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Communication Dans Un Congrès Année : 2007

Exact and approximate bayesian smoothing algorithms in partially observed Markov chains

Résumé

Let x = {x n } n∈IN be a hidden process, y = {y n } n∈IN an observed process and r = {r n } n∈IN some auxiliary process. We assume that t = {t n } n∈IN with t n = (x n , r n , y n-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, they reduce to a set of algorithms which includes, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms such as the RTS algorithms, the Two-Filter algorithm or the Bryson and Frazier algorithm. We finally propose particle filtering (PF) approximations for the general case.
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Dates et versions

hal-04415380 , version 1 (24-01-2024)

Identifiants

Citer

Boujemaa Ait-El-Fquih, François Desbouvries. Exact and approximate bayesian smoothing algorithms in partially observed Markov chains. 2006 IEEE Nonlinear Statistical Signal Processing Workshop (NSSPW), Sep 2006, Cambridge, France. pp.148-151, ⟨10.1109/NSSPW.2006.4378841⟩. ⟨hal-04415380⟩
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