CSSE463: Image Recognition
 This week
Day 31
Today: Intro to Kalman filtering for tracking
 Tomorrow: Project workday, status report due
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Questions?
Motion models for tracking
The Kalman filter is a probabilistic model
that combines noisy measurements with
the expected trajectory of the object. It
works even with occlusion.
Ideas presented here are from

http://www.cs.unc.edu/~welch/kalman/

chapter 15.4 of Russell and Norvig, Artificial Intelligence: A
Modern Approach, ed 2: Prentice Hall, 2003
Chapter 16.6 of Sonka et al.
Kevin Murphy’s toolbox:
http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html
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Scenarios
Imagine:
Viewing a small bird flying through a forest
 Tracking a missile given a blip every few
seconds
 Tracking planets, given intermittent
observations

Scenarios

Imagine:
Viewing a small bird flying through a forest
 Tracking a missile given a blip every few
seconds
 Tracking planets, given intermittent
observations

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In each case:
The observations are noisy
 But we can formulate an expectation about
the trajectory

Goal

We are trying to infer the state, X, of a
dynamic system, given only noisy
measurements, Z, over time
Q1
Example
Trajectory of a particle with acceleration
due to gravity
 State:


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Position, velocity, and acceleration
Observations

Position only, corrupted by Gaussian noise
Q2
Formalism of model
A linear system with Gaussian noise:
x k 1  Ax k  w k
and noisy measurements:
z k  Hx k  v k
Q3,4
Algorithm

 Give initial estimates of xˆ k  1 and Pk  1
Iteratively:
Predict
xˆ k
Pk



Correct


 A xˆ k 1  Bu

 AP k 1 A
T
k 1
Q
Kk 
xˆ k
Pk


Pk H

HP k H
 xˆ k

T
T
 R

 K k ( z k  H xˆ k )
 ( I  K k H ) Pk

Q3-4
Limitations
Must be a linear system
 Noise must be Gaussian
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Applications and Extensions

Beyond just tracking and physical
control…any system with continuous state
variables and noisy measurements:
Economies!
 Ecosystems!
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To overcome linearity constraint:
Extended Kalman filters
 Switching Kalman filters
 Particle filters: Monte Carlo method
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Demos
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Projectile motion (courtesy of Nathan Sickler)
Accelerometers:
http://www.youtube.com/watch?v=AWAFFZ7rPDc
Tracking:
http://www.youtube.com/user/rfengr (bright colors)
http://www.youtube.com/watch?v=86UeUvI7pLQ
(ES453: uniform ribbon)
http://www.youtube.com/watch?v=U1L0X4cts8o (RC car)
Balancing robots:
http://www.youtube.com/watch?v=46FswYw-m6o
(inverted pendulum)
http://www.youtube.com/watch?v=_TXfXoKyMzc&NR=1
(Boston Scientific’s Big Dog)