Adaptive matched field processing (AMFP) has proven effective for source localization in deep-water environments. However, when the target is in motion, the need for numerous snapshot samples can lead to distortion in covariance estimation, degrading AMFP performance. A synthetic AMFP method has been proposed to compensate for the phase of multi-snapshot signals, enhancing AMFP performance. Additionally, a rough estimation of target velocity is obtained. The efficacy of the method has been validated through numerical simulations and experimental data, with results showing that, within a 9 km range, the average localization error is reduced by 1.45 km compared to traditional AMFP.

The horizontal-transverse coherence of low-frequency (300 Hz) and long-range (10–40 km) acoustic fields near the bottom in deep water is investigated based on experimental data obtained from the South China Sea. The results indicate that the horizontal-transverse coherence length exhibits a strong dependence on the source-receiver distance, with fluctuations consistent with sound intensity trends. In high-intensity regions, the horizontal-transverse coherence is relatively high, with a coherence length exceeding 600 λ, where λ is the acoustic wavelength, whereas in low-intensity regions, the horizontal-transverse coherence decreases significantly, with the coherence length shortening to 10–30 λ. The physical mechanisms underlying the horizontal-transverse coherence are analyzed using the ray theory. In high-intensity regions, the energy of the dominant ray (the ray with the highest energy) accounts for over 70% of the total energy of the rays, exerting a decisive influence on the coherence coefficient and leading to stable horizontal-transverse coherence in the received acoustic field. In contrast, in low-intensity regions, the energy distribution is dispersed, and when amplitude and phase disturbances due to spatial inhomogeneity are introduced, the horizontal coherence deteriorates significantly. The numerical simulations are also performed, and the results are consistent with the experimental observations.

When an airborne sound source is in rapid motion, the acoustic signal detected by the underwater sensor experiences a substantial Doppler shift. This shift is intricately linked to the motion parameters of the sound source. Analyzing the Doppler shift characteristics of received acoustic signals enables not only the estimation of target motion parameters but also the localization of the airborne sound source. Currently, the predominant methods for estimating parameters of uniformly moving targets are grounded in classical approaches. In this study, the application of the Doppler warping transform, traditionally applicable to sound sources in uniform linear motion, is extended to encompass a broader spectrum of sound source trajectories. Theoretical and experimental data validate the efficacy of this transform in linearizing the Doppler shift induced by a source in curved motion. Building upon this foundation, a methodology is proposed for locating airborne acoustic sources in curved motion from underwater. Sea experimental data corroborate the method’s effectiveness in achieving underwater localization of a helicopter target during curved motion.