EURASIP Journal on Applied Signal Processing 
Volume 2002 (2002), Issue 8, Pages 865-875
doi:10.1155/S1110865702205089

Sequential Parameter Estimation of Time-Varying Non-Gaussian Autoregressive Processes

Petar M. Djurić,1 Jayesh H. Kotecha,2 Fabien Esteve,3 and Etienne Perret3

 1Department of Electrical and Computer Engineering, State University of New York at Stony Brook, Stony Brook 11794, NY, USA
2Department of Electrical and Computer Engineering, University of Wisconsin, Madison 53706, WI, USA
3ENSEEIHT/TéSA 2, rue Charles Camichel, BP 7122, Toulouse Cedex 7 31071, France
Received 1 August 2001; Revised 14 March 2002

Abstract

Parameter estimation of time-varying non-Gaussian autoregressive processes can be a highly nonlinear problem. The problem gets even more difficult if the functional form of the time variation of the process parameters is unknown. In this paper, we address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and particle weights. These sets are updated as new measurements become available using the principle of sequential importance sampling. From the samples and their weights we can compute a wide variety of estimates of the unknowns. In absence of exact modeling of the time variation of the process parameters, we exploit the concept of forgetting factors so that recent measurements affect current estimates more than older measurements. We investigate the performance of the proposed approach on autoregressive processes whose parameters change abruptly at unknown instants and with driving noises, which are Gaussian mixtures or Laplacian processes.