More copyediting changes.

Author: rlabbe

06-Multivariate-Kalman-Filters.ipynb

@@ -1804,7 +1804,7 @@
     "\n",
     "This notation allows a mathematician to express himself exactly, and when it comes to formal publications presenting new results this precision is necessary. As a programmer I find all of that fairly unreadable; I am used to thinking about variables changing state as a program runs, and do not use a different variable name for each new computation. There is no agreed upon format, so each author makes different choices. I find it challenging to switch quickly between books an papers, and so have adopted my admittedly less precise notation. Mathematicians will write scathing emails to me, but I hope the programmers and students will rejoice.\n",
     "\n",
-    "Here are some examples for how other authors write the prior: $X^*_{n+1,n}$, $\\underline{\\hat{x}}_k(-)$ (really!), $\\hat{\\textbf{x}}^-_{k+1}$, $\\hat{x}_{k}$. If you are lucky an author defines the notation; more often you have to read the equations in context to recognize what the author is doing. Of course, people write within a tradition; papers on Kalman filters in finance are likely to use one set of notations while papers on radar tracking is likely to use a different set. Over time you will start to become familiar with trends, and also instantly recognize when somebody just copied equations wholesale from another work. For example - the equations I gave above were copied from Wikipedia.[6]\n",
+    "Here are some examples for how other authors write the prior: $X^*_{n+1,n}$, $\\underline{\\hat{x}}_k(-)$ (really!), $\\hat{\\textbf{x}}^-_{k+1}$, $\\hat{x}_{k}$. If you are lucky an author defines the notation; more often you have to read the equations in context to recognize what the author is doing. Of course, people write within a tradition; papers on Kalman filters in finance are likely to use one set of notations while papers on radar tracking is likely to use a different set. Over time you will start to become familiar with trends, and also instantly recognize when somebody just copied equations wholesale from another work. For example - the equations I gave above were copied from the  Wikipedia [Kalman Filter](https://en.wikipedia.org/wiki/Kalman_filter#Details) [[1]](#[wiki_article]) article.\n",
     "\n",
     "The *Symbology* Chapter lists the notation used by various authors. This brings up another difficulty. Different authors use different variable names. $\\mathbf{x}$ is fairly universal, but after that it is anybody's guess. Again, you need to read carefully, and hope that the author defines their variables (they often do not).\n",
     "\n",
@@ -2901,16 +2901,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "- [1] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\n",
-    "\n",
-    "- [2] https://en.wikipedia.org/wiki/Kalman_filter\n",
-    "\n",
-    "- [3] Brown, Robert Grover. *Introduction to Random Signals and Applied Kalman Filtering* John Wiley & Sons, Inc. 2012\n",
-    "\n",
-    "- [4] `FilterPy` library. Roger Labbe.\n",
-    "https://github.com/rlabbe/filterpy\n",
-    "\n",
-    "- [6] 'Kalman Filters'. Wikipedia\n",
+    "- <A name=\"[wiki_article]\">[1]</A> 'Kalman Filters'. Wikipedia\n",
     "https://en.wikipedia.org/wiki/Kalman_filter#Details"
    ]
   }

08-Designing-Kalman-Filters.ipynb

@@ -280,6 +280,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "**Author's note: clean up ball example, add control input example.**\n",
+    "\n",
     "In the last chapter we worked with 'textbook' problems. These are problems that are easy to state, program in a few lines of code, and teach. Real world problems are rarely 'textbook'. In this chapter, and the remainder of the book, we will work with more realistic examples. \n",
     "\n",
     "We will begin by tracking a robot in a 2D space, such as a field or warehouse. We will start with a simple noisy sensor that outputs noisy $(x,y)$ coordinates which we will need to filter to generate a 2D track. Once we have mastered this concept, we will extend the problem significantly with more sensors and then adding control inputs. \n",
@@ -542,9 +544,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The measurement function $ \\mathbf{H}$ defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. In this case we have measurements for (x,y), so we will design $\\mathbf{z}$ as $\\begin{bmatrix}x& y\\end{bmatrix}^\\mathsf{T}$ which is dimension 2x1. Our state variable is size 4x1. We can deduce the required size for $\\textbf{H}$ by recalling that multiplying a matrix of size MxN by NxP yields a matrix of size MxP. Thus,\n",
+    "The measurement function $\\mathbf{H}$ defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. In this case we have measurements for (x,y), so we will design $\\mathbf{z}$ as $\\begin{bmatrix}x & y\\end{bmatrix}^\\mathsf{T}$ which is dimension 2x1. Our state variable is size 4x1. We can deduce the required size for $\\textbf{H}$ by recalling that multiplying a matrix of size MxN by NxP yields a matrix of size MxP. Thus,\n",
     "\n",
-    "$$ (2\\times 1) = (a\\times b)(4 \\times 1) = (2\\times 4)(4\\times 1)$$\n",
+    "$$(2\\times 1) = (a\\times b)(4 \\times 1) = (2\\times 4)(4\\times 1)$$\n",
     "\n",
     "So, $\\textbf{H}$ is 2x4.\n",
     "\n",