Title :
Exact and Approximate Bayesian Smoothing Algorithms in Partially Observed Markov Chains
Author :
Ait-El-Fquih, Boujemaa ; Desbouvries, François
Author_Institution :
GET / INT / Dépt. CITI and CNRS UMR 5157, 9 rue Charles Fourier, 91011 Evry, France
Abstract :
Let x = {Xn}n IN be a hidden process, y = {yn}n IN an observed process and r = {rn}n IN some auxiliary process. We assume that t = {tn}n IN with tn = (xn, rn, yn-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.
Keywords :
Bayesian methods; Filtering algorithms; Hidden Markov models; Noise measurement; Parameter estimation; Particle measurements; Probability density function; Smoothing methods; State-space methods; Stochastic processes;
Conference_Titel :
Nonlinear Statistical Signal Processing Workshop, 2006 IEEE
Conference_Location :
Cambridge, UK
Print_ISBN :
978-1-4244-0581-7
Electronic_ISBN :
978-1-4244-0581-7
DOI :
10.1109/NSSPW.2006.4378841