Deterministic filtering and max-plus methods for robust state estimation in multi-sensor settings

TL;DR

This paper introduces a deterministic filtering method using max-plus algebra for robust state estimation in multi-sensor systems, reformulating sensor selection as an optimal control problem and solving it efficiently with grid-free numerical techniques.

Contribution

It presents a novel max-plus based approach for sensor selection in robust state estimation, enabling efficient, grid-free computation within an optimal control framework.

Findings

Effective sensor selection improves state estimation accuracy.

Max-plus methods enable grid-free, efficient computation.

Simulation results demonstrate the approach's robustness and efficiency.

Abstract

A robust (deterministic) filtering approach to the problem of optimal sensor selection is considered herein. For a given system with several sensors, at each time step the output of one of the sensors must be chosen in order to obtain the best state estimate. We reformulate this problem in an optimal control framework which can then be solved using dynamic programming. In order to tackle the numerical computation of the solution in an efficient manner, we exploit the preservation of the min-plus structure of the optimal cost function when acted upon by the dynamic programming operator. This technique yields a grid free numerical approach to the problem. Simulations on an example problem serve to highlight the efficacy of this generalizable approach to robust multi-sensor state estimation.