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/custom.css

@@ -1,23 +1,62 @@
 <style>
 @import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');
-@import url('http://fonts.googleapis.com/css?family=Vollkorn');
-@import url('http://fonts.googleapis.com/css?family=Arimo');
-@import url('http://fonts.googleapis.com/css?family=Fira+sans');
+@import url('http://fonts.googleapis.com/css?family=Lora');
+
+//@import url('http://fonts.googleapis.com/css?family=Open+Sans');
+//@import url('http://fonts.googleapis.com/css?family=Vollkorn');
+//@import url('http://fonts.googleapis.com/css?family=Karla');
+//@import url('http://fonts.googleapis.com/css?family=Poppins');
+//@import url('http://fonts.googleapis.com/css?family=Arimo');
+//@import url('http://fonts.googleapis.com/css?family=Roboto');
+//@import url('http://fonts.googleapis.com/css?family=Lato');
+//@import url('http://fonts.googleapis.com/css?family=Domine');
+//@import url('http://fonts.googleapis.com/css?family=Chivo');
+//@import url('http://fonts.googleapis.com/css?family=Cardo');
+//@import url('http://fonts.googleapis.com/css?family=Arvo');
+//@import url('http://fonts.googleapis.com/css?family=Crimson+Text');
+//@import url('http://fonts.googleapis.com/css?family=Ubuntu');
+//@import url('http://fonts.googleapis.com/css?family=Fontin');
+//@import url('http://fonts.googleapis.com/css?family=Raleway');
+//@import url('http://fonts.googleapis.com/css?family=Merriweather');
+
 
 .CodeMirror pre {
     font-family: 'Source Code Pro', Consolas, monocco, monospace;
 }
     div.cell{
-        width: 900px;
+        width: 800px;
         margin-left: 0% !important;
         margin-right: auto;
     }
+    div.text_cell_render{
+        font-family: 'Lora';
+        //font-family: 'Open Sans';
+        //font-family: 'Karla',verdana,arial,sans-serif;
+        //font-family: 'Roboto',verdana,arial,sans-serif;
+        //font-family: 'Lato',verdana,arial,sans-serif;
+        //font-family: 'Domine',verdana,arial,sans-serif;
+        //font-family: 'Chivo',verdana,arial,sans-serif;
+        //font-family: 'Cardo',verdana,arial,sans-serif;
+        //font-family: 'Arvo',verdana,arial,sans-serif;
+        //font-family: 'Poppins',verdana,arial,sans-serif;   
+        //font-family: 'Ubuntu',verdana,arial,sans-serif;
+        //font-family: 'Fontin',verdana,arial,sans-serif;
+        //font-family: 'Raleway',verdana,arial,sans-serif;
+        //font-family: 'Merriweather',verdana,arial,sans-serif;
+        //font-family: 'Crimson Text', verdana,arial,sans-serif;
+        //font-family: verdana,arial,sans-serif;
+        //font-family: arial,sans-serif;
+        line-height: 125%;
+        font-size: 130%;
+        text-align: justify;
+        text-justify:inter-word;
+    }
     div.text_cell code {
         background: transparent;
         color: #000000;
-        font-weight: 600;
+        font-weight: 400;
         font-size: 12pt;
-        font-style: bold;
+        //font-style: bold;
         font-family:  'Source Code Pro', Consolas, monocco, monospace;
    }
     h1 {
@@ -96,13 +135,6 @@
         display: block;
         white-space: nowrap;
     }
-    div.text_cell_render{
-        /*font-family: 'Vollkorn', verdana,arial,sans-serif;*/
-        line-height: 150%;
-        font-size: 130%;
-        text-align: justify;
-        text-justify:inter-word;
-    }
     div.output_subarea.output_text.output_pyout {
         overflow-x: auto;
         overflow-y: scroll;

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()
+