A Differential Time-of-Arrival Localization Method for Underwater Moving Platforms Based on Time Reference Synchronization and Motion Compensation

Abstract Accurate localization is essential for underwater acoustic networks, but clock offsets among nodes and the motion of mobile platforms degrade traditional time-of-arrival (TOA) methods. High-precision time references, such as atomic clocks, can reduce synchronization errors but incur high cost and power consumption and cannot correct motion-induced propagation-time variations. This paper proposes a lightweight differential TOA (dTOA) localization framework based on time-reference synchronization and motion compensation. Leveraging the broadcast nature of underwater acoustic communications, each fixed beacon sequentially transmits acoustic signals, while the others listen and record reception timestamps. These inter-beacon listening observations establish and maintain a unified time reference without external clocks. For the moving receiver, a motion-compensation model projects measured TOAs onto the unified reference epoch within each localization cycle to remove displacement-induced timing bias. Based on synchronized references and motion-compensated TOAs, we derive a novel differential TOA estimator that directly cancels residual clock biases between the mobile node and the beacon network. Unlike previous approaches requiring absolute time or spatial references, the proposed method simultaneously resolves time asynchrony and motion-related TOA distortion. Simulation and sea-trial results show RRMSE reductions of up to 90% and over 93%, demonstrating the method’s robustness and its suitability for energy- and cost-constrained AUV deployments.