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.,
3Defence Evaluation and Research Agency, St. Andrews Road, Malvern, Worcestershire WR14 3PS, U.K.,

(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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