A lot of changes. I think a lot of changes to the notebooks are just

due to running them. In the process of adding a bunch of new .py
scripts to support the book. Most important is the DiscreteBayes1D.py
class, which implements a Discrete Bayesian filter in a generalized way.

DiscreteBayes1D.py

@@ -0,0 +1,149 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Fri May  2 11:48:55 2014
+
+@author: rlabbe
+"""
+from __future__ import division
+from __future__ import print_function
+
+import copy
+import numpy as np
+import bar_plot
+import numpy.random as random
+import matplotlib.pyplot as plt
+
+''' should this be a class? seems like both sense and update are very
+problem specific
+'''
+
+class DiscreteBayes1D(object):
+
+    def __init__(self, world_map, belief=None):
+        self.world_map = copy.deepcopy(world_map)
+        self.N = len(world_map)
+
+        if belief is None:
+            # create belief, make all equally likely
+            self.belief = np.empty(self.N)
+            self.belief.fill (1./self.N)
+
+        else:
+            self.belief = copy.deepcopy(belief)
+
+        # This will be used to temporarily store calculations of the new
+        # belief. 'k' just means 'this iteration'.
+        self.belief_k = np.empty(self.N)
+
+        assert self.belief.shape == self.world_map.shape
+
+
+    def _normalize (self):
+        s = sum(self.belief)
+        self.belief = self.belief/s
+
+    def sense(self, Z, pHit, pMiss):
+        for i in range (self.N):
+            hit = (self.world_map[i] ==Z)
+            self.belief_k[i] = self.belief[i] * (pHit*hit + pMiss*(1-hit))
+
+        # copy results to the belief vector using swap-copy idiom
+        self.belief, self.belief_k = self.belief_k, self.belief
+        self._normalize()
+
+    def update(self, U, kernel):
+        N = self.N
+        kN = len(kernel)
+        width = int((kN - 1) / 2)
+
+        self.belief_k.fill(0)
+
+        for i in range(N):
+            for k in range (kN):
+                index = (i + (width-k)-U) % N
+                #print(i,k,index)
+                self.belief_k[i] += self.belief[index] * kernel[k]
+
+        # copy results to the belief vector using swap-copy idiom
+        self.belief, self.belief_k = self.belief_k, self.belief
+
+def add_noise (Z, count):
+    n= len(Z)
+    for i in range(count):
+        j = random.randint(0,n)
+        Z[j] = random.randint(0,2)
+
+
+def animate_three_doors (loops=5):
+    world = np.array([1,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0])
+    #world = np.array([1,1,1,1,1])
+    #world = np.array([1,0,1,0,1,0])
+
+
+    f = DiscreteBayes1D(world)
+
+    measurements = np.tile(world,loops)
+    add_noise(measurements, 4)
+
+    for m in measurements:
+        f.sense (m, .8, .2)
+        f.update(1, (.05, .9, .05))
+
+        bar_plot.plot(f.belief)
+        plt.pause(0.01)
+
+
+def _test_filter():
+    def is_near_equal(a,b):
+        try:
+            assert sum(abs(a-b)) < 0.001
+        except:
+            print(a, b)
+            assert False
+
+    def test_update_1():
+        f = DiscreteBayes1D(np.array([0,0,1,0,0]), np.array([0,0,.8,0,0]))
+        f.update (1, [1])
+        is_near_equal (f.belief, np.array([0,0,0,.8,0]))
+
+        f.update (1, [1])
+        is_near_equal (f.belief, np.array([0,0,0,0,.8]))
+
+        f.update (1, [1])
+        is_near_equal (f.belief, np.array([.8,0,0,0,0]))
+
+        f.update (-1, [1])
+        is_near_equal (f.belief, np.array([0,0,0,0,.8]))
+
+        f.update (2, [1])
+        is_near_equal (f.belief, np.array([0,.8,0,0,0]))
+
+        f.update (5, [1])
+        is_near_equal (f.belief, np.array([0,.8,0,0,0]))
+
+
+    def test_undershoot():
+        f = DiscreteBayes1D(np.array([0,0,1,0,0]), np.array([0,0,.8,0,0]))
+        f.update (2, [.2, .8,0.])
+        is_near_equal (f.belief, np.array([0,0,0,.16,.64]))
+
+    def test_overshoot():
+        f = DiscreteBayes1D(np.array([0,0,1,0,0]), np.array([0,0,.8,0,0]))
+        f.update (2, [0, .8, .2])
+        is_near_equal (f.belief, np.array([.16,0,0,0,.64]))
+
+
+    test_update_1()
+    test_undershoot()
+
+if __name__ == "__main__":
+
+    _test_filter()
+
+
+
+    #animate_three_doors(loops=1)
+
+
+
+

Introduction.ipynb

@@ -15,14 +15,34 @@
       "\n",
       "The Kalman filter was introduced to the world via papers published in 1958 and 1960 by Rudolph E Kalman. This work built on work by Nobert Wiener. Kalman's early papers were extremely abstract, but researchers quickly realized that the papers described a very practical technique to  filter noisy data. From then until now it has been an ongoing topic of research, and there are many books and papers devoted not only to the basics, but many specializations and extensions to the technique. If you are reading this, you have likely come across some of them.\n",
       "\n",
-      "If you are like me, you probably find them nearly impenetrable. I find that almost all start with very abstract math, assume familiarity with notation and naming conventions that I haven't seen before, and focus heavily on proof rather than exposition and teaching. This is perhaps understandable, but it is a regrettable situation. \n",
+      "If you are like me, you probably find them nearly impenetrable. I find that almost all start with very abstract math, assume familiarity with notation and naming conventions that I haven't seen before, and focus heavily on proof rather than exposition and teaching. This is perhaps understandable, but it is a regrettable situation and not necessary. \n",
       "\n",
+      "After struggling through this material for some time, things finally began making sense. A majority of my 'aha' moments were due to implementing and experimenting with various simple filters. What to make of an equation like $K_k=P_{k}^{-}H^{T}_{k}[H_k P^{-}_{k} H^{T}_{k} + R_k]^{-1}$ is initially puzzing. This is especially true when it pops out as the result of two to three pages of linear algrebra, and each variable is given only a very abstract, mathematically rigorous definition. One book I have doesn't bother to define $R_k$ despite using it throuout its 4 pages of derivation of K. If instead I tell you that K is just a scaling factor for choosing how much of a measurement and how much of a prediction to use in the filter, what K is becomes obvious (although perhaps the computation is still a bit mysterious). After implementing a few Kalman filters for toy problems and varying the values of various matrices and constants I developed both an intuitive and fairly deep understanding of how Kalman filters work. This knowledge is indispensible; it is trivial to code the handful of linear equations for a Kalman filter, and they never change. I do mean a handful - you can implement the simplest Kalman filter in 10 lines of code. \n",
+      " "
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "** this needs a lot of editting. bored with it for now.**"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
       "While you do need to know some basic probability and some very basic linear algebra to understand and implement Kalman filters, by and large you really do not need to understand the complicated, multi-page derivations. The end result of all the math is a small handful of equations which you can use to perform very sophisticated filtering, smoothing, and tracking. Implementing the basic equations is never difficult. Kalman filter design is much more an art than a science - implementers spend a few minutes writing the basic equations, and then a lot of time tuning the filter for their specific problem. \n",
       "\n",
       "I compare this to a student learning the equation for the volume of a sphere: $V(r) = \\frac{4}{3}\\pi r^3$ A student can use this equation without even understanding the functional notation $V(r)$, and certainly they do not need to be able to derive the equation via calculus. Eventually, in some domains, knowledge of the calculus will become useful, but an enormous amount of work can be done by only knowing the equation and how to apply it. Also, it is often useful to understand facts about a sphere, such as it the shape that encloses the greatest volume with the smallest surface area. You do not have to know how to prove that to make use of that information to explain the reason for why bubbles are round, or to economically fence an area for livestock. \n",
       "\n",
-      "I argue the same is largely true with Kalman filters. In this book I will not prove the Kalman filter equations are correct, nor will I derive them. I will instead strive to build in you an physical, intuitive understanding of what the equations mean, and how they interact. Of course, if you are trying to navigate a spaceship to Mars you will require a more sophisticated understanding than I provide, and you will not view this as a useful resource. But the rest of people, who perhaps wants to track heads in video, or control a little hobby robot, or smooth some data, I think this approach should provide a lot of insight into how to create Kalman filters, and provide enough background that the standard texts are now approachable.\n",
-      "\n",
+      "I argue the same is largely true with Kalman filters. In this book I will not prove the Kalman filter equations are correct, nor will I derive them. I will instead strive to build in you an physical, intuitive understanding of what the equations mean, and how they interact. Of course, if you are trying to navigate a spaceship to Mars you will require a more sophisticated understanding than I provide, and you will not view this as a useful resource. But the rest of people, who perhaps wants to track heads in video, or control a little hobby robot, or smooth some data, I think this approach should provide a lot of insight into how to create Kalman filters, and provide enough background that the standard texts are now approachable."
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
       "#### Prerequisites\n",
       "\n",
       "While Kalman filters are used in many domains, they were initially created to solve problems with missle tracking and navigation. Most of my examples will draw from physical examples such as these. However, I do this not just from a sense of history, but because I believe that helps the student form strong pysical intuitions about what the filter is doing. For example, we will learn how the Kalman filter creates and uses something called \"hidden variables\". This is normally presented in a highly abstract manner. However, it is actually quite simple. Suppose I know your position at several points in time. From that I can calculate your velocity even though I don't have any sensor that directly measures your velocity. In a Kalman filter, if I have a position sensor, the filter will generate the hidden, or unobserved variable velocity. A lot of seemingly arcane terminology suddenly becomes concrete and clear. So you should have taken a basic physics course and understand equations like $d = \\frac{a}{2} t^2 + v_0 t + d_0$\n",
@@ -37,7 +57,7 @@
       "\n",
       "Since this is a book on doing Kalman filtering with Python I will expect that you know Python; I do not attempt to teach it. With that said, it is a very easy language to learn, and it reads much like pseudocode. If you are more familiar with another language I do not think you will have any major difficulties reading the source code. I purposefully restrict the code to the more basic features of Python to accomodate people with varying skill levels. If you use this code in your own work, feel free to use more advanced Python facilities if it strikes your fancy.\n",
       "\n",
-      "So that is a fair amount of prerequisites, but I think you will already have most of them if you are seriously trying to solve a problem where Kalman filters are useful. \n"
+      "So that is a fair amount of prerequisites, but I think you will already have most of them if you are seriously trying to solve a problem where Kalman filters are useful. "
      ]
     },
     {

Kalman Filters.ipynb

@@ -50,7 +50,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 12
+     "prompt_number": 3
     },
     {
      "cell_type": "markdown",
@@ -74,11 +74,11 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "0.9827 0.4385 1.6524 0.6318 -0.2302 -1.0772 -0.0953 0.1147 1.1092 1.6671 0.1331 0.5139 -0.5076 -0.9376 -0.7724 0.4346 -0.3805 -1.9624 -0.3980 -0.9907\n"
+        "-0.9868 -0.7268 -1.2716 1.8108 -0.0831 0.5857 0.3981 -0.2151 0.5696 0.7693 -2.0554 0.0504 -0.4504 0.2174 -0.0658 -0.7274 -1.7664 -0.1899 1.8342 1.9822\n"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
@@ -117,7 +117,7 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAEACAYAAACTXJylAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x28aa590>"
+        "<matplotlib.figure.Figure at 0x3998a50>"
        ]
       },
       {
@@ -128,7 +128,7 @@
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 5
     },
     {
      "cell_type": "markdown",
@@ -167,13 +167,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2e8cb50>"
+        "<matplotlib.figure.Figure at 0x39e8dd0>"
        ]
       }
      ],
-     "prompt_number": 15
+     "prompt_number": 6
     },
     {
      "cell_type": "markdown",
@@ -200,13 +200,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x28b11d0>"
+        "<matplotlib.figure.Figure at 0x39aa8d0>"
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 7
     },
     {
      "cell_type": "code",
@@ -220,13 +220,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2917e10>"
+        "<matplotlib.figure.Figure at 0x39b62d0>"
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 8
     },
     {
      "cell_type": "markdown",
@@ -259,11 +259,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2d9ff90>"
+        "<matplotlib.figure.Figure at 0x39b14d0>"
        ]
       }
      ],
-     "prompt_number": 18
+     "prompt_number": 9
     },
     {
      "cell_type": "markdown",
@@ -295,13 +295,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2e5a390>"
+        "<matplotlib.figure.Figure at 0x3998a90>"
        ]
       }
      ],
-     "prompt_number": 19
+     "prompt_number": 10
     },
     {
      "cell_type": "markdown",
@@ -379,11 +379,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2e8f250>"
+        "<matplotlib.figure.Figure at 0x3a5e410>"
        ]
       }
      ],
-     "prompt_number": 20
+     "prompt_number": 11
     },
     {
      "cell_type": "markdown",
@@ -424,11 +424,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2e6d650>"
+        "<matplotlib.figure.Figure at 0x38ebfd0>"
        ]
       }
      ],
-     "prompt_number": 21
+     "prompt_number": 12
     },
     {
      "cell_type": "markdown",
@@ -464,7 +464,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 22
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -483,7 +483,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 23
+     "prompt_number": 14
     },
     {
      "cell_type": "markdown",
@@ -513,30 +513,30 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "time: 0 position =  1.497 variance =  2.500\n",
-        "time: 1 position =  0.809 variance =  1.667\n",
-        "time: 2 position =  0.817 variance =  1.250\n",
-        "time: 3 position =  0.485 variance =  1.000\n",
-        "time: 4 position =  0.576 variance =  0.833\n",
-        "time: 5 position =  0.681 variance =  0.714\n",
-        "time: 6 position =  0.650 variance =  0.625\n",
-        "time: 7 position =  0.618 variance =  0.556\n",
-        "time: 8 position =  0.763 variance =  0.500\n",
-        "time: 9 position =  0.728 variance =  0.455\n",
-        "time: 10 position =  0.611 variance =  0.417\n",
-        "time: 11 position =  0.546 variance =  0.385\n",
-        "time: 12 position =  0.529 variance =  0.357\n",
-        "time: 13 position =  0.541 variance =  0.333\n",
-        "time: 14 position =  0.527 variance =  0.312\n",
-        "time: 15 position =  0.432 variance =  0.294\n",
-        "time: 16 position =  0.351 variance =  0.278\n",
-        "time: 17 position =  0.326 variance =  0.263\n",
-        "time: 18 position =  0.337 variance =  0.250\n",
-        "time: 19 position =  0.350 variance =  0.238\n"
+        "time: 0 position =  1.439 variance =  2.500\n",
+        "time: 1 position =  1.151 variance =  1.667\n",
+        "time: 2 position =  1.143 variance =  1.250\n",
+        "time: 3 position =  1.171 variance =  1.000\n",
+        "time: 4 position =  0.915 variance =  0.833\n",
+        "time: 5 position =  1.102 variance =  0.714\n",
+        "time: 6 position =  1.095 variance =  0.625\n",
+        "time: 7 position =  0.984 variance =  0.556\n",
+        "time: 8 position =  0.943 variance =  0.500\n",
+        "time: 9 position =  0.957 variance =  0.455\n",
+        "time: 10 position =  0.804 variance =  0.417\n",
+        "time: 11 position =  0.907 variance =  0.385\n",
+        "time: 12 position =  0.605 variance =  0.357\n",
+        "time: 13 position =  0.626 variance =  0.333\n",
+        "time: 14 position =  0.612 variance =  0.312\n",
+        "time: 15 position =  0.610 variance =  0.294\n",
+        "time: 16 position =  0.718 variance =  0.278\n",
+        "time: 17 position =  0.648 variance =  0.263\n",
+        "time: 18 position =  0.589 variance =  0.250\n",
+        "time: 19 position =  0.564 variance =  0.238\n"
        ]
       }
      ],
-     "prompt_number": 24
+     "prompt_number": 15
     },
     {
      "cell_type": "markdown",
@@ -595,7 +595,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 25
+     "prompt_number": 16
     },
     {
      "cell_type": "markdown",
@@ -645,47 +645,47 @@
        "stream": "stdout",
        "text": [
         "UPDATE: 1.0000 , 502.0000\n",
-        "SENSE: 2.5641 , 9.8047\n",
+        "SENSE: 1.8930 , 9.8047\n",
         "\n",
-        "UPDATE: 3.5641 , 11.8047\n",
-        "SENSE: 0.8489 , 5.4138\n",
+        "UPDATE: 2.8930 , 11.8047\n",
+        "SENSE: 2.6048 , 5.4138\n",
         "\n",
-        "UPDATE: 1.8489 , 7.4138\n",
-        "SENSE: 2.1796 , 4.2574\n",
+        "UPDATE: 3.6048 , 7.4138\n",
+        "SENSE: 3.7046 , 4.2574\n",
         "\n",
-        "UPDATE: 3.1796 , 6.2574\n",
-        "SENSE: 3.1866 , 3.8490\n",
+        "UPDATE: 4.7046 , 6.2574\n",
+        "SENSE: 6.3120 , 3.8490\n",
         "\n",
-        "UPDATE: 4.1866 , 5.8490\n",
-        "SENSE: 3.7578 , 3.6904\n",
+        "UPDATE: 7.3120 , 5.8490\n",
+        "SENSE: 6.4078 , 3.6904\n",
         "\n",
-        "UPDATE: 4.7578 , 5.6904\n",
-        "SENSE: 4.2545 , 3.6267\n",
+        "UPDATE: 7.4078 , 5.6904\n",
+        "SENSE: 7.5106 , 3.6267\n",
         "\n",
-        "UPDATE: 5.2545 , 5.6267\n",
-        "SENSE: 5.4039 , 3.6007\n",
+        "UPDATE: 8.5106 , 5.6267\n",
+        "SENSE: 7.1136 , 3.6007\n",
         "\n",
-        "UPDATE: 6.4039 , 5.6007\n",
-        "SENSE: 7.8103 , 3.5900\n",
+        "UPDATE: 8.1136 , 5.6007\n",
+        "SENSE: 6.3304 , 3.5900\n",
         "\n",
-        "UPDATE: 8.8103 , 5.5900\n",
-        "SENSE: 8.9480 , 3.5856\n",
+        "UPDATE: 7.3304 , 5.5900\n",
+        "SENSE: 7.6277 , 3.5856\n",
         "\n",
-        "UPDATE: 9.9480 , 5.5856\n",
-        "SENSE: 11.1128 , 3.5838\n",
+        "UPDATE: 8.6277 , 5.5856\n",
+        "SENSE: 8.4180 , 3.5838\n",
         "\n"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2917fd0>"
+        "<matplotlib.figure.Figure at 0x39f0810>"
        ]
       }
      ],
-     "prompt_number": 26
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -797,13 +797,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x28b19d0>"
+        "<matplotlib.figure.Figure at 0x3a57a50>"
        ]
       }
      ],
-     "prompt_number": 27
+     "prompt_number": 18
     },
     {
      "cell_type": "markdown",
@@ -848,13 +848,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2e60150>"
+        "<matplotlib.figure.Figure at 0x3a57b50>"
        ]
       }
      ],
-     "prompt_number": 28
+     "prompt_number": 19
     },
     {
      "cell_type": "markdown",
@@ -899,13 +899,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2d9aa10>"
+        "<matplotlib.figure.Figure at 0x3a83590>"
        ]
       }
      ],
-     "prompt_number": 29
+     "prompt_number": 20
     },
     {
      "cell_type": "markdown",
@@ -951,13 +951,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x2930650>"
+        "<matplotlib.figure.Figure at 0x3d75410>"
        ]
       }
      ],
-     "prompt_number": 30
+     "prompt_number": 21
     },
     {
      "cell_type": "markdown",
@@ -1011,13 +1011,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x28aaad0>"
+        "<matplotlib.figure.Figure at 0x39f0050>"
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 22
     },
     {
      "cell_type": "markdown",
@@ -1041,12 +1041,64 @@
      "collapsed": false,
      "input": [
       "author notes:\n",
-      "    clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end."
+      "    clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end.\n",
+      "    \n",
+      "    "
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 31
+     "outputs": [
+      {
+       "ename": "SyntaxError",
+       "evalue": "invalid syntax (<ipython-input-23-1e7762f04e9a>, line 1)",
+       "output_type": "pyerr",
+       "traceback": [
+        "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-23-1e7762f04e9a>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    author notes:\u001b[0m\n\u001b[1;37m               ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
+       ]
+      }
+     ],
+     "prompt_number": 23
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "sensor_error = 30\n",
+      "movement_error = 2\n",
+      "pos = (1000,500)\n",
+      "\n",
+      "zs = []\n",
+      "ps = []\n",
+      "\n",
+      "\n",
+      "for i in range(100):\n",
+      "    pos = update(pos[0], pos[1], movement, movement_error)\n",
+      "\n",
+      "    Z = math.sin(i/3.)*5.\n",
+      "    zs.append(Z)\n",
+      "    \n",
+      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+      "    ps.append(pos[0])\n",
+      "\n",
+      "\n",
+      "p1, = plot(zs,c='r', linestyle='dashed')\n",
+      "p2, = plot(ps, c='b')\n",
+      "legend([p1,p2], ['measurement', 'filter'], 2)\n",
+      "show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEACAYAAABfxaZOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x3a7ab50>"
+       ]
+      }
+     ],
+     "prompt_number": 27
     }
    ],
    "metadata": {}

KalmanFilter1D.py

@@ -0,0 +1,129 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu May  1 19:48:54 2014
+
+@author: rlabbe
+"""
+from __future__ import division
+import gauss as g;
+import math
+import matplotlib.pyplot as plt
+import noise
+import numpy.random as random
+
+
+class KalmanFilter1D(object):
+
+    def __init__ (self, est_0=g.gaussian(0,1000)):
+        self.estimate = est_0
+
+    def update_estimate(self, Z):
+        self.estimate = self.estimate * Z
+
+    def project_ahead(self, U):
+        self.estimate = self.estimate + U
+
+
+
+def fixed_error_kf(measurement_error, motion_error, noise_factor = 1.0):
+    mu = 0
+    sig = 1000
+    measurements = [x+5 for x in range(100)]
+    f = KalmanFilter1D (g.gaussian(mu,sig))
+
+    ys = []
+    errs = []
+    xs = []
+
+    for i in range(len(measurements)):
+        r = noise.white_noise (noise_factor)
+        m = measurements[i] + r
+        f.update_estimate (g.gaussian(m, measurement_error))
+
+        xs.append(m)
+        ys.append(f.estimate.mu)
+        errs.append (f.estimate.sigma)
+
+        f.project_ahead (g.gaussian(20, motion_error))
+
+    plt.clf()
+
+    p1, = plt.plot (measurements, 'r')
+    p2, = plt.plot (xs,'g')
+    p3, = plt.plot (ys, 'b')
+    plt.legend ([p1,p2,p3],['actual', 'measurement', 'filter'], 2)
+    #plt.errorbar (x=range(len(ys)), color='b', y=ys, yerr=errs)
+    plt.show()
+
+def varying_error_kf(noise_factor=1.0):
+    motion_sig = 2.
+    mu = 0
+    sig = 1000
+
+
+    f = KF1D (mu,sig)
+    ys = []
+    us = []
+    errs = []
+    xs = []
+
+    for i in range(len(measurements)):
+        r = random.randn() * noise_factor
+        m = measurements[i] + r
+        print (r)
+        f.update (m, abs(r*10))
+        xs.append(m)
+        #print ("measure:" + str(f.estimate))
+        ys.append(f.estimate.mu)
+        errs.append (f.estimate.sigma)
+
+        f.predict (1.0, motion_sig)
+        #print ("predict:" + str(f.estimate))
+
+    plt.clf()
+    plt.plot (measurements, 'r')
+    plt.plot (xs,'g')
+    plt.errorbar (x=range(len(ys)), color='b', y=ys, yerr=errs)
+    plt.show()
+
+
+def _test_foo ():
+    sensor_error = 1
+    movement = .1
+    movement_error = .1
+    pos = g.gaussian(1,500)
+
+    zs = []
+    ps = []
+    filter_ = KalmanFilter1D(pos)
+    m_1 = filter_.estimate.mu
+
+    for i in range(300):
+        filter_.update_estimate(g.gaussian(movement, movement_error))
+
+        Z = math.sin(i/12.) + math.sqrt(abs(noise.white_noise(.02)))
+        movement = filter_.estimate.mu - m_1
+        m_1 = filter_.estimate.mu
+
+        print movement, filter_.estimate.sigma
+        zs.append(Z)
+
+        filter_.project_ahead (g.gaussian(Z, sensor_error))
+        ps.append(filter_.estimate[0])
+
+
+    p1, = plt.plot(zs,c='r', linestyle='dashed')
+    p2, = plt.plot(ps, c='b')
+    plt.legend([p1,p2], ['measurement', 'filter'], 2)
+    plt.show()
+
+if __name__ == "__main__":
+
+    if 1:
+        # use same seed to get repeatable results
+        random.seed(10)
+
+    fixed_error_kf(measurement_error=100.,
+                   motion_error=.1,
+                   noise_factor=50)
+    #_test_foo()

Multidimensional Kalman Filters.ipynb

@@ -206,7 +206,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x4087550>"
+        "<matplotlib.figure.Figure at 0x3106550>"
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@@ -250,7 +250,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x467ae50>"
+        "<matplotlib.figure.Figure at 0x3272bd0>"
        ]
       },
       {
@@ -258,7 +258,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4a11b90>"
+        "<matplotlib.figure.Figure at 0x371a1d0>"
        ]
       },
       {
@@ -266,11 +266,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4a61ed0>"
+        "<matplotlib.figure.Figure at 0x3795710>"
        ]
       }
      ],
-     "prompt_number": 50
+     "prompt_number": 8
     },
     {
      "cell_type": "markdown",
@@ -319,7 +319,7 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4080a10>"
+        "<matplotlib.figure.Figure at 0x3106410>"
        ]
       }
      ],
@@ -349,7 +349,7 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAWgAAAEACAYAAACeQuziAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x4731890>"
+        "<matplotlib.figure.Figure at 0x325fad0>"
        ]
       }
      ],
@@ -371,7 +371,9 @@
       "e1 = g.sigma_ellipses(cov, x=1, y=1, sigma=sigma)\n",
       "e2 = g.sigma_ellipses(cov, x=2, y=2, sigma=sigma)\n",
       "e3 = g.sigma_ellipses(cov, x=3, y=3, sigma=sigma)\n",
-      "g.plot_sigma_ellipses([e1, e2, e3], axis_equal=True,x_lim=[0,4],y_lim=[0,15])"
+      "g.plot_sigma_ellipses([e1, e2, e3], axis_equal=True,x_lim=[0,4],y_lim=[0,15])\n",
+      "plt.ylim([0,11])\n",
+      "show()"
      ],
      "language": "python",
      "metadata": {},
@@ -379,13 +381,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x468b210>"
+        "<matplotlib.figure.Figure at 0x371e050>"
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -410,7 +412,7 @@
       "isct = Ellipse(xy=(2,2), width=.2, height=1.2, edgecolor='r', fc='None', lw=4)\n",
       "plt.figure().gca().add_artist(isct)\n",
       "g.plot_sigma_ellipses([e1, e2, e3, ev], axis_equal=True,x_lim=[0,4],y_lim=[0,15])\n",
-      "\n",
+      "plt.ylim([0,11])\n",
       "plt.show()"
      ],
      "language": "python",
@@ -419,13 +421,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x490c8d0>"
+        "<matplotlib.figure.Figure at 0x3719990>"
        ]
       }
      ],
-     "prompt_number": 49
+     "prompt_number": 15
     },
     {
      "cell_type": "markdown",
@@ -441,41 +443,36 @@
      "metadata": {},
      "source": [
       "### Kalman Filter Algorithm\n",
-      "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the **measurement function**. Then we predict the next position by using the current estimate and something called the **state transition function**. In our example above, *new_position = old_position + velocity&ast;time*. Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the **residual**. Finally, we use something called the **Kalman gain** to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa."
+      "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the **measurement function**. Then we predict the next position by using the current estimate and something called the **state transition function**. In our example above, *new_position = old_position + velocity&ast;time*. Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the **residual**. Finally, we use something called the **Kalman gain** to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. \n",
+      "\n",
+      "The chart shows a prior estimate of $x=1$ and $\\dot{x}=1$ ($\\dot{x}$ is the shorthand for the derivative of x, which is velocity). Therefore we predict $\\hat{x}=2$. However, the new measurement $x^{'}=1.3$, giving a residual $r=0.7$. Finally, Kalman filter gain $k$ gives us a new estimate of $\\hat{x^{'}}=1.8$.\n",
+      "\n",
+      "** CHECK SYMBOLOGY!!!!**"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "xlim([0.9,2.5]);ylim([0,3])\n",
-      "\n",
-      "scatter ([1,2,2],[1,2,1.3])\n",
-      "ax = plt.axes()\n",
-      "ax.arrow(1, 1, .83, .83, head_width=0.1, head_length=0.2, fc='r', ec='r',label='estimate')\n",
-      "ax.annotate('prediction', xy=(2, 2.15))\n",
-      "ax.annotate('measurement', xy=(2, 1.1))\n",
-      "ax.annotate('residual', xy=(2.1,1.6), color='b')\n",
-      "ax.annotate('', xy=(2,2), xytext=(2,1.3), \n",
-      "            arrowprops=dict(arrowstyle=\"<->\",\n",
-      "                            connectionstyle=\"bar\",\n",
-      "                            ec=\"b\",\n",
-      "                            shrinkA=3, shrinkB=3))\n",
-      "show()"
+      "from mkf_internal import *\n",
+      "show_residual_chart()"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAEACAYAAAB8nvebAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x4a34890>"
+       "ename": "NameError",
+       "evalue": "global name 'xlim' is not defined",
+       "output_type": "pyerr",
+       "traceback": [
+        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+        "\u001b[1;32m<ipython-input-19-cd0500ac6f58>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mmkf_internal\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mshow_residual_chart\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+        "\u001b[1;32m/var/host/media/removable/chrome/CS373/book/mkf_internal.py\u001b[0m in \u001b[0;36mshow_residual_chart\u001b[1;34m()\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mshow_residual_chart\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m     \u001b[0mxlim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0.9\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2.5\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[0mylim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2.5\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m     \u001b[0mscatter\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1.3\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+        "\u001b[1;31mNameError\u001b[0m: global name 'xlim' is not defined"
        ]
       }
      ],
-     "prompt_number": 133
+     "prompt_number": 19
     },
     {
      "cell_type": "code",
@@ -483,7 +480,8 @@
      "input": [],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [],
+     "prompt_number": 13
     }
    ],
    "metadata": {}

bar_plot.py

@@ -0,0 +1,16 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Fri May  2 12:21:40 2014
+
+@author: rlabbe
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+
+def plot(pos):
+    plt.cla()
+    ax = plt.gca()
+    x = np.arange(len(pos))
+    ax.bar(x, pos)
+    plt.ylim([0,1])
+    plt.xticks(x+0.5, x)

gauss.py

@@ -50,68 +50,9 @@ class KF1D(object):
         self.estimate = self.estimate + gaussian (U,var)
 
 
-measurements = [x+5 for x in range(100)]
 
 
 
-def fixed_error_kf(measurement_error, noise_factor = 1.0):
-    motion_sig = 2.
-    mu = 0
-    sig = 1000
-
-    f = KF1D (mu,sig)
-
-    ys = []
-    errs = []
-    xs = []
-
-    for i in range(len(measurements)):
-        r = random.randn() * noise_factor
-        m = measurements[i] + r
-        f.update (m, measurement_error)
-
-        xs.append(m)
-        ys.append(f.estimate.mu)
-        errs.append (f.estimate.sigma)
-
-        f.predict (1.0, motion_sig)
-
-    plt.clf()
-
-    plt.plot (measurements, 'r')
-    plt.plot (xs,'g')
-    plt.errorbar (x=range(len(ys)), color='b', y=ys, yerr=errs)
-    plt.show()
-
-def varying_error_kf(noise_factor=1.0):
-    motion_sig = 2.
-    mu = 0
-    sig = 1000
 
 
-    f = KF1D (mu,sig)
-    ys = []
-    us = []
-    errs = []
-    xs = []
-
-    for i in range(len(measurements)):
-        r = random.randn() * noise_factor
-        m = measurements[i] + r
-        print (r)
-        f.update (m, abs(r*10))
-        xs.append(m)
-        #print ("measure:" + str(f.estimate))
-        ys.append(f.estimate.mu)
-        errs.append (f.estimate.sigma)
-
-        f.predict (1.0, motion_sig)
-        #print ("predict:" + str(f.estimate))
-
-    plt.clf()
-    plt.plot (measurements, 'r')
-    plt.plot (xs,'g')
-    plt.errorbar (x=range(len(ys)), color='b', y=ys, yerr=errs)
-    plt.show()
-
-varying_error_kf( noise_factor=100)
+#varying_error_kf( noise_factor=100)

gaussian.py

@@ -96,8 +96,6 @@ def plot_sigma_ellipse(ellipse,title=None):
 
 def plot_sigma_ellipses(ellipses,title=None,axis_equal=True,x_lim=None,y_lim=None):
     """ plots the ellipse produced from sigma_ellipse."""
-    isct = plt.Circle((2,2),1,color='b',fill=False)
-    plt.figure().gca().add_patch(isct)
 
     if x_lim is not None:
         axis_equal = False

mkf_internal.py

@@ -0,0 +1,27 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu May  1 16:56:49 2014
+
+@author: rlabbe
+"""
+
+def show_residual_chart():
+    xlim([0.9,2.5]);ylim([0.5,2.5])
+
+    scatter ([1,2,2],[1,2,1.3])
+    scatter ([2],[1.8],marker='o')
+    ax = plt.axes()
+    ax.annotate('', xy=(2,2), xytext=(1,1),
+                arrowprops=dict(arrowstyle='->', ec='b',shrinkA=3, shrinkB=4))
+    ax.annotate('prediction', xy=(1.7,2), color='b')
+    ax.annotate('measurement', xy=(2.05, 1.28))
+    ax.annotate('prior measurement', xy=(1, 0.9))
+    ax.annotate('residual', xy=(2.04,1.6), color='r')
+    ax.annotate('new estimate', xy=(2,1.8),xytext=(2.15,1.9),
+                arrowprops=dict(arrowstyle='->', shrinkA=3, shrinkB=4))
+    ax.annotate('', xy=(2,2), xytext=(2,1.3),
+                arrowprops=dict(arrowstyle="<->",
+                                ec="r",
+                                shrinkA=5, shrinkB=5))
+    title("Kalman Filter Prediction Update Step")
+    show()

noise.py

@@ -0,0 +1,13 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Fri May  2 10:28:27 2014
+
+@author: rlabbe
+"""
+import numpy.random
+def white_noise (sigma2=1.):
+    return sigma2 * numpy.random.randn()
+
+
+if __name__ == "__main__":
+    assert white_noise(.0) == 0.