A Putting it all together Estimate the continuous state for each mode sequence Update the posterior probability of each mode sequence 1. prediction(transition expansion) 2. observation hoti=Pr(m:xit-1, ud,t-1)ht-1xil Hybrid update equations Hofbaur williams 2002 htx; h,txi. t Po(yc, xit) ∑,hxPo(etxt) Old estimate New estimate: (4-.d2).xg,Cm 0- Po b(dd ). coy (b(d d,=(d,-PP) prediction observation Hybrid Mode Estimation and Gaussian Filtering with Hybrid HMM Models 16412/6.834 Lecture,15 March2004 Outline Applications: fault diagnosis, visual tracking Switching linear Gaussian models exact filtering Probabilistic Hybrid Automata filtering Approximate Gaussian filtering with hybrid HMM models 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 27 Putting it all together z Estimate the continuous state for each mode sequence z Update the posterior probability of each mode sequence 1. prediction (transition expansion) 2. observation Hybrid update equations Hofbaur & Williams 2002 Po Pt prediction observation ( ) 1 ( ) 1 1 1 ( ... ), ˆ , i t i b d dt xt C  Old estimate: New estimate: ( ) ( ) 1 ( ... ), ˆ , i t i b d dt xt C t t PtPo b(d ...d ) b(d ...d ) 1 1 1 Hybrid Mode Estimation and Gaussian Filtering with Hybrid HMM Models 16.412 / 6.834 Lecture, 15 March 2004 28 Outline z Applications: fault diagnosis, visual tracking z Switching linear Gaussian models + exact filtering z Probabilistic Hybrid Automata + filtering z Approximate Gaussian filtering with hybrid HMM models