Moving horizon estimation for discrete-time linear systems with binary sensors: algorithms and stability results

TL;DR

This paper develops Moving Horizon Estimation algorithms for discrete-time linear systems using binary sensors, providing stability analysis and demonstrating effectiveness through simulations.

Contribution

It introduces new MHE algorithms tailored for binary sensor measurements with stability guarantees and explores different cost functions and constraints.

Findings

Stability of the proposed MHE algorithms is proven under bounded disturbances.

The quadratic and piece-wise quadratic cost functions improve estimation accuracy.

Simulation results validate the effectiveness of the algorithms in practical scenarios.

Abstract

The paper addresses state estimation for linear discrete-time systems with binary (threshold) measurements. A Moving Horizon Estimation (MHE) approach is followed and different estimators, characterized by two different choices of the cost function to be minimized and/or by the possible inclusion of constraints, are proposed. Specifically, the cost function is either quadratic, when only the information pertaining to the threshold-crossing instants is exploited, or piece-wise quadratic, when all the available binary measurements are taken into account. Stability results are provided for the proposed MHE algorithms in the presence of unknown but bounded disturbances and measurement noises. Performance of the proposed techniques is also assessed by means of a simulation example.