TY - GEN

T1 - Bayesian fixed-interval smoothing algorithms in singular state-space systems

AU - Ait El Fquih, Boujemaa

AU - Desbouvries, F.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.c, 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.

AB - 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.c, 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.

UR - http://www.scopus.com/inward/record.url?scp=77950958257&partnerID=8YFLogxK

U2 - 10.1109/MLSP.2009.5306257

DO - 10.1109/MLSP.2009.5306257

M3 - Conference contribution

AN - SCOPUS:77950958257

SN - 9781424449484

T3 - Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009

BT - Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009

T2 - Machine Learning for Signal Processing XIX - 2009 IEEE Signal Processing Society Workshop, MLSP 2009

Y2 - 2 September 2009 through 4 September 2009

ER -