check in prior to blowing away this chroot.

Kalman_Filter_Math.ipynb

@@ -1,7 +1,7 @@
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   "name": "",
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@@ -53,7 +53,7 @@
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@@ -70,8 +70,8 @@
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         "    } \n",
@@ -116,7 +116,7 @@
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         "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
         "        line-height: 135%;\n",
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+        "        font-size: 110%;\n",
         "        width:750px;\n",
         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -244,7 +244,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
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+        "<IPython.core.display.HTML at 0x14fac90>"
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@@ -254,9 +254,11 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "This chapter is optional, especially the first time you go through this material. If you are a hobbiest you will be able to get quite far by just skipping this chapter and going on to learn the examples. However, to have any hope of reading the original Kalman filter or optimal estimation literature you will have to acquire some of the more formal mathematics. I will not endevour to teach linear algebra, statistics, or calculus here as each topic deserves a book on its own. \n",
+      "This chapter is optional, especially the first time you go through this material. If you are a hobbiest you will be able to get quite far by just skipping this chapter and going on to learn the examples. However, to have any hope of reading the literature or to design more sophsticated kilters you will have to acquire some of the more formal mathematics. I will not endevour to teach linear algebra, statistics, or calculus here as each topic deserves a book on its own. \n",
       "\n",
-      "blah blah blah"
+      "blah blah blah\n",
+      "\n",
+      "**authors note: need to start with continuous equations with $\\phi$, etc. Then discuss linearization into discrete case.**"
      ]
     },
     {
@@ -382,6 +384,11 @@
       "\n",
       "$\\mathbf{FPF}^T$ is the way we put $\\mathbf{P}$ into the process space using linear algebra so that we can add in the process noise $\\mathbf{Q}$ to it."
      ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": []
     }
    ],
    "metadata": {}

Multidimensional_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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@@ -116,7 +116,7 @@
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         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -244,7 +244,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
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      ],
@@ -524,7 +524,7 @@
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truncated
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+        "<matplotlib.figure.Figure at 0x350fb90>"
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@@ -568,7 +568,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x420d190>"
+        "<matplotlib.figure.Figure at 0x32ab190>"
        ]
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@@ -658,7 +658,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4211550>"
+        "<matplotlib.figure.Figure at 0x32b05d0>"
        ]
       }
      ],
@@ -685,7 +685,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x4113750>"
+        "<matplotlib.figure.Figure at 0x31b2290>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x42115d0>"
+        "<matplotlib.figure.Figure at 0x31b2290>"
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@@ -743,7 +743,7 @@
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        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x46ecb50>"
+        "<matplotlib.figure.Figure at 0x32a74d0>"
        ]
       }
      ],
@@ -755,7 +755,7 @@
      "source": [
       "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n",
       "\n",
-      "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Cleary the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way.  "
+      "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way.  "
      ]
     },
     {
@@ -796,7 +796,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x421de10>"
+        "<matplotlib.figure.Figure at 0x1f04890>"
        ]
       }
      ],
@@ -1315,9 +1315,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4209550>"
+        "<matplotlib.figure.Figure at 0x3bb2cd0>"
        ]
       },
       {
@@ -1325,7 +1325,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x3de2c90>"
+        "<matplotlib.figure.Figure at 0x32a38d0>"
        ]
       }
      ],
@@ -1494,17 +1494,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x46e1790>"
+        "<matplotlib.figure.Figure at 0x378d7d0>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x4218250>"
+        "<matplotlib.figure.Figure at 0x35b3490>"
        ]
       }
      ],
@@ -1583,7 +1583,17 @@
       "\n",
       "$$U_n = \\begin{bmatrix}\\frac{a{\\Delta t}^2}{2} \\\\ \\Delta t\\end{bmatrix}$$\n",
       "\n",
-      "So white noise has the variance $U_n$ and a mean of 0, which we notate as $w \\sim \\mathcal{N}(0,Q)$. \n"
+      "So white noise has the variance $U_n$ and a mean of 0, which we notate as $w \\sim \\mathcal{N}(0,Q)$. \n",
+      "\n",
+      "Finding an analytic value for $\\textbf{Q}$ in a simple problem like this is not difficult, but it quickly becomes difficult to impossible as the number of state variables increase. So in this chapter we will use the simplification that only the variance of the last term is important. In the Kalman filter math chapter we will discuss finding an analytic solution ofr $\\textbf{Q}$, and then present C. F. van Loan's extremely useful numerical technique for finding $\\textbf{Q}$, which is what you will typically use in practice. \n"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Designing R"
      ]
     },
     {
@@ -1605,9 +1615,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x3de2c90>"
+        "<matplotlib.figure.Figure at 0x3771310>"
        ]
       }
      ],
@@ -1677,7 +1687,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x421d410>"
+        "<matplotlib.figure.Figure at 0x3285850>"
        ]
       }
      ],
@@ -1706,7 +1716,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x41fe0d0>"
+        "<matplotlib.figure.Figure at 0x31b8510>"
        ]
       }
      ],
@@ -1795,17 +1805,17 @@
       {
        "metadata": {},
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        "text": [
-        "<matplotlib.figure.Figure at 0x410e810>"
+        "<matplotlib.figure.Figure at 0x32bad10>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x46ffe90>"
+        "<matplotlib.figure.Figure at 0x378dc10>"
        ]
       }
      ],
@@ -1872,7 +1882,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4b22d10>"
+        "<matplotlib.figure.Figure at 0x32ab190>"
        ]
       }
      ],

g-h_filter.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:d6a065bada82f52a1594d059481391c11dc03d589aca8e9e3b225011088ca167"
+  "signature": "sha256:c95a43951094c5ec86b654934c7bbbd79ece1d3f2eb3fb3cf541ddc9d6483a2a"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -244,7 +244,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0xdf8890>"
+        "<IPython.core.display.HTML at 0x1c62b90>"
        ]
       }
      ],