A Comparison of Set-Based Observers for Nonlinear Systems

TL;DR

This paper provides the first comprehensive, tool-supported comparison of various set-based observers for nonlinear discrete-time systems, evaluating their computational effort, scalability, and conservatism.

Contribution

It offers a unified evaluation framework and publicly available implementations for comparing guaranteed state estimators in nonlinear systems.

Findings

Trade-offs between observer categories and set representations identified

Evaluation on common benchmarks highlights differences in computational effort and conservatism

Publicly available implementations support reproducibility and future research

Abstract

Set-based state estimation computes sets of states consistent with a system model given bounded sets of disturbances and noise. Bounding the set of states is crucial for safety-critical applications so that one can ensure that all specifications are met. While numerous approaches have been proposed for nonlinear discrete-time systems, a unified evaluation under comparable conditions is lacking. This paper reviews and implements a representative selection of set-based observers within the CORA framework. To provide an objective comparison, the methods are evaluated on common benchmarks, and we examine computational effort, scalability, and the conservatism of the resulting state bounds. This study highlights characteristic trade-offs between observer categories and set representations, as well as practical considerations arising in their implementation. All implementations are made publicly available to support reproducibility and future development. This paper thereby offers the first broad, tool-supported comparison of guaranteed state estimators for nonlinear discrete-time systems.