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Underwater acoustic localization is an important, yet challenging problem: (1) node mobility issue, (2) Doppler effect, and (3) clock imperfection. To be specific, underwater nodes are not stationary in real-life due to unpredictable currents. Relative motion between a transmitter and a receiver causes the time scaling problem on the received signals, where the time scaling factor is termed as Doppler scale. Then, due to the slow acoustic signal propagation speed, the underwater Doppler scale becomes more severe compared with the one in terrestrial environments. Thus, the differential Doppler scale (DDS) measurements should also be collected, other than the time measurements like time-difference-of-arrival (TDOA), for enhancing the underwater localization. Since DDS/TDOA measurements and clock skew are tightly coupled, clock synchronization is essential for accurate localization. However, due to the stringent cost and power constrains of underwater nodes, low-cost clocks with relative low precision are normally employed, which makes it even more difficult to guarantee a perfect clock synchronization between transmitter/receiver pairs. In order to cope with those issues, we propose an algebraic underwater localization method using the hybrid DDS/TDOA measurements, which is particularly robust against the node clock imperfection. A new DDS/TDOA measurement model with clock imperfection is first presented by analyzing the received signals over underwater acoustic channels. Then, we devise a two-step weighted least square-based estimator, and the analytical study shows that our estimator can achieve the Cramer-Rao lower bound (CRLB) accuracy under small noise. Simulations corroborate the theoretical results and the good performance of the proposed method.

Underwater Localization Using Differential Doppler Scale and TDOA Measurements with Clock Imperfection