Point-Based Value Iteration and Approximately Optimal Dynamic Sensor Selection for Linear-Gaussian Processes

TL;DR

This paper introduces a point-based value iteration method for sensor selection in linear-Gaussian processes, providing a computationally feasible approach with theoretical guarantees on near-optimality over an infinite horizon.

Contribution

It formulates an approximate sensor selection policy using point-based value iteration on a finite covariance matrix mesh, with proven bounds on suboptimality.

Findings

The method achieves near-optimal sensor policies with bounded suboptimality.

Numerical examples demonstrate the effectiveness compared to existing approaches.

Abstract

The problem of synthesizing an optimal sensor selection policy is pertinent to a variety of engineering applications ranging from event detection to autonomous navigation. We consider such a synthesis problem over an infinite time horizon with a discounted cost criterion. We formulate this problem in terms of a value iteration over the continuous space of covariance matrices. To obtain a computationally tractable solution, we subsequently formulate an approximate sensor selection problem, which is solvable through a point-based value iteration over a finite "mesh" of covariance matrices with a user-defined bounded trace. We provide theoretical guarantees bounding the suboptimality of the sensor selection policies synthesized through this method and provide numerical examples comparing them to known results.