Abstract
A broadband sound source depth estimation method based on the BDRM model is proposed for the shallow sea to address the problem that the traditional Warping transform is limited by the ideal waveguide and cannot handle the real marine environment localization of structures with variable sound speed profiles. The modified Warping transform operator compensates for the propagation and reflection phases of the received signals in double phase, compresses the modes of the received signals under different sound speed profiles to approximate a single frequency, and projects the modified signals using time-frequency analysis (TFR). As a result, the modes of the received signals are clearly separated in the time-frequency domain. Then, the corresponding bandpass filters are designed considering the different marine environments. After that, the modal energies are extracted, and the depth estimation function is constructed based on the matched modal energies to achieve the depth estimation of the pulsed signal target under the non-ideal waveguide conditions with a variable speed of sound profile. Compared to the short-time Fourier transform (STFT) and the dispersion-dissipation transform (DDT), the modified Warping transform (MWT) achieves a clearer separation of the modes of the target received signal under the variable sound speed profile of the non-ideal waveguide. The depth estimation method proposed in this study effectively resolves the issues of passive source depth estimation under variable sound speed profiles, which typically result in a significant decrease in estimation accuracy. Simulation results indicate that under the conditions of the Pekeris waveguide, negative sound speed gradient waveguide, and Qingdao shallow sea waveguide, the success rate of the method for target depth estimation reaches more than 95% under a signal-to-noise ratio (SNR) of 10 dB. This demonstrates both high accuracy and stability. In Qingdao, the target depth can be estimated accurately when the signal-to-noise ratio is above 5 dB. In real sea area experiments, the method effectively separates the first four orders of the normal modes and achieves the estimation of the depth of the airgun pulse source. Compared to the traditional Warping transform, the method proposed in this study provides a wider application range and greater practical value in engineering.