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.

中文翻译：

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具有基于正常模式的内核的高斯过程，用于匹配场处理

高斯过程 (GP) 通过利用不同接收深度处声场的相关性来模拟海洋波导中的声场。因此，对于稀疏分布阵列的测量声场，GP 可以预测虚拟接收器处的密集场。核函数反映了不同接收深度之间现场测量的相关性。本文提出了一种基于正态模态模态深度函数（NMBK）的核函数，用于高斯过程回归进行去噪和插值。然后将预测场与匹配场处理 (MFP) 方法相结合以进行无源源定位。还通过密集接收深度处的声学传播模型来计算副本。使用来自SWellEx-96 Event S5环境的模拟数据和真实数据来验证所提方法的有效性。与传统的MFP方法相比，结合GP的MFP方法具有更好的定位性能和更低的模糊面旁瓣。此外，与径向基函数相比，所提出的 NMBK 更好地描述了海洋波导的特性。因此，它具有更好的声场预测性能，并且对模糊位置更少的MFP方法进行了显着改进。