Exact recursive updating of uncertainty sets

TL;DR

This paper introduces a new recursive algorithm for efficiently updating the uncertainty sets of linear discrete-time systems with bounded disturbances and noise, improving over existing methods.

Contribution

It provides two theorems that fully characterize the evolution of uncertainty sets, enabling an exact and efficient recursive updating algorithm.

Findings

Numerical simulations show improved performance over existing methods.

Theorems fully describe the evolution of uncertainty sets.

Algorithm achieves exact recursive updates efficiently.

Abstract

This paper addresses the classical problem of determining the set 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 two theorems which describe completely how they evolve with time, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods.