Evaluating Gaussian processes for matched-field processing localization using minimum mean squared error criterion

Area of Science:

• Signal Processing
• Machine Learning
• Geophysics

Background:

• Gaussian processes (GPs) are utilized for signal interpolation and denoising.
• Matched-field processing (MFP) is a technique used for signal localization.
• GPs have shown potential in enhancing MFP localization accuracy and robustness.

Purpose of the Study:

• To propose a minimum mean squared error (MMSE) criterion for evaluating GP interpolation performance in MFP.
• To compare the performance of different kernel and likelihood functions for GPs in MFP.
• To identify optimal hyperparameters and assess challenges in data-limited scenarios for GPs-MFP.

Main Methods:

• Utilizing a known true field to evaluate GP interpolation.
• Applying the MMSE criterion to quantify performance.
• Comparing various kernel and likelihood functions within the GP framework.
• Analyzing interpolation and localization results under different conditions.

Main Results:

• The MMSE criterion effectively evaluates GP interpolation and MFP localization performance.
• Performance comparison of different GP components (kernels, likelihoods) is facilitated.
• Optimal hyperparameters and interpolation strategies can be identified.
• Challenges and performance upper bounds for GPs-MFP are highlighted, especially with limited data.

Conclusions:

• The proposed MMSE criterion provides a robust method for assessing GP performance in MFP.
• GP methods can significantly improve MFP localization, but performance is sensitive to data availability and model choice.
• This work establishes a benchmark for GPs-MFP and guides future research in data-scarce environments.