Robust Dynamic Trajectory Optimization for UAV-aided Localization of Ground Target

In this paper, we consider employing an unmanned aerial vehicle (UAV) equipped with an onboard radar transceiver to localize a ground target at an unknown position. Exploiting the UAV's mobility, we aim to gather line-of-sight (LoS) range measurements from favorable waypoints and improve the ensuing multi-lateration process while estimating the target's location. To this end, we introduce a novel localization error metric, characterized geometrically by the radius of a defined confidence region where the target resides at a predetermined confidence level. Additionally, we investigate robust dynamic optimization of the UAV's trajectory to minimize the defined localization error metric online, utilizing sequentially available but delayed range estimates. The formulated optimization problem belongs to a convex-nonconcave minimax problem, which is generally intractable. To solve this problem, we further propose two iterative online algorithms based on semidefinite programming (SDP) relaxation and alternating/sequential convex optimization techniques. Simulation results show that the proposed online schemes outperform several benchmarks, either in the final localization accuracy or in the rate of decreasing the localization error.