MAXIMUM A POSTERIORI SEQUENCE ESTIMATION USING MONTE CARLO PARTICLE FILTERS

SIMON GODSILL ARNAUD DOUCET^{1} AND MIKE WEST^{2}

1Signal Processing Laboratory, University of Cambridge, Cambridge CB2 1PZ, U.K.,

e-mail: sjg@eng.cam.ac.uk; ad2@eng.cam.ac.uk

2Institute of Statistics and Decision Sciences, Duke University, Durham NC 27708-0251, U.S.A., e-mail: mw@isds.duke.edu

(Received May 8, 2000; revised August 12, 2000)

Abstract. We develop methods for performing maximum a posteriori (MAP) sequence estimation in non-linear non-Gaussian dynamic models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. MAP sequence estimation is then performed using a classical dynamic programming technique applied to the discretised version of the state space. In contrast with standard approaches to the problem which essentially compare only the trajectories generated directly during the filtering stage, our method efficiently computes the optimal trajectory over all combinations of the filtered states. A particular strength of the method is that MAP sequence estimation is performed sequentially in one single forwards pass through the data without the requirement of an additional backward sweep. An application to estimation of a non-linear time series model and to spectral estimation for time-varying autoregressions is described.

Key words and phrases: Bayesian estimation, filtering, Monte Carlo methods, nonlinear non-Gaussian state space model, maximum a posteriori estimation, particle filter, smoothing.