Sensor Pairing Optimization and Analytical Solution for Distributed TDOA Localization

Time difference of arrival (TDOA) positioning estimates the location of a signal source by measuring the time difference of arrival across multiple sensors. It is widely applied in navigation, acoustic localization, and surveillance. Traditional centralized approaches require all sensors to transmit raw data to a reference sensor, imposing substantial demands on its computational and communication resources. This paper proposes a distributed TDOA localization framework with a closed-form solution. A submodular lazy greedy sensor pairing strategy is introduced to efficiently select high-quality pairings under communication and computation constraints. The resulting configuration distributes communication and processing tasks across different sensors, effectively balancing network resource usage. Based on this topology, a three-stage weighted least squares (WLS) algorithm is developed to analytically estimate the source position. Simulation results show that the proposed three-stage WLS achieves localization accuracy close to the Cramér-Rao lower bound (CRLB) under low SNR conditions, while maintaining fast computation. Moreover, the obtained pairing configurations yield lower CRLB values compared to traditional centralized schemes.