Sparse Bayesian learning with Bernoulli-Gaussian priors for off-grid matched field processing

Conventional matched field processing (MFP) computes replicas at predefined discrete grid points, which introduces error when a source position does not coincide with the grid. This grid mismatch phenomenon is termed basis mismatch in compressed sensing (CS) frameworks. However, conventional methods for mitigating basis mismatch cannot be applied directly to the MFP problem due to their high computational complexity or the need for closed-form expressions of atomic functions. To address this issue, this paper proposes a grid-adaptive model that alleviates the mismatch effect through the localized optimization of grid nodes. Building on this foundation, this paper develops an off-grid Bernoulli-Gaussian sparse Bayesian learning algorithm based on variational expectation-maximization principles. The grid adjustment problem is reformulated as a boundary-constrained linear least squares optimization that guarantees solution uniqueness. The proposed method overcomes the grid constraints inherent in conventional CS-MFP approaches and enables precise off-grid source localization. Furthermore, by incorporating the Bernoulli-Gaussian sparsity-promoting priors, the algorithm enhances the sparsity constraints without requiring prior sparsity-level information. Numerical simulations and the SwellEX-96 experimental results demonstrate that the proposed method exhibits superior performance in both localization success rate and sidelobe suppression compared to conventional Bartlett and sparse Bayesian learning processors.