An improvement to the interacting multiple model (IMM) algorithm

Computing the optimal conditional mean state estimate for a jump Markov linear system requires exponential complexity, and hence, practical filtering algorithms are necessarily suboptimal. In the target tracking literature, suboptimal multiple-model filtering algorithms, such as the interacting multiple model (IMM) method and generalized pseudo-Bayesian (GPB) schemes, are widely used for state estimation of such systems. We derive a reweighted interacting multiple model algorithm. Although the IMM algorithm is an approximation of the conditional mean state estimator, our algorithm is a recursive implementation of a maximum a posteriori (MAP) state sequence estimator. This MAP estimator is an instance of a previous version of the EM algorithm known as the alternating expectation conditional maximization (AECM) algorithm. Computer simulations indicate that the proposed reweighted IMM algorithm is a competitive alternative to the popular IMM algorithm and GPB methods.

I. Introduction

JUMP Markov linear systems (JMLSs) are linear systems whose parameters evolve according to the realization of a finite-state Markov chain. JMLSs have been used to model a wide variety of signal processing systems [1] and control systems [2] in which the system model (behavior) switches between a number of modes. They are also widely studied as dynamic linear models [3] and dependent mixture distributions [4] in the statistical literature. In particular, JMLSs are ideal for modeling vehicular motion in maneuvering target applications as state space models can be set up to model trajectories in periods of varying conditions: constant velocity, acceleration, regions of differing SNR, and so on. Unfortunately, computing the optimal (conditional mean) state estimates of a JMLS requires exponential complexity for a length -mode JMLS. As a result, numerous suboptimal approximations have been proposed. See the work of [1] and [5] for state-of-the-art deterministic and randomised algorithms for state estimation of JMLS.