Non-Line-of-Sight Ultraviolet Positioning via Time Difference of Arrival

Abstract

For challenging environments where conventional line-of-sight (LOS) systems are not available, we propose a novel non-line-of-sight (NLOS) ultraviolet (UV) positioning system based on time difference of arrival (TDOA). The system operates through two complementary procedures: constructing a geometric model by optimizing the reception angle according to signal intensity and transmitter beam characteristics, and estimating the time difference of arrival via UV synchronization to resolve the positioning equations. To further improve positioning accuracy, a symbol broadening matching synchronization scheme is developed, which employs the pulsed response function of the UV single-scattering channel obtained from initial positioning results. An upper bound on the mean square error (MSE) applicable to this synchronization process is also derived. Simulation results confirm that the proposed approach significantly enhances the synchronization estimation accuracy and effectively constrains the final positioning error within the theoretical bounds. We also verify the robustness of the algorithm under different environmental conditions. An average decrease of 34.03% for the synchronization standard deviation is achieved, and an average decrease of 32.67% for the positioning error is achieved. Additionally, the proposed positioning algorithm effectively compensates for the systematic bias present in the initial estimates, bringing the corrected center closer to the ground truth. To optimize system deployment, we propose efficient impulse response approximation instead of time-consuming Monte Carlo simulations, achieving a 28.64% reduction in positioning error.