Adjusted to use upper case x for filter state.

01_gh_filter/g-h_filter.ipynb

@@ -1,7 +1,7 @@
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05_Kalman_Filters/Kalman_Filters.ipynb

@@ -275,7 +275,7 @@
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-      "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style."
+      "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step."
      ]
     },
     {
@@ -2331,25 +2331,6 @@
       "\n",
       "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
      ]
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-    {
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-     "metadata": {},
-     "source": [
-      "**author notes**:\n",
-      "    clean up the code - same stuff duplicated over and over - write a 'clean implementation' at the end.\n",
-      "    \n",
-      "    "
-     ]
     }
    ],
    "metadata": {}

07_Kalman_Filter_Math/Kalman_Filter_Math.ipynb

@@ -363,7 +363,7 @@
       "\n",
       "$$\\mathbf{v}=\\dot{\\mathbf{x}}$$\n",
       "\n",
-      "where $\\dot{\\mathbf{x}}$ is the notation for the derivative of $\\mathbf{x}$, or $\\frac{d \\mathbf{x}}{d t}$.\n",
+      "where $\\dot{\\mathbf{x}}$ is the notation for the derivative of $\\mathbf{x}$ with respect to t, or $\\frac{d \\mathbf{x}}{d t}$.\n",
       "\n",
       "In general terms we can then say that a dynamic system consists of equations of the form\n",
       "\n",
@@ -441,7 +441,7 @@
       "\n",
       "$$ \\Phi(t) = e^{\\mathbf{F}t} = \\mathbf{I} + \\mathbf{F}t  + \\frac{(\\mathbf{F}t)^2}{2!} + \\frac{(\\mathbf{F}t)^3}{3!} + ... $$\n",
       "\n",
-      "This is much easier to compute, and is the typical approach used in Kalman filter design when the filter is reasonably small. If you are wondering where $e$ came from, I again point to wikipedia - this time the matrix exponential article [2]. Here the important point is to recognize the very simple and regular form this equation takes.\n",
+      "This is much easier to compute, and is the typical approach used in Kalman filter design when the filter is reasonably small. If you are wondering where $e$ came from, I again point to wikipedia - this time the matrix exponential article [2]. Here the important point is to recognize the very simple and regular form this equation takes. We will put this form into use in the next chapter, so I will not belabor its use here. \n",
       "\n",
       "Finally, there are numerical techniques to find $\\Phi$. As filters get larger finding analytical solutions becomes very tedious (though packages like Sympy make it easier). C. F. van Loan [3] has developed a technique that finds both $\\Phi$ and $Q$ numerically.\n",
       "\n",
@@ -489,7 +489,7 @@
       "I will start with the update step, as that is what we started with in the one dimensional Kalman filter case. Our first equation is\n",
       "\n",
       "$$\n",
-      "\\mathbf{\\gamma} = \\mathbf{z} - \\mathbf{H x}\\tag{3}\n",
+      "\\mathbf{y} = \\mathbf{z} - \\mathbf{H x}\\tag{3}\n",
       "$$\n",
       "\n",
       "On the right we have $\\mathbf{Hx}$. That should be recognizable as the measurement function. Multiplying $\\mathbf{H}$ with $\\mathbf{x}$ puts $\\mathbf{x}$ into *measurement space*; in other words, the same basis and units as the sensor's measurements. The variable $\\mathbf{z}$ is just the measurement; it is typical, but not universal to use $\\mathbf{z}$ to denote measurements in the literature ($\\mathbf{y}$ is also sometimes used). Do you remember this chart?"
@@ -520,7 +520,7 @@
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-      "The blue point labeled \"prediction\" is the output of $\\mathbf{Hx}$, and the dot labeled \"measurement\" is $\\mathbf{z}$. Therefore, $\\gamma = \\mathbf{z} - \\mathbf{Hx}$ is how we compute the residual, drawn in red, where $\\gamma$ is the residual.\n",
+      "The blue point labeled \"prediction\" is the output of $\\mathbf{Hx}$, and the dot labeled \"measurement\" is $\\mathbf{z}$. Therefore, $\\mathbf{y} = \\mathbf{z} - \\mathbf{Hx}$ is how we compute the residual, drawn in red, where $\\mathbf{z}$ is the residual.\n",
       "\n",
       "The next two lines are the formidable:\n",
       "\n",
@@ -587,7 +587,7 @@
      "metadata": {},
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       "Our next line is:\n",
-      " $$\\mathbf{x}=\\mathbf{x}' +\\mathbf{K\\gamma}\\tag{5}$$\n",
+      " $$\\mathbf{x}=\\mathbf{x}' +\\mathbf{Ky}\\tag{5}$$\n",
       "\n",
       "This just multiplies the residual by the Kalman gain, and adds it to the state variable. In other words, this is the computation of our new estimate.\n",
       "\n",

09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
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@@ -129,9 +131,9 @@
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