Robust Multi-UAV Placement Optimization for AOA-Based Cooperative Localization

Unmanned aerial vehicle (UAV) swarm-based localization technology has become increasingly popular due to its exceptional maneuverability, versatile coverage capabilities, and reliable line-of-sight (LoS) connectivity. However, the accuracy improvement by exploiting UAVs' placement poses a new challenge on multi-UAV localization system. This paper investigates the placement optimization problem for a multi-UAV localization network, where each UAV is equipped with a uniform circular array (UCA) to locate the target by adopting the angle-ofarrival (AOA) measurement. To measure the accuracy of the UCA-based localization system, we characterize the measurement error to be dependent on target-to-UAV distance and present a comprehensive derivation of the Cramer-Rao lower bound ´ (CRLB). Next, we formulate the problem as a non-convex semi-infinite optimization, aiming to minimize the worst-case squared position error bound (SPEB) by designing the robust placement strategy under some stringent geometric position constraints. We address this problem by alternatively solving two sub-problems, corresponding to a slave problem for calculating the worstcase SPEB of the uncertainty region under a fixed deployment of UAVs, as well as a master problem for optimizing UAVs' placement. By virtue of the particular problem structure, we develop the gradient projection-based method for the slave problem. Meanwhile, considering the lack of a closed expression for the maximum SPEB concerning UAVs' deployment in the master problem, we devise an iterative algorithm to acquire an efficient solution with the aid of Gibbs Sampling approach. Extensive simulation results demonstrate the efficacy of the proposed algorithms.