Monte Carlo Mixture Kalman Filter Based on the Particle Filter Approach

• Activity Number: 85
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Tomoyuki Higuchi*+
• Companies: Institute of Statistical Mathematic
• Keywords: time series ; model averaging ; Kalman filter ; particle filter ; non-Gaussian ; nonlinear

Abstract

In this paper we develop Monte Carlo method for filtering and smoothing method in the conditional dynamic linear model (CDLM) (Chen and Liu, 2000; Liu et al., 2001). The CDLM is a direct generalization of the dynamic linear model (DLM) and retains a capability of dealing with outliers, sudden jumps, clutters, and other nonlinear features (Liu et al., 2001). The CDLM includes other types of generalization of DLM, e.g., partial non-Gaussian state space model, Markov switching state space model, and dynamic linear models with switching. The indicator vector I_t in CDLM is a discrete latent variable which takes an integer value between 1 and M. Usually a number of models treated in the Mixture Kalman filter is about 2 to 3, but we consider a problem of dealing with a large number of models, M =100. There are various ways of giving a time-dependent structure for I_t. An evolution of I_t is in this study realized by considering Markovian switching prior. A transition matrix is assumed to be constant matrix for simplicity. We develop the filtering and smoothing procedures for obtaining a distribution function of the trajectory of I_t based on the particle filter approach.