Exact Fast Computation of Optimal Filter in Gaussian Switching Linear Systems
Stéphane Derrode, Wojciech Pieczynski · IEEE Signal Processing Letters · 2013
We consider triplet Markov Gaussian linear systems (X,R,Y), whereXis hidden continuous random sequence,Ris hidden discrete Markov chain,Yis observed continuous random sequence, and (X,Y) is Gaussian conditionally onR. In the classical “Conditionally Gaussian Linear State-Space Model” (CGLSSM), optimal filter is not workable with a reasonable complexity. The aim of the paper is to propose a new model, quite close to the CGLSSM, belonging to the general and recently proposed family of models, called “Conditionally Markov Switching Hidden Linear Models” (CMSHLMs), in which the computation of optimal filter with complexity linear in the number of observations is feasible. The new model and related filtering are immediately applicable in all situations where the classical CGLSSM is used via approximated filtering.