Joint state and parameter estimation based on constrained zonotopes

TL;DR

This paper introduces a unified set-based estimation method using constrained zonotopes for discrete-time systems, improving accuracy by maintaining dependencies and refining enclosures through measurements.

Contribution

It extends set-based state estimation to include parameter identification within a constrained zonotope framework, enhancing accuracy over interval-based methods.

Findings

Maintains dependencies between states and parameters across time.

Refines state and parameter enclosures using measurements.

Demonstrates advantages through numerical examples.

Abstract

This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples.