A simple suboptimal moving horizon estimation scheme with guaranteed robust stability

TL;DR

This paper introduces a suboptimal moving horizon estimation scheme for nonlinear systems that guarantees robust stability by leveraging a Lyapunov function, with practical verification and demonstrated effectiveness on a benchmark example.

Contribution

It proposes a suboptimal MHE method with stability guarantees based on Lyapunov functions, simplifying implementation and verification.

Findings

Single iteration improves estimation significantly

Method guarantees robust stability under verifiable conditions

Effective on standard nonlinear benchmark example

Abstract

We propose a suboptimal moving horizon estimation (MHE) scheme for a general class of nonlinear systems. To this end, we consider an MHE formulation that optimizes over the trajectory of a robustly stable observer. Assuming that the observer admits a Lyapunov function, we show that this function is an M-step Lyapunov function for suboptimal MHE. The presented sufficient conditions can be easily verified in practice. We illustrate the practicability of the proposed suboptimal MHE scheme with a standard nonlinear benchmark example. Here, performing a single iteration is sufficient to significantly improve the observer's estimation results under valid theoretical guarantees.