Exact recursive estimation of linear systems subject to bounded disturbances

TL;DR

This paper introduces an exact and computationally simple recursive method for estimating the possible states of linear systems affected by bounded disturbances and noise, updating uncertainty sets over time.

Contribution

It presents a novel recursive procedure for propagating boundary points of uncertainty sets in linear systems with bounded disturbances and noise.

Findings

Exact boundary propagation method for uncertainty sets

Computational simplicity of the proposed procedure

Applicable to linear systems with bounded disturbances and noise

Abstract

This paper addresses the classical problem of determining the sets of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with time as new measurements become available. We present an exact, computationally simple procedure that propagates a point on the boundary of the uncertainty set at some time instant to a set of points on the boundary of the uncertainty set at the next time instant.