1. CSSE463: Image Recognition Day 31 This week This week Today: Intro to Kalman filtering for tracking Today: Intro to Kalman filtering for tracking Tomorrow: Project workday, status report due Tomorrow: Project workday, status report due Questions? Questions?

2. 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/ http://www.cs.unc.edu/~welch/kalman/ 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 15.4 of Russell and Norvig, Artificial Intelligence: A Modern Approach, ed 2: Prentice Hall, 2003 Chapter 16.6 of Sonka et al. Chapter 16.6 of Sonka et al. Kevin Murphy’s toolbox: http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html Kevin Murphy’s toolbox: http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html

3. Scenarios Imagine: Viewing a small bird flying through a forest Viewing a small bird flying through a forest Tracking a missile given a blip every few seconds Tracking a missile given a blip every few seconds Tracking planets, given intermittent observations Tracking planets, given intermittent observations

4. Scenarios Imagine: Imagine: Viewing a small bird flying through a forest Viewing a small bird flying through a forest Tracking a missile given a blip every few seconds Tracking a missile given a blip every few seconds Tracking planets, given intermittent observations Tracking planets, given intermittent observations In each case: In each case: The observations are noisy The observations are noisy But we can formulate an expectation about the trajectory But we can formulate an expectation about the trajectory

5. Goal We are trying to infer the state, X, of a dynamic system, given only noisy measurements, Z, over time We are trying to infer the state, X, of a dynamic system, given only noisy measurements, Z, over time Q1

6. Example Trajectory of a particle with acceleration due to gravity Trajectory of a particle with acceleration due to gravity State: State: Position, velocity, and acceleration Position, velocity, and acceleration Observations Observations Position only, corrupted by Gaussian noise Position only, corrupted by Gaussian noise Q2

7. Formalism of model A linear system with Gaussian noise: and noisy measurements: Q3,4

8. Algorithm Give initial estimates of Give initial estimates ofIteratively:PredictCorrect Q3-4

9. Limitations Must be a linear system Must be a linear system Noise must be Gaussian Noise must be Gaussian

10. Applications and Extensions Beyond just tracking and physical control…any system with continuous state variables and noisy measurements: Beyond just tracking and physical control…any system with continuous state variables and noisy measurements: Economies! Economies! Ecosystems! Ecosystems! To overcome linearity constraint: To overcome linearity constraint: Extended Kalman filters Extended Kalman filters Switching Kalman filters Switching Kalman filters Particle filters: Monte Carlo method Particle filters: Monte Carlo method

11. Demos Projectile motion (courtesy of Nathan Sickler) Projectile motion (courtesy of Nathan Sickler) Accelerometers: http://www.youtube.com/watch?v=AWAFFZ7rPDc Accelerometers: http://www.youtube.com/watch?v=AWAFFZ7rPDc 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) 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) http://www.youtube.com/user/rfengr http://www.youtube.com/watch?v=86UeUvI7pLQ http://www.youtube.com/watch?v=U1L0X4cts8o http://www.youtube.com/user/rfengr http://www.youtube.com/watch?v=86UeUvI7pLQ http://www.youtube.com/watch?v=U1L0X4cts8o 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) 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) http://www.youtube.com/watch?v=46FswYw-m6o http://www.youtube.com/watch?v=_TXfXoKyMzc&NR=1 http://www.youtube.com/watch?v=46FswYw-m6o http://www.youtube.com/watch?v=_TXfXoKyMzc&NR=1