Active target depth discrimination in shallow water based on the linear initial-phase feature of the broadband complex sound pressure ratio

To address the problem of target depth discrimination in shallow-water thermocline environments, the formation mechanism of the phase of the broadband complex pressure ratio (PBPR) between any two elements of a horizontal array is theoretically analyzed. It is clarified that the linear initial phase (LIP) in the PBPR, which is determined by the equivalent average horizontal wavenumber, the equivalent group slowness, and the element spacing, serves as the key feature for distinguishing target depth. To this end, a broadband coherent projection method is proposed. By means of vector projection optimization, the linear feature is robustly extracted without conventional phase unwrapping, and a target depth discrimination framework based on the PBPR-LIP feature is constructed. This framework reduces the original two-dimensional phase spectrum matching problem to the comparison of a single scalar parameter. Simulation results demonstrate that, while maintaining the discrimination performance, the proposed method achieves a computational efficiency improvement of more than one order of magnitude over the method matching the PBPR feature, and exhibits enhanced robustness against environmental mismatch. The results of at-sea experimental data processing validate the effectiveness of the method.