Robust Deployment of Sensing UAVs for TDOA Localization with Distance-Dependent Noise

Traditional ground-based sensor deployment for time difference of arrival (TDOA) localization usually assumes distance-independent measurement error between the target and the sensors. With the growing popularity of using unmanned aerial vehicles (UAVs) for radio localization, existing TDOA sensor deployment solutions could be no longer applicable due to the high mobility of UAVs. This paper considers a robust deployment problem of the sensing UAVs for TDOA localization with the target located in a circular uncertainty area. The objective is to minimize the Cramér-Rao Bound (CRB), in which the covariance matrix of the TDOA measurement noise is formulated as a function of the distance between the target and the sensing UAVs. To tackle the highly non-convex problem, we reformulate it in a master-slave manner as two subproblems. Inspired by the prevailing Gibbs sampling method, we propose a grid-based dual-space stepwise optimization (GDSSO) algorithm to solve the master problem, while the slave problem for finding the worst-case point in the uncertainty area could be efficiently solved through gradient projection. Simulation results demonstrate the rationality of our problem formulation as well as the effectiveness of the proposed algorithm.