MAP moving horizon state estimation with binary measurements

TL;DR

This paper introduces a convex optimization-based MAP moving horizon estimator for linear systems with binary measurements, demonstrating its effectiveness through simulation in diffusion field estimation.

Contribution

It develops a convex optimization approach for MAP moving horizon state estimation using binary measurements in linear systems, applicable to diffusion field estimation.

Findings

The estimator involves solving a convex optimization problem at each step.

Simulation results confirm the effectiveness of the proposed method.

Application to diffusion field estimation demonstrates practical utility.

Abstract

The paper addresses state estimation for discrete-time systems with binary (threshold) measurements by following a Maximum A posteriori Probability (MAP) approach and exploiting a Moving Horizon (MH) approximation of the MAP cost-function. It is shown that, for a linear system and noise distributions with log-concave probability density function, the proposed MH-MAP state estimator involves the solution, at each sampling interval, of a convex optimization problem. Application of the MH-MAP estimator to dynamic estimation of a diffusion field given pointwise-in-time-and-space binary measurements of the field is also illustrated and, finally, simulation results relative to this application are shown to demonstrate the effectiveness of the proposed approach.