TY - GEN

T1 - Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains

AU - Ait El Fquih, Boujemaa

AU - Desbouvries, François

PY - 2006/12/1

Y1 - 2006/12/1

N2 - Let x = {xn}n∈IN be a hidden process, y = {yn}n∈IN an observed process and r = {r n}n∈IN some auxiliary process. We assume that t = {tn}n∈IN with tn = (xn, r n, 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.

AB - Let x = {xn}n∈IN be a hidden process, y = {yn}n∈IN an observed process and r = {r n}n∈IN some auxiliary process. We assume that t = {tn}n∈IN with tn = (xn, r n, 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.

UR - http://www.scopus.com/inward/record.url?scp=48049103010&partnerID=8YFLogxK

U2 - 10.1109/NSSPW.2006.4378841

DO - 10.1109/NSSPW.2006.4378841

M3 - Conference contribution

AN - SCOPUS:48049103010

SN - 1424405815

SN - 9781424405817

T3 - NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

BT - NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

T2 - NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

Y2 - 13 September 2006 through 15 September 2006

ER -