Minimum variance constrained estimator

TL;DR

This paper introduces a stable constrained state estimator for discrete-time linear systems using minimum variance duality, offering two algorithms and demonstrating their effectiveness through numerical comparison.

Contribution

It presents a novel constrained state estimation method based on minimum variance duality, with two algorithms and stability analysis, differing from traditional minimum energy approaches.

Findings

The proposed estimator is stable as an observer.

Two algorithms (FIE and MHE) are developed for constrained estimation.

Numerical comparison shows the method's effectiveness on a benchmark model.

Abstract

This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or estimate). By use of the minimum variance duality, the estimation problem is converted into an optimal control problem. Two algorithmic solutions are described: the full information estimator (FIE) and the moving horizon estimator (MHE). The main result is to show that the proposed estimator is stable in the sense of an observer. The proposed algorithm is distinct from the standard algorithm for constrained state estimation based upon the use of the minimum energy duality. The two are compared numerically on the benchmark batch reactor process model.