Open Access

Global Sampling for Sequential Filtering over Discrete State Space

EURASIP Journal on Advances in Signal Processing20042004:106356

https://doi.org/10.1155/S1110865704407173

Received: 21 June 2003

Published: 7 November 2004

Abstract

In many situations, there is a need to approximate a sequence of probability measures over a growing product of finite spaces. Whereas it is in general possible to determine analytic expressions for these probability measures, the number of computations needed to evaluate these quantities grows exponentially thus precluding real-time implementation. Sequential Monte Carlo techniques (SMC), which consist in approximating the flow of probability measures by the empirical distribution of a finite set of particles, are attractive techniques for addressing this type of problems. In this paper, we present a simple implementation of the sequential importance sampling/resampling (SISR) technique for approximating these distributions; this method relies on the fact that, the space being finite, it is possible to consider every offspring of the trajectory of particles. The procedure is straightforward to implement, and well-suited for practical implementation. A limited Monte Carlo experiment is carried out to support our findings.

Keywords and phrases

particle filters sequential importance sampling sequential Monte Carlo sampling sequential filtering conditionally linear Gaussian state-space models autoregressive models

Authors’ Affiliations

(1)
École Nationale Supérieure des Télécommunications

Copyright

© Cheung-Mon-Chan and Moulines. 2004