Particle Filtering for Non-Linear/Non-Gaussian System

1. Particle Filtering for Non-Linear/Non-Gaussian System Bohyung Han bhhan@cs.umd.edu

2. Outline • Introduction • Kalman Filter and its extensions • Bayesian Framework • Particle Filter • Applications

3. Introduction • Estimation • Parameter space • Observation space • Probabilistic mapping from parameter space to observation space • Estimation rule: Bayesian • Filter • Kind of a tool for estimation

4. Two Models • Process model • Measurement model

5. Kalman Filter • Kalman filter • Recursive solution to discrete-data filtering problem (1960’s) • Optimal solution for Gaussian model and linear system • Extended Kalman filter • Using the first order Taylor expansion • Approx. to non-linear system • Still valid only for Gaussian model

6. Bayesian Filtering • State variable: x • Measurement variable: z • Bayesian filtering • Bayesian equation • Markov assumption • Discrete time t

7. Particle Filter (1) • Advantage • Non-linear system • Non-Gaussian model • Density representation • Particle (sample) and its weight • If the number of samples is infinite, the density by sampling will converge to the real density. • Variations • Several sampling strategies

8. Particle Filter (2) • Prediction • Measurement • Update • Resample

9. CONDENSATION Algorithm (1) • Overview • Conditional Density Propagation • Isard and Blake [ECCV’96] • A variation of particle filter • The first application to computer vision problem

10. CONDENSATION Algorithm (2)

11. CONDENSATION Algorithm (3)

12. Extension and Applications • Extension • ICONDENSATION • Applications • Contour tracking • Color-based tracking • Advantage for tracking problem with the complex state variable