KolZKhRw3IyWICPP/6AK1cuk5VVh7tRd93d6wOQkZGKotgC\nQnm3sbFBUZS7lksq3hKJRCKRSMoFVVXJyMjA1tb2nhWWyoq9vXF/4dyN0KdPxQljDG9vsTxw2NOy\nZaDZelNVFZ1OR0ZGBvb29nd9LUtXE4lEIpFIJOVCdnY2tra2WFlZ3ZdKt+TBQVEUrKyssLW1JTs7\n+677qZqK9306XSWRSCQSyf2ETqcrs2+tRFKZ0Wg09+Q2VfX+DS++CD4+kJRkaUkkEolEIpGUgrR0\nS+4n7vV6rnqK97ffQkQErFljaUkkEolEIpFIJBKTqXqKt57MTEtLIJFIJBKJRCKRmEzVU7zri/Qu\nUvGWSCQSiURS2bh27RoajYYlS5bkrfv555/RaDSEh4dbUDJJZaDqKd6ffgqvvw4PPWRpSSQSiURS\nEZw6BT17wsyZlpZEIgHyFWljyyuvvIKiKKX6Av/222988cUXFSSxxJwkJibe9b5VL4/34MFikUgk\nEsmDQXg4bNsmlj/+EIq4jY2lpZJImD17Ng0bNjRY5+/vz+rVq7G2LlnF+u233zh79iyTJk0qTxEl\n5UBKSgqenp53tW/VU7wlEolE8mBx507++/Pn4cgR6NTJcvJIJLn07t2bDh063PX+5ZHxJT09HQcH\nB7P3K8mnbt3ad71v1XM1kUgkEsmDRVyc4edt2ywjh0RiAsZ8vAvTrVs3Nm3alNdWv+hRVZUFCxbQ\nsmVLHBwc8PT0ZOzYscQV+i/4+vrSt29ftm/fTlBQEA4ODnz44Yfldm4SPdmoqnpXe0rFWyKRSCSV\nG72y0bq1eN2+3XKySCQFSEhIIDY21mDRU5I1e8aMGbRp04aaNWuybNmyvEXPhAkTeOONN+jYsSNf\nfvkl48eP548//iA4OJjMAsklFEUhLCyMoUOHEhwczIIFC+jYsWP5nKwkj7S0ZJ59djh//fVXmfet\nWq4mW7bAwoXQv78opCORSCSS+x+94j14sPDvPngQUlPB0dGycknMzqtfDCrX/r+ctNas/fXp08fg\ns6IonDp1qtT9evToQd26dUlISOCZZ54x2HbgwAEWL17M0qVLefbZZw2O1aVLF3755RfGjRsHCMv4\n5cuXWb9+PY8//rgZzkhiCklJKfj716ZHjx5l3tesFu89e/bwxBNP4O3tXew0y7vvvouXlxfVqlUj\nODiY0NBQ0w9w4QJs3AiTJ8OMGeLGK5FIzENEBIwZA/PnW1oSicSQ11+Hv/6CkSOhbVvQauHkSUtL\nJZGwYMECtm3blrds3boVe3v7e+pz5cqVODk50atXLwNLur+/Px4eHuzcudOgfb169aTSXcHUsbfl\nv1cuY5N1s8z7mtXinZqaSqtWrXj++ecZNWpUkWmW+fPn8+mnn7JkyRKaNGnCe++9R8+ePblw4QJO\nTk6lHyAhQbxmZsL//gejRkGTJuY8BYme9HT44gt46in5HT8oRETAjz9Chw4wdaqlpZFI8mncWCwA\nv/wCdeqAm5tlZZJIgPbt2xcJrrx27do99Xnx4sUSs2bExMQYfPbz87un40nugpOXUH75C/zqsevR\nweh0Gh577DGTdjWr4t23b1/69u0LwOjRow22qarK559/zvTp03nyyScBWLJkCR4eHvz222+MHz++\n9APoFW890dFSKSwvvvoKpk+H//4XsrIsLY2kItD/v1xdLSuHRFISzZpZWgKJpFzR6XTUqFGDFStW\nGN3u7u5u8FlmMLEctw6G8OziNXz33Y8m71NhPt5Xr14lOjqaXr165a2zt7ena9euHDhw4O4U76go\nM0spyeP8efGanW1ZOSQVh74gwNatYhpfH8gmkUgkFYS5fbArM8UFXzZs2JBt27YRFBSEo4xjqNTU\nycrhzJnfcXUNMHmfCstqEpWrJBeeOvHw8MjbVirx8eR2Il6jo80lnqQwHh7576Xy/WBQcGBbyIdQ\nIpFIJObF0dGReL1eU4Dhw4ej0+l47733imzTarUkFDZCSiqcpNZ+MPv/UL6agru7M4oSiVabQURE\nRKn7VoqsJiWl3Dl69Gjee4ehQ7Hr3BmXgwfx+PNPbp44wc0C2yXmw6lBAxrUrUtc377cPHYMSqnA\nZWmOyuvgnql99izeue9vnThB5H38ncrrRWIq8lq5N3x8fO452PB+pX379qxcuZLJkyfToUMHNBoN\nw4cPp0uXLkycOJGPPvqIU6dO0atXL+zs7AgLC2P16tW8//77jBo1ytLiP9DEpacS/VRHrMiA0FBi\nYxN5442R1KjhVayLkJ4K06Zq1xZVfqKjo/H29s5bHx0dnbetNNL9/Un39yfH2ZkcNzeS27cvF1kl\nkBIYyOl16ywthqQCSezYEbcdO3A6exabgpUCJRILYh0fT6M33yTD25trs2fnrdekp+MYGkpy27YW\nlE7yIFPWqpOF27/00kucPn2aZcuWsWDBAkBYu0FkSwkMDOSbb75hxowZWFtb4+Pjw7BhwwyC+Mqj\n8qWkdLQ6LWFRN/Cv6wOAi4sjgwY9TL9+z5SyJyjq3ZbeKQVnZ2cWLlyYNypTVRUvLy9eeeUVpk+f\nDkBGRgaenp58/PHHeTkpARL1vqaAqwz0kpSA3hrVrl07C0tyn7BxIwwYAH36wObNlpbG7MjrpQpy\n9iwEBEDTpnDunFin00Ht2hATA+HhUK+e2Q8rrxXzkJGRIS3ekvuOM2FHWXfga6Y/NwFNgcGPqtqQ\nlOST99mYDmtWH+/U1FRCQkIICQlBp9Nx/fp1QkJCuHHjBoqiMHnyZObPn8+aNWs4c+YMo0ePxtnZ\nuUjyeIlEYiFk/ISksqEvnlOjRv46jQYefli8l1UsJRKJBYiOj+P05fMG6xSl9Jg4syreR44cITAw\nkMDAQDIyMpg1axaBgYHMmjULgClTpvDaa68xceJE2rdvT3R0NP/884+M2pVIKgs+PjB+PBSoliaR\nWBS921P16obru3cXr1LxlkgkFuKfI/sp6DiSnZ1T6j5m9fHu1q0bOp2uxDazZs3KU8QlEkklw8MD\nvv3W0lJIJPkYs3iDoeKtqiB9XSUSSQXhHp8OqkrvuWvJfnU5tmHrwNUJG5vS1eoKSyd4z0RGihvt\nhAmWluT+R1Xhrbdgzhxh/WzRAq5ft7RUEonkQURv8S6seLdoIVyjbt3KrzsgkUgkFUCWrRUoCm6J\n6djGJpJ6+JTJ+1buHHEFuX0bduzIt358/z2EhsIbb4CXl2Vlu99IT4ePPwY7O+jUSXzPoaHCDUFy\n//Lyy5CTAx98IMtxSyoPI0dChw4imLIgigJDhoh4BK3WMrJJJJIHkix7GwAivVypfyORU3+up2Ov\nTibtW3Us3vqE8XqF4Oef4bPPICzMYiLdt+gT+ru7Q/Pm4n1oqOXkkVQMS5dWHjcTrVYM/k6etLQk\nd8/hw9Cjh7TG3it16sCjj4K/f9FtX30Fq1aJrCcSiURSQbjkxpxEeOVmLQm5yMkw0+71VVfx1ls/\nZNl481MwmKlZM/Fen8ZLcn+i00Fysnjv7GxZWQB++UW4O7VpY2lJ7p4ffxT+xx99ZGlJJBKJRGJG\n3JxcqOdRh8hcxds7MpFVOzeTlpFe6r5VV/GWac/Kj4IWb6l4PxgkJQnffhcXOHpUuJvs2mU5eW7f\nttyxzUXLluLV1tayckgkEonErCgKPNNjALe8hE7qcTuFlOQk1uzZWuq+VU7xVl1dReoWafEuP4qz\neJdPrSVJZUA/sHV1FbEU06dbtoBObvU2ClS5rXLUrSteb960rBzlxdatwtVDYjFu3Line truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d2d828>"
+       "<matplotlib.figure.Figure at 0x794c860>"
       ]
      },
      "metadata": {},
@@ -1814,7 +1803,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEjCAYAAADqsm07AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86aa8d0>"
+       "<matplotlib.figure.Figure at 0x7900d68>"
       ]
      },
      "metadata": {},
@@ -1824,16 +1813,13 @@
    "source": [
     "sensor_variance = 30\n",
     "movement_sensor = 30\n",
-    "pos = (0,500)\n",
+    "pos = (0, 500)\n",
     "\n",
     "dog = DogSensor(0, velocity=movement, \n",
     "                measurement_variance=sensor_variance,\n",
     "                process_variance=0.5)\n",
     "\n",
-    "zs = []\n",
-    "ps = []\n",
-    "vs = []\n",
-    "\n",
+    "zs, ps, vs = [], [], []\n",
     "for i in range(100):\n",
     "    Z = dog.sense_position()\n",
     "    zs.append(Z)\n",
@@ -1844,7 +1830,7 @@
     "\n",
     "    pos = predict(pos[0], pos[1], movement + random.randn(), movement_variance)\n",
     "\n",
-    "bp.plot_filter(ps)\n",
+    "bp.plot_filter(ps, vars=vs)\n",
     "bp.plot_measurements(zs)\n",
     "plt.legend()\n",
     "plt.show()\n",
@@ -1896,9 +1882,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x870e710>"
+       "<matplotlib.figure.Figure at 0x75d5668>"
       ]
      },
      "metadata": {},
@@ -1961,9 +1947,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8635c50>"
+       "<matplotlib.figure.Figure at 0x75d5630>"
       ]
      },
      "metadata": {},
@@ -2026,9 +2012,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cac898>"
+       "<matplotlib.figure.Figure at 0x765d198>"
       ]
      },
      "metadata": {},
@@ -2078,9 +2064,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cac9e8>"
+       "<matplotlib.figure.Figure at 0x80e00b8>"
       ]
      },
      "metadata": {},
@@ -2197,9 +2183,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9f2f6a0>"
+       "<matplotlib.figure.Figure at 0x819d550>"
       ]
      },
      "metadata": {},
@@ -2304,9 +2290,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9f7e828>"
+       "<matplotlib.figure.Figure at 0x97ad6d8>"
       ]
      },
      "metadata": {},
@@ -2394,9 +2380,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ed1908>"
+       "<matplotlib.figure.Figure at 0x8156320>"
       ]
      },
      "metadata": {},

Appendix_A_Installation.ipynb

@@ -20,7 +20,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Installation, Python, Numpy, and filterpy"
+    "# Installation, Python, NumPy, and FilterPy"
    ]
   },
   {
@@ -271,7 +271,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This book is written in IPython Notebook, a browser based interactive Python environment that mixes Python, text, and math. I choose it because of the interactive features - I found Kalman filtering nearly impossible to learn until I started working in an interactive environment. It is difficult to form an intuition of the effect of many of the parameters that you can tune until you can change them rapidly and immediately see the output. An interactive environment also allows you to play 'what if' scenarios out. \"What if I set $\\mathbf{Q}$ to zero?\" It is trivial to find out with Ipython Notebook.\n",
+    "This book is written in IPython Notebook, a browser based interactive Python environment that mixes Python, text, and math. I choose it because of the interactive features - I found Kalman filtering nearly impossible to learn until I started working in an interactive environment. It is difficult to form an intuition of the effect of many of the parameters that you can tune until you can change them rapidly and immediately see the output. An interactive environment also allows you to play 'what if' scenarios out. \"What if I set $\\mathbf{Q}$ to zero?\" It is trivial to find out with IPython Notebook.\n",
     "\n",
     "Another reason I choose it is because I find that a typical textbook leaves many things opaque. For example, there might be a beautiful plot next to some pseudocode. That plot was produced by software, but software that is not available to me as a reader. I want everything that went into producing this book to be available to the reader. How do you plot a covariance ellipse? You won't know if you read most books. With IPython Notebook all you have to do is look at the source code.\n",
     "\n",
@@ -300,6 +300,22 @@
     "There are other choices for installing the SciPy stack. The SciPy stack provides instructions here: http://scipy.org/install.html"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Installing FilterPy\n",
+    "\n",
+    "FilterPy is a Python library that implements all of the filters used in this book, and quite a few not used by this book. Installation is easy using Pip. Issue the following command from the command prompt.\n",
+    "\n",
+    "     pip install filterpy\n",
+    "     \n",
+    "     \n",
+    "FilterPy is written by me, and the latest development version is always available at github.com/rlabbe/filterpy.\n",
+    "     \n",
+    "     "
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -775,7 +791,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.2"
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,

animations/Gaussians_Animations.ipynb

@@ -1,324 +1,551 @@
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-  "signature": "sha256:67b73f8366759bb2837043e5a461a7ce4ff077967115f36e8017eaa1318f1c0f"
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   {
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+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from __future__ import division, print_function\n",
-      "%matplotlib inline\n",
-      "import sys\n",
-      "sys.path.insert(0,'..') # allow us to format the book\n",
-      "sys.path.insert(0,'../code') \n",
-      "# use same formatting as rest of book so that the plots are\n",
-      "# consistant with that look and feel.\n",
-      "import book_format\n",
-      "book_format.load_style(directory='..')"
-     ],
-     "language": "python",
+     "data": {
+      "text/html": [
+       "<style>\n",
+       "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
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+       "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
+       "\n",
+       "    div.cell{\n",
+       "        width: 850px;\n",
+       "        margin-left: 0% !important;\n",
+       "        margin-right: auto;\n",
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+       "        line-height: 125%;\n",
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+       "        margin-left:auto;\n",
+       "        margin-right:auto;\n",
+       "        text-align:justify;\n",
+       "        text-justify:inter-word;\n",
+       "    }\n",
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+       "        overflow-x: auto;\n",
+       "        overflow-y: scroll;\n",
+       "        max-height: 50000px;\n",
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+       "    div.output_subarea.output_stream.output_stdout.output_text {\n",
+       "        overflow-x: auto;\n",
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+       "\n",
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+       "      font-size: 70%;\n",
+       "    }\n",
+       "    .rendered_html code{\n",
+       "    background-color: transparent;\n",
+       "    }\n",
+       "    ul{\n",
+       "        margin: 2em;\n",
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+       "        padding-left: 0.2em; \n",
+       "        margin-bottom: 0.2em; \n",
+       "        margin-top: 0.2em; \n",
+       "    }\n",
+       "    ol{\n",
+       "        margin: 2em;\n",
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+       "    ol li{\n",
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+       "        margin-bottom: 0.5em; \n",
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+       "       font-weight: bold;\n",
+       "       color: #1d3b84;\n",
+       "    }\n",
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+       "       font-weight: bold;\n",
+       "       color: #1d3b84;\n",
+       "    }\n",
+       "    a:focus{\n",
+       "       font-weight: bold;\n",
+       "       color:#447adb;\n",
+       "    }\n",
+       "    a:active{\n",
+       "       font-weight: bold;\n",
+       "       color:#447adb;\n",
+       "    }\n",
+       "    .rendered_html :link {\n",
+       "       text-decoration: underline; \n",
+       "    }\n",
+       "    .rendered_html :hover {\n",
+       "       text-decoration: none; \n",
+       "    }\n",
+       "    .rendered_html :visited {\n",
+       "      text-decoration: none;\n",
+       "    }\n",
+       "    .rendered_html :focus {\n",
+       "      text-decoration: none;\n",
+       "    }\n",
+       "    .rendered_html :active {\n",
+       "      text-decoration: none;\n",
+       "    }\n",
+       "    .warning{\n",
+       "        color: rgb( 240, 20, 20 )\n",
+       "    } \n",
+       "    hr {\n",
+       "      color: #f3f3f3;\n",
+       "      background-color: #f3f3f3;\n",
+       "      height: 1px;\n",
+       "    }\n",
+       "    blockquote{\n",
+       "      display:block;\n",
+       "      background: #fcfcfc;\n",
+       "      border-left: 5px solid #c76c0c;\n",
+       "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
+       "      width:680px;\n",
+       "      padding: 10px 10px 10px 10px;\n",
+       "      text-align:justify;\n",
+       "      text-justify:inter-word;\n",
+       "      }\n",
+       "      blockquote p {\n",
+       "        margin-bottom: 0;\n",
+       "        line-height: 125%;\n",
+       "        font-size: 100%;\n",
+       "      }\n",
+       "</style>\n",
+       "<script>\n",
+       "    MathJax.Hub.Config({\n",
+       "                        TeX: {\n",
+       "                           extensions: [\"AMSmath.js\"]\n",
+       "                           },\n",
+       "                tex2jax: {\n",
+       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
+       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
+       "                },\n",
+       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
+       "                \"HTML-CSS\": {\n",
+       "                    scale:85,\n",
+       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
+       "                }\n",
+       "        });\n",
+       "</script>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "execution_count": 17,
      "metadata": {},
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-        "<style>\n",
-        "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
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-        "\t}\n",
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-        "    }\n",
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-        "        overflow-x: auto;\n",
-        "        overflow-y: scroll;\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: 50000px;\n",
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-        "    code{\n",
-        "      font-size: 70%;\n",
-        "    }\n",
-        "    .rendered_html code{\n",
-        "    background-color: transparent;\n",
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-        "      background: #fcfcfc;\n",
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-        "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "      width:680px;\n",
-        "      padding: 10px 10px 10px 10px;\n",
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-      }
-     ],
-     "prompt_number": 3
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import numpy as np\n",
-      "import matplotlib.pyplot as plt\n",
-      "from gif_animate import animate\n",
-      "from stats import gaussian\n",
-      "\n",
-      "def plt_g (mu, variance):\n",
-      "    xs = np.arange(2,8,0.05)\n",
-      "    ys = [gaussian (x, mu, variance) for x in xs]\n",
-      "    plt.plot (xs, ys)\n",
-      "    plt.ylim((0,1))\n",
-      "\n",
-      "\n",
-      "mu = 2\n",
-      "sigma = 0.6\n",
-      "def ganimate(frame):\n",
-      "    global mu, sigma\n",
-      "    if frame < 25:\n",
-      "        mu += .2\n",
-      "    elif frame == 25:\n",
-      "        mu = 5\n",
-      "    elif frame < 37:\n",
-      "        sigma -= 0.05\n",
-      "    else:\n",
-      "        sigma += 0.05\n",
-      "        \n",
-      "    plt.cla()\n",
-      "    plt_g(mu,sigma)\n",
-      "\n",
-      "animate('04_gaussian_animate.gif', ganimate, frames=80, interval=50)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7fc8aff6f9e8>"
-       ]
-      }
-     ],
-     "prompt_number": 4
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 2
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "<img src='04_gaussian_animate.gif'>"
-     ]
+     "output_type": "execute_result"
     }
    ],
-   "metadata": {}
+   "source": [
+    "from __future__ import division, print_function\n",
+    "%matplotlib inline\n",
+    "import sys\n",
+    "sys.path.insert(0,'..') # allow us to format the book\n",
+    "sys.path.insert(0,'../code') \n",
+    "# use same formatting as rest of book so that the plots are\n",
+    "# consistant with that look and feel.\n",
+    "import book_format\n",
+    "book_format.load_style(directory='..')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
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+       "4t577xVdyrRbunQpqqqqxrXV1NQgMDBQTEECHDhwAHZ2dnj88cdFl2IWkiRBLh+/9EAul094Tdjs\n",
+       "QfTjH/8Yv//97/Hpp5/C1dV1bINUZ2dnODo6mrscs/rJT36C1atXw8/PD729vfjjH/+IkydP4tCh\n",
+       "Q6JLm1Y375v6JgcHB7i5uSE6OlpQVebx4osvYs2aNVCr1Whvb8f27dsxMDCAH/zgB6JLm3bPP/88\n",
+       "0tLS8MYbb2DDhg04f/483n77bbz55puiSzMLSZLwu9/9Do899hgcHBxEl2MWa9euxc9//nMEBQUh\n",
+       "Ojoa58+fx69+9auJ/3+frkO027l5SkYmk43789prr5m7FLPbtGmTFBAQINna2kpKpVJatWqVdPjw\n",
+       "YdFlCWEpixUee+wxycfHR7KxsZF8fX2ldevWSZWVlaLLMpsvvvhCSkhIkOzs7KSIiAjp7bffFl2S\n",
+       "2Rw7dkySy+Vz/hrwN/X19Un/8R//IQUGBkr29vZScHCw9F//9V/S0NCQyXHc4oeIiIQSfh8RERFZ\n",
+       "NgYREREJxSAiIiKhGERERCQUg4iIiIRiEBERkVAMIiIiEopBREREQjGIiIhIqP8DiW6VK9nFPOgA\n",
+       "AAAASUVORK5CYII=\n"
+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fc3f902ea58>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from gif_animate import animate\n",
+    "from stats import gaussian\n",
+    "import matplotlib.pylab as pylab\n",
+    "from matplotlib import animation\n",
+    "\n",
+    "\n",
+    "def plt_g (mu, variance):\n",
+    "    xs = np.arange(2,8,0.05)\n",
+    "    ys = [gaussian (x, mu, variance) for x in xs]\n",
+    "    plt.plot (xs, ys)\n",
+    "    plt.ylim((0,1))\n",
+    "\n",
+    "\n",
+    "mu = 2\n",
+    "sigma = 0.6\n",
+    "def ganimate(frame):\n",
+    "    global mu, sigma\n",
+    "    if frame < 25:\n",
+    "        mu += .2\n",
+    "    elif frame == 25:\n",
+    "        mu = 5\n",
+    "    elif frame < 37:\n",
+    "        sigma -= 0.05\n",
+    "    else:\n",
+    "        sigma += 0.05\n",
+    "\n",
+    "    plt.cla()\n",
+    "    plt_g(mu,sigma)\n",
+    "\n",
+    "animate('04_gaussian_animate.gif', ganimate, \n",
+    "        frames=80, interval=50, figsize=(6,4))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<img src='04_gaussian_animate.gif'>"
+   ]
   }
- ]
-}
+ ],
+ "metadata": {
+  "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": "3.4.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}

code/book_plots.py

@@ -72,19 +72,34 @@ def plot_residual_limits(Ps):
                  facecolor='#ffff00', alpha=0.3)
 
 
-def plot_track(xs, ys=None, label='Track', c='k', lw=2):
+def plot_track(xs, ys=None, label='Track', c='k', lw=2, **kwargs):
     if ys is not None:
-        plt.plot(xs, ys, c=c, lw=lw, label=label)
+        plt.plot(xs, ys, c=c, lw=lw, label=label, **kwargs)
     else:
-        plt.plot(xs, c=c, lw=lw, label=label)
+        plt.plot(xs, c=c, lw=lw, label=label, **kwargs)
 
 
 #c='#013afe'
-def plot_filter(xs, ys=None, c='#6d904f', label='Filter', **kwargs):
-    if ys is not None:
-        plt.plot(xs, ys, c=c, label=label, **kwargs)
-    else:
-        plt.plot(xs, c=c, label=label, **kwargs)
+def plot_filter(xs, ys=None, c='#6d904f', label='Filter', vars=None, **kwargs):
+
+    if ys is None:
+        ys = xs
+        xs = range(len(ys))
+
+    plt.plot(xs, ys, c=c, label=label, **kwargs)
+        
+    if vars is None:
+        return
+    vars = np.asarray(vars)
+    
+    std = np.sqrt(vars)
+    std_top = ys+std
+    std_btm = ys-std
+
+    plt.plot(xs, ys+std, linestyle=':', c='k', lw=2)
+    plt.plot(xs, ys-std, linestyle=':', c='k', lw=2)
+    plt.fill_between(xs, std_btm, std_top,
+                     facecolor='yellow', alpha=0.2)
 
 
 if __name__ == "__main__":

code/gaussian_internal.py

@@ -11,6 +11,22 @@ import matplotlib.pyplot as plt
 import numpy as np
 import stats
 
+def plot_height_std(x, lw=10):
+    m = np.mean(x)
+    s = np.std(x)
+
+    for i, height in enumerate(x):
+        plt.plot([i+1, i+1], [0, height], color='k', lw=lw)
+    plt.xlim(0,len(x)+1)
+    plt.axhline(m-s, ls='--')
+    plt.axhline(m+s, ls='--')
+    plt.fill_between((0, len(x)+1), m-s, m+s, 
+                     facecolor='yellow', alpha=0.4)
+    plt.xlabel('student')
+    plt.ylabel('height (m)')
+    plt.show()
+
+    
 def plot_gaussian (mu, variance,
                    mu_line=False,
                    xlim=None,
@@ -31,8 +47,6 @@ def plot_gaussian (mu, variance,
     plt.show()
 
 def display_stddev_plot():
-    figsize = pylab.rcParams['figure.figsize']
-    pylab.rcParams['figure.figsize'] = 12,6
     xs = np.arange(10,30,0.1)
     var = 8; stddev = math.sqrt(var)
     p2, = plt.plot (xs,[stats.gaussian(x, 20, var) for x in xs])

code/gh_internal.py

@@ -6,7 +6,7 @@ import book_plots
 def create_predict_update_chart(box_bg = '#CCCCCC',
                 arrow1 = '#88CCFF',
                 arrow2 = '#88FF88'):
-    plt.figure(figsize=(6,6), facecolor='w')
+    plt.figure(figsize=(4,4), facecolor='w')
     ax = plt.axes((0, 0, 1, 1),
                   xticks=[], yticks=[], frameon=False)
     #ax.set_xlim(0, 10)
@@ -187,13 +187,12 @@ def plot_hypothesis5():
     plt.show()
 
 def plot_g_h_results(measurements, filtered_data, 
-                     title='', z_label='Scale', ):    
+                     title='', z_label='Measurements', **kwargs):  
+    book_plots.plot_filter(filtered_data, **kwargs)
     book_plots.plot_measurements(measurements, label=z_label)
-    book_plots.plot_filter(filtered_data)
     book_plots.show_legend()
     plt.title(title)
     plt.gca().set_xlim(left=0,right=len(measurements))
-    plt.show()
     
 if __name__ == '__main__':
     create_predict_update_chart()

code/stats.py

@@ -157,6 +157,7 @@ def multivariate_gaussian(x, mu, cov):
 def plot_gaussian(mean, variance,
                   mean_line=False,
                   xlim=None,
+                  ylim=None,
                   xlabel=None,
                   ylabel=None):
     """ plots the normal distribution with the given mean and variance. x-axis
@@ -182,6 +183,9 @@ def plot_gaussian(mean, variance,
     plt.plot(xs,n.pdf(xs))
     plt.xlim((min_x, max_x))
 
+    if ylim is not None:
+        plt.ylim(ylim)
+
     if mean_line:
         plt.axvline(mean)
     if xlabel: