Linear minimum mean square filters for Markov jump linear systems

TL;DR

This paper introduces a family of linear minimum mean square estimators for Markov jump linear systems that balance estimation accuracy and computational complexity through cluster-based filtering.

Contribution

It proposes a new class of filters based on cluster information structure, unifying the linear Markovian and Kalman filters within a lattice framework.

Findings

The proposed filters interpolate between Markovian and Kalman filters.

Increasing cluster size reduces estimation error but increases computational load.

Formulas for gain pre-computation and filter properties are provided.

Abstract

New linear minimum mean square estimators are introduced in this paper by considering a cluster information structure in the filter design. The set of filters constructed in this way can be ordered in a lattice according to the refines of clusters of the Markov chain, including the linear Markovian estimator at one end (with only one cluster) and the Kalman filter at the other hand (with as many clusters as Markov states). The higher is the number of clusters, the heavier are pre-compuations and smaller is the estimation error, so that the cluster cardinality allows for a trade-off between performance and computational burden. In this paper we propose the estimator, give the formulas for pre-computation of gains, present some properties, and give an illustrative numerical example.