Geometric-Based Passive Bearing-Only Localization Model for UAV Flight

In order to conduct pure bearing passive localization for UAV formations and enable adjustments of UAVs within the formation, this paper is based on geometric properties and establishes a pure bearing passive localization model, providing a position adjustment scheme. For the passive receiving signal UAVs with deviations, we establish a UAV polar coordinate positioning model, considering the positional relationship between the passive receiving signal UAV and two transmitting signal UAVs, to obtain the position expression of the receiving signal UAV. Next, we consider the passive localization problem in the case of unknown numbering. Apart from one UAV at the center and one UAV in the surrounding area, we need two UAVs emitting signals. By using a three-circle intersection positioning model, we can obtain the positions of all UAVs. In the actual UAV formation scheme, we set up a fixed UAV group based on the initial positions. Then, we propose the step-by-step circular model and the angle equal distribution arrangement model, achieving an even distribution of UAVs on the circumference, and providing their final positions. Finally, based on the formula, the maximum error is approximately 10.5%. This paper rigorously reasons about the above situations and proposes corresponding localization models and adjustment schemes.