Bayesian fixed-interval smoothing algorithms in singular state-space systems

Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far : the regular case, i.e. with positive definite covariance matrix; and the perfect measurement case, i.e. with...

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Bibliographic Details
Published in2009 IEEE International Workshop on Machine Learning for Signal Processing pp. 1 - 5
Main Authors Ait-El-Fquih, B., Desbouvries, F.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2009
Subjects
Bayesian methods
Calculus
Covariance matrix
Hidden Markov models
Noise measurement
Smoothing methods
Speech enhancement
State-space methods
Technological innovation
Telecommunications
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Summary:Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far : the regular case, i.e. with positive definite covariance matrix; and the perfect measurement case, i.e. with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite (p.s.d.) with arbitrary rank. We exploit the singularity of the model in order to transform the original state-space system into a pairwise Markov chain (PMC) with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.
ISBN:1424449472
9781424449477
ISSN:1551-2541
2378-928X
DOI:10.1109/MLSP.2009.5306257