The position of a non-cooperative underwater pulse signal source can be estimated by applying target motion analysis techniques to the direction of arrival (DOA) and frequency of arrival (FOA) measurements obtained from a hydrophone array. However, the harsh underwater acoustic environment, with its pronounced multipath propagation, high signal attenuation, and sparse detectable pulses, introduces considerable errors into the estimation of DOA and FOA. These errors can degrade the performance of conventional estimators such as the pseudolinear estimation (PLE) method, leading to significant bias and divergence issues. To address these issues, this paper proposes a method based on nonlinear batch processing for underwater non-cooperative target localization. A cost function is constructed based on a nonlinear observation model and the weighted least squares principle to ensure high modeling fidelity. Subsequently, a multi-start grid search combined with a trust region dogleg algorithm is employed for global iterative optimization of the cost function, enhancing the accuracy and stability of the final position estimate. Numerical simulation results demonstrate that the proposed method achieves high convergence speed and localization accuracy under adverse noise conditions and with a limited number of received pulses. Moreover, the sea trial results confirm that the algorithm attained a convergence rate of 93% with only 25 received pulses, and outperformed the conventional PLE method by approximately 80% in terms of positioning accuracy.

When the array aperture is constrained to no more than three wavelengths, accurate estimation of the direction of arrival (DOA) and reliable acquisition of the corresponding target signals become increasingly challenging, particularly for underwater co-frequency line spectrum targets. In this article, we propose a novel super-resolution wideband spatial spectrum estimation and signal recovery method, named generalized sparse amplitude asymptotics and phase estimation (GSAPE), which enables accurate DOA estimation and target signal recovery within a unified framework. To further enhance algorithmic performance, a fast weighted atomic norm minimization (FWAN) method is proposed to adaptively determine the sparsity parameter in the GSAPE method, ensuring the consistency between the covariance matrix with respect to the estimated spatial spectrum and the received signals under the atomic norm constraint. Moreover, based on an analytical investigation of the factors influencing signal recovery accuracy, a theoretical upper bound for the signal recovery error is derived. Simulation and sea trial results demonstrate that the proposed method achieves superior performance compared with existing state-of-the-art methods.

Tracking underwater non-cooperative targets with Doppler-bearing target motion analysis relies on pulse signal parameters estimated via sonar arrays. However, successfully implementing a Kalman filter for this purpose requires key parameters, including the noise covariance matrices, which cannot be known a priori in practical scenarios. A more critical challenge is that uncertainties in the marine environment and target-array geometry corrupt the parameter estimates with measurement outliers. Existing nonlinear variational Bayesian (VB) filters are not robust to this issue, as their fundamental reliance on Gaussian models and deterministic sampling degrades their convergence rate and tracking accuracy. For high-precision tracking under these conditions, this paper proposes an outlier-tolerant nonlinear VB adaptive Kalman filter that utilizes a hierarchical inverse-Wishart-gamma mixture distribution model to robustly identify outliers and more accurately approximate the measurement noise covariance matrix, while also employing the adaptive high-order cubature sampling method to improve the estimation accuracy of the expectation. The validity of this combined method is verified via rigorous numerical simulations and sea trials. Simulation results highlight the performance superiority of the proposed filter over traditional approaches utilizing inverse Wishart noise modeling and deterministic integral sampling. Furthermore, superior performance on sea trial data confirmed the filter's effectiveness and robustness.