2. Stanford CS223B Computer Vision, Winter 2006 Lecture 11 Filters / Motion Tracking Professor Sebastian Thrun CAs: Dan Maynes-Aminzade, Mitul Saha, Greg Corrado

3. Sebastian Thrun Stanford University CS223B Computer Vision This Lecture is also known as…. All of CS226

4. Sebastian Thrun Stanford University CS223B Computer Vision Moving Objects

5. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter Tracking

6. Sebastian Thrun Stanford University CS223B Computer Vision Particle Filter Tracking

7. Sebastian Thrun Stanford University CS223B Computer Vision Mixture of KF / PF (Unscented PF)

8. Sebastian Thrun Stanford University CS223B Computer Vision Tracking: First Idea! updateinitial position x y x y prediction x y measurement x y

9. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filters

10. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filters prior Measurement evidence posterior

11. Sebastian Thrun Stanford University CS223B Computer Vision A Quiz prior Measurement evidence posterior?

12. Sebastian Thrun Stanford University CS223B Computer Vision The Quiz Derived prior Measurement evidence

13. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter n Linear Measurement model n Linear Change

14. Sebastian Thrun Stanford University CS223B Computer Vision Partially Observable Markov Chains statestate x 4 state x 3 state x 2 state x 1 z2z2 z3z3 z4z4 measurement z 1 state x 4 state x 3 state x 2 state x 1 Bayes filters: HMMs DBNs POMDPs Kalman filters Condensation

15. Sebastian Thrun Stanford University CS223B Computer Vision Bayes Filters x = state z = observation u = control t = time [Kalman 60, Rabiner 85] Markov Bayes Markov

16. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter: Measurement Update n Linear Measurement model

17. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter: Prediction n Linear Change

18. Sebastian Thrun Stanford University CS223B Computer Vision Putting It All Together n Measurements n Change n Prediction n Measurement Update updateinitial position x y x y prediction x y measurement x y

19. Sebastian Thrun Stanford University CS223B Computer Vision Can We Do Better?

20. Sebastian Thrun Stanford University CS223B Computer Vision Kalman, Better! initial positionpredictionmeasurement next prediciton update

21. Sebastian Thrun Stanford University CS223B Computer Vision We Can Estimate Velocity! past measurements prediction

22. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter For 2D Tracking n Linear Measurement model (now with 4 state variables) n Linear Change

23. Sebastian Thrun Stanford University CS223B Computer Vision Putting It Together Again n Measurements n Change n Prediction n Measurement Update

24. Sebastian Thrun Stanford University CS223B Computer Vision Why Linear??

25. Sebastian Thrun Stanford University CS223B Computer Vision Nonlinear Functions…

26. Sebastian Thrun Stanford University CS223B Computer Vision Linearization: Extended Kalman Filter

27. Sebastian Thrun Stanford University CS223B Computer Vision Unscented Kalman Filter

28. Sebastian Thrun Stanford University CS223B Computer Vision Linearization: An example:

29. Sebastian Thrun Stanford University CS223B Computer Vision Summary Kalman Filter n Estimates state of a system –Position –Velocity –Many other continuous state variables possible n KF maintains –Mean vector for the state –Covariance matrix of state uncertainty n Implements –Time update = prediction –Measurement update n Standard Kalman filter is linear-Gaussian –Linear system dynamics, linear sensor model –Additive Gaussian noise (independent) –Nonlinear extensions: extended KF, unscented KF: linearize n More info: –CS226 –Probabilistic Robotics (Thrun/Burgard/Fox, MIT Press)