Added algorithm pseudocode to help link chapters.

I don't think the commonality of the algorithms was made as
expllicit as it could be. More work needs to be done in this regard.

01_g-h_filter.ipynb

@@ -1026,7 +1026,27 @@
     "\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 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.\n",
+    "\n",
+    "We can express this as an algorithm:\n",
+    "\n",
+    "**Initialization**\n",
+    "\n",
+    "    1. Initialize the state of the filter\n",
+    "    2. Initialize our belief in the state - how accurate do we think it is\n",
+    "    \n",
+    "**Predict**\n",
+    "\n",
+    "    1. Based on the system behavior, predict state at the next time step\n",
+    "    2. Adjust belief in that state to account for the uncertainty in prediction\n",
+    "    \n",
+    "**Update**\n",
+    "\n",
+    "    1. Get a measurement and associated belief about its accuracy\n",
+    "    2. Compute difference (residual) between our estimated state and measurement\n",
+    "    3. Update state based on predicted state plus some proportion of the residual\n",
+    "    \n",
+    "We will use this same algorithm throughout the book, albeit with some modifications. "
    ]
   },
   {
@@ -2322,7 +2342,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.4.1"
   }
  },
  "nbformat": 4,

02_Discrete_Bayes.ipynb

@@ -351,7 +351,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c97860>"
+       "<matplotlib.figure.Figure at 0x6ebc630>"
       ]
      },
      "metadata": {},
@@ -489,7 +489,7 @@
      "data": {
       "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cae2b0>"
+       "<matplotlib.figure.Figure at 0x6f35a90>"
       ]
      },
      "metadata": {},
@@ -541,7 +541,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x84b3e48>"
+       "<matplotlib.figure.Figure at 0x6faf550>"
       ]
      },
      "metadata": {},
@@ -617,7 +617,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x850eef0>"
+       "<matplotlib.figure.Figure at 0x6fa6048>"
       ]
      },
      "metadata": {},
@@ -687,7 +687,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x84fed30>"
+       "<matplotlib.figure.Figure at 0x6f9fa58>"
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@@ -737,7 +737,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8513668>"
+       "<matplotlib.figure.Figure at 0x75f5908>"
       ]
      },
      "metadata": {},
@@ -771,7 +771,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x84f1160>"
+       "<matplotlib.figure.Figure at 0x46ef7f0>"
       ]
      },
      "metadata": {},
@@ -807,7 +807,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x859eb38>"
+       "<matplotlib.figure.Figure at 0x76376a0>"
       ]
      },
      "metadata": {},
@@ -1020,7 +1020,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x85dd438>"
+       "<matplotlib.figure.Figure at 0x6faf198>"
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      "metadata": {},
@@ -1059,7 +1059,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86044e0>"
+       "<matplotlib.figure.Figure at 0x6ed9240>"
       ]
      },
      "metadata": {},
@@ -1090,7 +1090,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86d5a90>"
+       "<matplotlib.figure.Figure at 0x764f400>"
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      },
      "metadata": {},
@@ -1121,7 +1121,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x860a7f0>"
+       "<matplotlib.figure.Figure at 0x7521ac8>"
       ]
      },
      "metadata": {},
@@ -1154,7 +1154,7 @@
      "data": {
       "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x867f3c8>"
+       "<matplotlib.figure.Figure at 0x76bd160>"
       ]
      },
      "metadata": {},
@@ -1170,7 +1170,27 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This filter is just a form of the g-h filter. Here we are using the percentages for the errors to implicitly compute the *g* and *h* parameters. We could express the discrete Bayes algorithm as a g-h filter, but that would obscure the logic of this filter."
+    "This filter is just a form of the g-h filter. Here we are using the percentages for the errors to implicitly compute the *g* and *h* parameters. We could express the discrete Bayes algorithm as a g-h filter, but that would obscure the logic of this filter.\n",
+    "\n",
+    "We can express this in pseudocode. I am going to u that won't immediately strike you as being identical to what we have done in this chapter.\n",
+    "\n",
+    "**Initialization**\n",
+    "\n",
+    "    1. Initialize our belief in the state\n",
+    "    \n",
+    "**Predict**\n",
+    "\n",
+    "    1. Based on the system behavior, predict state at the next time step\n",
+    "    2. Adjust belief in that state to account for the uncertainty in prediction\n",
+    "    \n",
+    "**Update**\n",
+    "\n",
+    "    1. Get a measurement and associated belief about its accuracy\n",
+    "    2. Compute difference (residual) between our estimated state and measurement\n",
+    "    3. Determine whether whether the measurement matches each state\n",
+    "    4. Update state belief if it matches the measurement\n",
+    "\n",
+    "When we cover the Kalman filter we will use this exact same algorithm; just the details of the computation will differ. "
    ]
   },
   {
@@ -1215,7 +1235,7 @@
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x85a7b00>"
+       "<matplotlib.figure.Figure at 0x74b97b8>"
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      "metadata": {},
@@ -1253,7 +1273,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x85575c0>"
+       "<matplotlib.figure.Figure at 0x76b9f98>"
       ]
      },
      "metadata": {},
@@ -1284,7 +1304,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ce6780>"
+       "<matplotlib.figure.Figure at 0x7746cc0>"
       ]
      },
      "metadata": {},
@@ -1344,7 +1364,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x84eb860>"
+       "<matplotlib.figure.Figure at 0x7638f28>"
       ]
      },
      "metadata": {},
@@ -1534,7 +1554,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88020b8>"
+       "<matplotlib.figure.Figure at 0x77c3c50>"
       ]
      },
      "metadata": {},
@@ -1592,7 +1612,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8807630>"
+       "<matplotlib.figure.Figure at 0x77d9550>"
       ]
      },
      "metadata": {},
@@ -1626,7 +1646,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cf5d68>"
+       "<matplotlib.figure.Figure at 0x6f14e10>"
       ]
      },
      "metadata": {},
@@ -1798,7 +1818,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.4.1"
   }
  },
  "nbformat": 4,

04_One_Dimensional_Kalman_Filters.ipynb

@@ -1601,7 +1601,7 @@
     "    \n",
     "**Predict**\n",
     "\n",
-    "    1. Based on the system behaves, predict its state at the next time step\n",
+    "    1. Based on the system behavior, predict state at the next time step\n",
     "    2. Adjust belief in that state to account for the uncertainty in prediction\n",
     "    \n",
     "**Update**\n",
@@ -2472,7 +2472,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.4.1"
   }
  },
  "nbformat": 4,