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.

Bearing-only multi-target localization (BOMTL) determines the positions of multiple targets by intersecting bearing lines from multiple spatial locations. However, non-ideal measurements can result in a large number of ghost targets. A β-S-dimensional assignment (β-SDA) method incorporating waveguide characteristics is proposed to address the BOMTL problem in shallow water with low detection rates. The estimated distance for the warping transformation is derived from the intersection points of the bearing lines, then the autocorrelation function of the broadband beamforming output is transformed using a warping operator to obtain the corresponding characteristic spectrum. The peaks in the characteristic spectrum correspond to the cross-correlation terms of the normal modes, with the frequencies of these peaks related to the ratio of the actual distance to the estimated distance of the sound source. The global target localization results are obtained using the proposed method, which incorporates confidence coefficients derived from the characteristic spectrum and geometric intersection information from the bearing lines. Simulation and sea trial data demonstrate that the β-SDA method effectively overcomes the limitation of pure bearing-only localization in low detection rate scenarios under a given signal-to-noise ratio (SNR), and can localize target positions without requiring precise prior environmental parameters.

To address the performance degradation of traditional adaptive beamforming algorithms in low signal-to-noise ratio (SNR) marine environments, a weighted nuclear norm minimization optimized minimum variance distortionless response beamformer (WNNM-MVDR) is proposed. The method integrates low-rank matrix processing with beamforming and applies singular-value-dependent weighting to the sample covariance matrix, thereby retaining dominant signal components while suppressing noise-subspace components. The shrinkage parameter is initialized using a random-matrix-theory estimate of the upper edge of the noise spectrum. Simulation and sea-trial results evaluate the method under limited snapshots, array mismatch, varying SNRs, and coherent multipath. Under ideal conditions without array mismatch and with sufficient snapshots, the algorithm consistently achieves an output SNR gain of more than 4 dB for input SNRs above −20 dB. Sea-trial results further show a 1.68 dB output SNR improvement over conventional MVDR, a 2.67 dB extension of the practical weak-target detection limit, and reliable robustness to array-position errors up to 0.204 wavelengths. These results indicate that WNNM-MVDR can improve adaptive beamforming performance in the marine scenarios considered here.