Optimal Motion Planning for Estimating Relative States of Mobile Agents With Range Measurements

In this paper, we focus on the problem of optimal trajectory design for mobile agents to achieve precise relative localization in anchor-free environments. Given the challenges posed by range measurement noise and the lack of prior information about neighboring agents, we propose an approach that maximizes localization accuracy under a fixed number of movements. The method leverages the Fisher Information Matrix (FIM) to optimize the agent's trajectory and is extended to scenarios involving multiple agents. In particular, we quantitatively establish a link between localization variance and the number of movements, and the simulation demonstrate the superiority of our algorithm.