An Information-geometric Approach to Sensor Management

TL;DR

This paper introduces an information-geometric framework for sensor management, where optimal sensor configurations are navigated along geodesic curves in a manifold of possible configurations, accommodating various priors and information measures.

Contribution

It presents a novel geometric approach to sensor management using Riemannian metrics and geodesics, extending beyond Jeffreys priors to include informative priors.

Findings

Geodesic curves optimize sensor configuration trajectories.

Fisher and Shannon information divergences lead to the same metric.

The framework generalizes existing sensor management methods.

Abstract

An information-geometric approach to sensor management is introduced that is based on following geodesic curves in a manifold of possible sensor configurations. This perspective arises by observing that, given a parameter estimation problem to be addressed through management of sensor assets, any particular sensor configuration corresponds to a Riemannian metric on the parameter manifold. With this perspective, managing sensors involves navigation on the space of all Riemannian metrics on the parameter manifold, which is itself a Riemannian manifold. Existing work assumes the metric on the parameter manifold is one that, in statistical terms, corresponds to a Jeffreys prior on the parameter to be estimated. It is observed that informative priors, as arise in sensor management, can also be accommodated. Given an initial sensor configuration, the trajectory along which to move in sensor configuration space to gather most information is seen to be locally defined by the geodesic structure of this manifold. Further, divergences based on Fisher and Shannon information lead to the same Riemannian metric and geodesics.