Bounded-error constrained state estimation of LTV systems in presence of sporadic measurements

TL;DR

This paper introduces a recursive set-membership approach for state estimation in linear time-varying systems with sporadic measurements, handling unknown disturbances and equality constraints, and optimizing ellipsoid size under stability considerations.

Contribution

It develops novel algorithms for ellipsoidal state characterization considering non-invertible shape matrices due to equality constraints in LTV systems with sporadic measurements.

Findings

Algorithms minimize ellipsoid volume and axes length.

Ensures input-to-state stability of the estimation error.

Handles degenerate zonotopes and polytopes in state estimation.

Abstract

This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for discrete-time linear time-varying models with additive unknown disturbances vectors, bounded by possibly degenerate zonotopes and polytopes, impacting respectively, the state evolution equation and the sporadic measurement vectors, which are expressed as linear inequality and equality constraints on the state vector. New algorithms are designed considering the unprecedented fact that, due to equality constraints, the shape matrix of the ellipsoid characterizing all possible values of the state vector is non invertible. The two main size minimizing criteria (volume and sum of squared axes lengths) are examined in the time update step and also in the observation updating, in addition to a third one, minimizing some error norm and ensuring the input-to-state stability of the estimation error. The author's papers [1] and [2] were combined into this longer, more comprehensive version. It includes all the proofs and a few images and is meant to be a support for the reader. There is no introduction, no conclusion, and no application examples.