Abstract
Autonomous relative positioning is a critical challenge for unmanned aerial vehicle (UAV) swarms. In this study, we address the optimization of measurement constraint selection in the distributed relative positioning process of large-scale UAV swarms. We introduce a distributed graph optimization (DGO) scheme for swarm relative positioning, which enables global consistent relative position estimation through limited inter-UAV information sharing. To prevent the calculation time from escalating with swarm size, this method allows users to specify the number of relative measurement constraints used in the calculation. Building on the Cramér-Rao Lower Bound (CRLB) and Fisher Information Matrix (FIM) theory, we further propose a theoretically optimal method for selecting relative measurement constraints. Different from traditional distributed optimization methods that use fixed constraints, the proposed method can adaptively select the most theoretically advantageous constraints to improve accuracy, resulting in higher precision and improved adaptability to dynamic environments. To validate the effectiveness of the proposed method, we conducted numerical experiments with different swarm sizes and sensing error conditions. The results show that the proposed method has higher accuracy and stability compared to self-pose estimation methods and other measurement selection approaches, while having a low computational load. This work represents the first attempt to incorporate the FIM into constraint selection for distributed localization of UAV swarms.