A RBPF for Hybrid HMMs Funiak Williams 2003 p(xd.o) (1)Initialization step draw samples from the initial distribution over the modes initialize the corresponding {c20,f inuous state estimate p(xa, tlx. 0: t-1, 31: t-1)(2)Importance sampling step evolve each sample trajector mak1)(() according to the transition model and previous continuous estimates d o: tf (3)Selection(resampling) step P ation model for each sample update continuous estimates Hybrid Mode Estimation and Gaussian Filtering with Hybrid HMM Models 16412/6.834 Lecture,15 March2004 Do we really need hybrid? Alternatives: HMM, grid-based methods: Course discretization ineffective for tracking a dynamic system Kalman filter Unimodal distribution too weak Particle filter: Sample size too large Hybrid Mode Estimation and Gaussian Filtering with Hybrid HMM Models 6412/6.834 Lecture,15 March2004Hybrid Mode Estimation and Gaussian Filtering with Hybrid HMM Models 16.412 / 6.834 Lecture, 15 March 2004 33 RBPF for Hybrid HMMs mok,0 (1) Initialization step (2) Importance sampling step (3) Selection (resampling) step mok,0 mok,1 mok,1 mok,0 mok,1 mf,0 mf,1 (4) Exact (Kalman Filtering) step draw samples from the initial distribution over the modes initialize the corresponding continuous state estimates evolve each sample trajectory according to the transition model and previous continuous estimates determine transition & observ￾ation model for each sample update continuous estimates mok,0 mok,0 mok,0 mok,1 mok,1 mok,1 mok,1 mf,1 mok,1 mok,1 mok,0 mok,0 mok,0 mok,1 mok,1 mok,1 Funiak & Williams 2003 Hybrid Mode Estimation and Gaussian Filtering with Hybrid HMM Models 16.412 / 6.834 Lecture, 15 March 2004 34 Do we really need hybrid? Alternatives: ƒ HMM, grid-based methods: Course discretization ineffective for tracking a dynamic system! ƒ Kalman Filter: Unimodal distribution too weak ƒ Particle filter: Sample size too large