Sample-based Moving Horizon Estimation

TL;DR

This paper introduces a sample-based moving horizon estimation method for nonlinear systems that handles irregular measurements and guarantees stability under certain detectability conditions, with demonstrated effectiveness through simulation.

Contribution

It proposes a novel sample-based MHE scheme for nonlinear systems, establishing stability conditions and connecting observability with sample-based detectability, applicable to linear systems.

Findings

Achieves robust global exponential stability under sample-based detectability.

Effectively estimates states with irregular and infrequent measurements.

Validated through simulation example demonstrating practical effectiveness.

Abstract

In this paper, we propose a sample-based moving horizon estimation (MHE) scheme for general nonlinear systems to estimate the current system state using irregularly and/or infrequently available measurements. The cost function of the MHE optimization problem is suitably designed to accommodate these irregular output sequences. We also establish that, under a suitable sample-based detectability condition known as sample-based incremental input/output-to-state stability (i-IOSS), the proposed sample-based MHE achieves robust global exponential stability (RGES). Additionally, for the case of linear systems, we draw connections between sample-based observability and sample-based i-IOSS. This demonstrates that previously established conditions for linear systems to be sample-based observable can be utilized to verify or design sampling strategies that satisfy the conditions to guarantee RGES of the sample-based MHE. Finally, the effectiveness of the proposed sample-based MHE is illustrated through a simulation example.