Copy edit of math chapter.

Got rid of the duplicates and crud. Ordered sections in logical order,
and better explained the idea of state-space methods.

06-Multivariate-Kalman-Filters.ipynb

@@ -1501,7 +1501,19 @@
     "\n",
     "$$\\mathbf{\\bar{P}} = \\mathbf{FPF}^\\mathsf{T}$$\n",
     "\n",
-    "Expressions in the form $\\mathbf{ABA}^\\mathsf{T}$ are common in linear algebra. You can think of it as *projecting* the middle term by the outer term. We will be using this many times in the rest of the book. I explain its derivation in the *Kalman Math* chapter. \n",
+    "Expressions in the form $\\mathbf{ABA}^\\mathsf{T}$ are common in linear algebra. You can think of it as *projecting* the middle term by the outer term. We will be using this many times in the rest of the book. \n",
+    "\n",
+    "I admit this may be a 'magical' equation to you. If you have some experience with linear algebra and statistics, this may help. The covariance due to the prediction can be modeled as the expected value of the error in the prediction step, given by this equation. \n",
+    "\n",
+    "$$\\begin{aligned}\n",
+    "\\bar{\\mathbf{P}} &= E[(\\mathbf{Fx})(\\mathbf{Fx})^\\mathsf{T}]\\\\\n",
+    " &= E[\\mathbf{Fxx}^\\mathsf{T}\\mathbf{F}^\\mathsf{T}] \\\\\n",
+    " &= \\mathbf{F}\\, E[\\mathbf{xx}^\\mathsf{T}]\\, \\mathbf{F}^\\mathsf{T}\n",
+    "\\end{aligned}$$\n",
+    "\n",
+    "Of course, $E[\\mathbf{xx}^\\mathsf{T}]$ is just $\\mathbf{P}$, giving us\n",
+    "\n",
+    "$$\\bar{\\mathbf{P}} = \\mathbf{FPF}^\\mathsf{T}$$\n",
     "\n",
     "For now we will look at its effect. Here I use $\\mathbf{F}$ from our filter and project the state forward 6/10ths of a second. I do this five times so you can see how $\\mathbf{\\bar{P}}$ continues to change. "
    ]