Observer path planning for maximum information. (3rd April 2022)

• Record Type: Journal Article
• Authors: Yalçın Kaya, C.
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 1097
• Page End: 1116
• Publication Date: 2022-04-03
• Subjects: Observer path planning -- target localization -- optimal control -- bang–bang and singular control -- Fisher information; 49K15 -- 49M25 -- 65K99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2011868
• Languages: English
• ISSNs: 0233-1934

Abstract

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.