Recursive state estimation for noncausal discrete-time descriptor systems under uncertainties

TL;DR

This paper introduces a minimax-based online state estimation method for noncausal descriptor systems with uncertainties, extending Kalman filtering to singular and noncausal systems using dynamical programming.

Contribution

It develops a novel causality index and minimax estimator for noncausal descriptor systems, generalizing Kalman filtering to singular and time-varying cases.

Findings

The estimator coincides with Kalman's filter for regular systems.

Numerical example demonstrates effectiveness on 2D noncausal descriptor system.

Method provides guaranteed estimation under uncertainties.

Abstract

This paper describes a method for the online state estimation of systems described by a general class of linear noncausal time-varying difference descriptor equations subject to uncertainties. The method is based on the notions of a linear minimax estimation and an index of causality introduced here for singular difference equations. The online minimax estimator is derived by the application of the dynamical programming and Moore's pseudoinverse theory to the minimax estimation problem. It coincides with Kalman's filter for regular systems. A numerical example of the state estimation for 2D noncasual descriptor system is presented. Keywords: Kalman filtering, online state observer, guaranteed estimation, descriptor systems, singular systems, DAEs.