Rewrites for orthogonal version of eqns

The changes in the univariate chapter, where I derived the
eqn for K continue to ripple through the chapters.

04-One-Dimensional-Kalman-Filters.ipynb

@@ -546,7 +546,7 @@
     " \n",
     "The equation for Gaussian addition is derived by basic algebra. I assure you it is correct. Therefore it is reasonable to expect that if we are using Gaussians to model physical events, the results must correctly describe those events.\n",
     "\n",
-    "Here is our implementation of the predict function, where `pos` and `movements` are Gaussian tuples:"
+    "Here is our implementation of the predict function, where `pos` and `movement` are Gaussian tuples:"
    ]
   },
   {
@@ -1389,9 +1389,9 @@
     "\\hline\n",
     "\\text{Equation} & \\text{Implementation}\\\\\n",
     "\\hline\n",
-    " x = L\\bar x & y = z - \\mu_z \\\\\n",
+    " x = L\\bar x & y = z - \\bar\\mu \\\\\n",
     " & K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2} \\\\\n",
-    " & x = \\bar x + Ky \\\\\n",
+    " & \\mu = \\bar \\mu + Ky \\\\\n",
     " & \\sigma^2 = \\frac {\\bar\\sigma^2 \\sigma_z^2} {\\bar\\sigma^2 + \\sigma_z^2} \\\\\n",
     "\\hline\n",
     "\\end{array}$\n",

code/mkf_internal.py

@@ -79,7 +79,7 @@ def plot_track_ellipses(N, zs, ps, cov, title):
     plt.show()
 
 
-def show_residual_chart():
+def show_residual_chart(show_eq=True, show_H=False):
     est_y = ((164.2-158)*.8 + 158)
 
     ax = plt.axes(xticks=[], yticks=[], frameon=False)
@@ -105,10 +105,15 @@ def show_residual_chart():
     plt.text (1.0, 164.4, r"measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue')
     plt.text (0, 157.8, r"posterior ($x_{t-1}$)", ha='center', va='top',fontsize=18)
     plt.text (1.02, est_y-1.5, "residual($y$)", ha='left', va='center',fontsize=18)
-    plt.text (1.02, est_y-2.2, r"$y=z-\bar x_t$", ha='left', va='center',fontsize=18)
+    if show_eq:
+        if show_H:
+            plt.text (1.02, est_y-2.2, r"$y=z-H\bar x_t$", ha='left', va='center',fontsize=18)
+        else:
+            plt.text (1.02, est_y-2.2, r"$y=z-\bar x_t$", ha='left', va='center',fontsize=18)
     plt.text (0.9, est_y, "new estimate ($x_t$)", ha='right', va='center',fontsize=18)
     plt.text (0.8, est_y-0.5, "(posterior)", ha='right', va='center',fontsize=18)
-    plt.text (0.75, est_y-1.2, r"$\bar{x}_t + Ky$", ha='right', va='center',fontsize=18)
+    if show_eq:
+        plt.text (0.75, est_y-1.2, r"$\bar{x}_t + Ky$", ha='right', va='center',fontsize=18)
     plt.xlabel('time')
     ax.yaxis.set_label_position("right")
     plt.ylabel('state')
@@ -233,6 +238,7 @@ def show_x_error_chart(count):
         stats.plot_covariance_ellipse ((5,5), ellipse=e3, variance=sigma,
                                        edgecolor='r', alpha=0.25)
         stats.plot_covariance_ellipse (m4[:,0], ellipse=e4, variance=sigma)
+        plt.ylim((-9, 16))
 
     #plt.ylim([0,11])
     #plt.xticks(np.arange(1,4,1))

pdf/build_book

@@ -1,7 +1,7 @@
 #! /bin/bash
 
 #echo "merging book..."
-python merge_book.py
+ipython merge_book.py
 
 echo "creating pdf..."
 ipython nbconvert --to latex --template book book.ipynb

pdf/build_book.bat

@@ -1,4 +1,4 @@
-python merge_book.py
+ipython merge_book.py
 
 ipython nbconvert --to latex --template book book.ipynb
 ipython to_pdf.py

pdf/merge_book.py

@@ -49,6 +49,5 @@ if __name__ == '__main__':
          '../14-Adaptive-Filtering.ipynb',
          '../Appendix-A-Installation.ipynb',
          '../Appendix-B-Symbols-and-Notations.ipynb',
-         #'../Appendix-C-Walking-Through-KF-Code.ipynb',
          '../Appendix-D-HInfinity-Filters.ipynb',
          '../Appendix-E-Ensemble-Kalman-Filters.ipynb'])