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

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

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

4. Two Models Process model Process model Measurement model Measurement model

5. Kalman Filter Kalman filter Kalman filter –Recursive solution to discrete-data filtering problem (1960’s) –Optimal solution for Gaussian model and linear system Extended Kalman filter 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 State variable: x Measurement variable: z Measurement variable: z Bayesian filtering Bayesian filtering –Bayesian equation –Markov assumption –Discrete time t

7. Particle Filter (1) Advantage Advantage –Non-linear system –Non-Gaussian model Density representation 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 Variations –Several sampling strategies

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

9. CONDENSATION Algorithm (1) Overview 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 Extension –ICONDENSATION Applications Applications –Contour tracking –Color-based tracking –Advantage for tracking problem with the complex state variable