OPTIMAL ESTIMATION AND CRAMÉR-RAO BOUNDS FOR PARTIAL NON-GAUSSIAN STATE SPACE MODELS

NICLAS BERGMAN^{1}, ARNAUD DOUCET^{2} AND NEIL GORDON^{3}

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.