Observer path planning for maximum information

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 verify 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.

Keywords:

• Observer path planning
• target localization
• optimal control
• bang–bang and singular control
• Fisher information

Mathematics Subject Classifications:

• 49K15
• 49M25
• 65K99

Acknowledgments

The author would like to offer his warm thanks to the anonymous reviewer for their careful reading of the manuscript and suggestions. He acknowledges useful discussions with Sanjeev Arulampalam of Defence Science and Technology in 2016, after which he started to look at the problem studied in the current paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).