Gaussian processes with normal-mode-based kernels for matched field processing

The Gaussian processes (GPs) model the acoustic field in the ocean waveguide by exploiting the correlation of the acoustic field at different receiving depths. Therefore, for the measured acoustic field of a sparsely distributed array, the GPs can predict the dense field at the virtual receivers. The kernel function reflects the correlation of field measurements between different receiving depths. This paper proposes a kernel function based on the modal depth functions of normal modes (NMBK), which is used for Gaussian process regression for denoising and interpolation. The predicted field is then combined with the matched field processing (MFP) method for passive source localization. Replicas are also calculated by an acoustic propagation model at the dense receiving depths. Both simulated data and real data from the SWellEx-96 Event S5 environment are used to verify the validity of the proposed method. Compared with the traditional MFP method, the MFP method combined with the GPs has better localization performance and lower sidelobes on the ambiguity surface. Moreover, the proposed NMBK better describes the characteristics of the ocean waveguide compared to the radial basis function. Therefore, it has better acoustic field prediction performance and makes significant improvements on the MFP method with fewer ambiguous positions.