Energy Minimization for Underwater Multipath Time-Delay Estimation

To address the multipath delay estimation problem in distributed hydrophone passive localization systems, a global energy minimization-based method is proposed in this paper. In this method, correlation pulses are treated as tracking targets, and their trajectories are estimated from correlograms formed by multiple frames. Specifically, an energy function is designed to jointly encode pulse similarity, motion continuity, trajectory persistence, data fidelity, and regularization, thereby reformulating multipath delay estimation as a global optimization problem. In order to balance the discreteness of observations and the continuity of trajectories, the optimization process is implemented alternating between discrete association (solved via α-expansion) and continuous trajectory fitting (using weighted cubic splines). Furthermore, a dynamic hypothesis space expansion strategy based on trajectory merging and splitting is introduced to improve robustness while accelerating convergence. By exploiting both the intrinsic characteristics of correlation pulses in multi-frame processing and the physical properties of motion trajectories, the proposed method achieves higher tracking accuracy without requiring prior knowledge of the number of delay trajectories in a noisy environment. Numerical simulations under various noise conditions and sea trial results validate the superiorities of the proposed multipath delay estimation method.