AISM 53, 97-112
© 2001 British Crown Copyright

Optimal estimation and Cramér-Rao bounds for partial non-Gaussian state space models

Niclas Bergman1, Arnaud Doucet2 and Neil Gordon3

1Division of Automatic Control, Linköping University, S-581 83 Linköping, Sweden
2Signal Processing Group, Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, U.K., e-mail:ad2@eng.cam.ac.uk
3Defence Evaluation and Research Agency, St. Andrews Road, Malvern, Worcestershire WR14 3PS, U.K., e-mail:N.Gordon@signal.dera.gov.uk

(Received May 1, 2000; revised August 4, 2000)

Abstract.    Partial non-Gaussian state-space models include many models of interest while keeping a convenient analytical structure. In this paper, two problems related to partial non-Gaussian models are addressed. First, we present an efficient sequential Monte Carlo method to perform Bayesian inference. Second, we derive simple recursions to compute posterior Cramér-Rao bounds (PCRB). An application to jump Markov linear systems (JMLS) is given.

Key words and phrases:    Optimal estimation, Bayesian inference, sequential Monte Carlo methods, posterior Cramér-Rao bounds.

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