Observer Path Planning for Maximum Information

TL;DR

This paper develops an optimal control framework for planning observer paths that maximize information gain for stationary target localization using bearing measurements, with analytical and numerical results.

Contribution

It formulates the observer path planning as an optimal control problem maximizing Fisher information and derives analytical conditions for optimality.

Findings

Numerical solutions verify the necessary conditions of optimality.

Multiple locally optimal paths are identified.

Graphical analysis confirms the theoretical results.

Abstract

This paper is concerned with finding an optimal path for an observer, or sensor, moving at a constant speed, which is to estimate the position of a stationary target, using only bearing angle measurements. The generated path is optimal in the sense that, along the path, information, and thus the efficiency of a potential estimator employed, is maximized. In other words, an observer path is deemed optimal if it maximizes information so that the location of the target is estimated with smallest uncertainty, in some sense. We formulate this problem as an optimal control problem maximizing the determinant of the Fisher information matrix, which is one of the possible measures of information. We derive analytical results for optimality using the Maximum Principle. We carry out numerical experiments and discuss the multiple (locally) optimal solutions obtained. We check graphically that the necessary conditions of optimality are verified by the numerical solutions. Finally we provide a comprehensive list of possible extensions for future work.