LMMSE Filtering in Feedback Systems with White Random Modes: Application to Tracking in Clutter

TL;DR

This paper introduces a generalized LMMSE filtering approach for feedback systems with random mode switching, applicable to target tracking in clutter, and demonstrates its effectiveness compared to nonlinear methods.

Contribution

A novel LMMSE filtering formulation for systems with white random mode switching, incorporating recent estimates into dynamics and measurement models.

Findings

Effective in target tracking in clutter environments

Competitive performance with popular nonlinear filters

Applicable to feedback control systems with random modes

Abstract

A generalized state space representation of dynamical systems with random modes switching according to a white random process is presented. The new formulation includes a term, in the dynamics equation, that depends on the most recent linear minimum mean squared error (LMMSE) estimate of the state. This can model the behavior of a feedback control system featuring a state estimator. The measurement equation is allowed to depend on the previous LMMSE estimate of the state, which can represent the fact that measurements are obtained from a validation window centered about the predicted measurement and not from the entire surveillance region. The LMMSE filter is derived for the considered problem. The approach is demonstrated in the context of target tracking in clutter and is shown to be competitive with several popular nonlinear methods.