Major rewrites due to discrete bayes changes.

I've derived the x + Ky form for the univariate kalman filter.
I completely reordered material, cutting about 10 pages (pdf)
of material. I made the connection between the bayesian form
and orthogonal form more explicit.

Probably there are a lot of grammatical errors, but I wanted to get
these checked in.

I also altered the css - mainly the font.

code/kf_internal.py

@@ -17,7 +17,12 @@ from __future__ import (absolute_import, division, print_function,
                         unicode_literals)
 
 import book_plots as bp
+import filterpy.stats as stats
+from math import sqrt
 import matplotlib.pyplot as plt
+import numpy as np
+from numpy.random import randn, seed
+
 
 def plot_dog_track(xs, dog, measurement_var, process_var):
     N = len(xs)
@@ -42,4 +47,47 @@ def print_variance(positions):
     print('Variance:')
     for i in range(0, len(positions), 5):
         print('\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(
-                *[v[1] for v in positions[i:i+5]]))
+                *[v[1] for v in positions[i:i+5]]))
+
+
+
+def gaussian_vs_histogram():
+
+    seed(15)
+    xs = np.arange(0, 20, 0.1)
+    ys = np.array([stats.gaussian(x-10, 0, 2) for x in xs])
+    bar_ys = abs(ys + randn(len(xs)) * stats.gaussian(xs-10, 0, 10)/2)
+    plt.gca().bar(xs[::5]-.25, bar_ys[::5], width=0.5, color='g')
+    plt.plot(xs, ys, lw=3, color='k')
+    plt.xlim(5, 15)
+
+
+class DogSimulation(object):
+    def __init__(self, x0=0, velocity=1,
+                 measurement_var=0.0,
+                 process_var=0.0):
+        """ x0 : initial position
+            velocity: (+=right, -=left)
+            measurement_var: variance in measurement m^2
+            process_var: variance in process (m/s)^2
+        """
+        self.x = x0
+        self.velocity = velocity
+        self.meas_std = sqrt(measurement_var)
+        self.process_std = sqrt(process_var)
+
+    def move(self, dt=1.0):
+        """Compute new position of the dog in dt seconds."""
+        dx = self.velocity + randn()*self.process_std
+        self.x += dx * dt
+
+    def sense_position(self):
+        """ Returns measurement of new position in meters."""
+        measurement = self.x + randn()*self.meas_std
+        return measurement
+
+    def move_and_sense(self):
+        """ Move dog, and return measurement of new position in meters"""
+        self.move()
+        return self.sense_position()
+