Distributed planning method for detection array of UAV formation with bearing-only sensor network

Abstract Unmanned aerial vehicle (UAV) formations for bearing-only passive detection are increasingly important in modern military confrontations, and the array of the formation is one of the decisive factors affecting the detection accuracy of the system. How to plan the optimal geometric array in bearing-only detection is a complex nondeterministic polynomial problem, and this paper proposed the distributed stochastic subgradient projection algorithm (DSSPA) with layered constraints to solve this challenge. Firstly, based on the constraints of safe flight altitude and fixed baseline, the UAV formation is layered, and the system model for bearing-only cooperative localisation is constructed and analysed. Then, the calculation formula for geometric dilution of precision (GDOP) in the observation plane is provided, this nonlinear objective function is appropriately simplified to obtain its quadratic form, ensuring that it can be adapted and used efficiently in the system model. Finally, the proposed distributed stochastic subgradient projection algorithm (DSSPA) combines the idea of stochastic gradient descent with the projection method. By performing a projection operation on each feasible solution, it ensures that the updated parameters can satisfy the constraints while efficiently solving the convex optimisation problem of array planning. In addition to theoretical proof, this paper also conducts three simulation experiments of different scales, validating the effectiveness and superiority of the proposed method for bearing-only detection array planning in UAV formations. This research provides essential guidance and technical reference for the deployment of UAV formations and path planning of detection platforms.