Multi-Fidelity Gaussian Process Regression and Sequential Active Sampling for Surrogate Modeling: A Methodological Study with Validation on a Synthetic Radar Angle Tracking Benchmark

To address the challenge of limited evaluations of expensive high-complexity functions in surrogate modeling, this paper proposes a methodological framework that integrates multi-fidelity Gaussian process (MFGP) regression, sequential active sampling, and global sensitivity analysis, using a radar angle tracking accuracy (ATA)-inspired synthetic function as the validation benchmark. An autoregressive MFGP model with composite kernel functions is constructed to capture the complex nonlinear characteristics of the synthetic response surface. A sequential active sampling strategy based on the maximum uncertainty criterion, combined with fixed resource allocation and a neighboring sample avoidance mechanism, is designed to achieve efficient sample collection under a limited evaluation budget. Sobol global sensitivity analysis is then performed on the trained MFGP surrogate model to quantify the main and interaction effects of each input parameter on the synthetic ATA function. Experimental results demonstrate that with the complete sequential sampling procedure, the proposed MFGP model achieves an R2 of 0.8515 and an RMSE of 0.0850 on the test set, significantly outperforming the single-fidelity GP model that relies solely on high-complexity samples. Sobol analysis identifies the Jamming-to-Signal Ratio (JSR) and lateral distance as the most critical influencing factors within the synthetic benchmark. The proposed framework substantially improves sample efficiency under limited evaluation budgets, providing an effective methodological reference for surrogate modeling in similar high-cost computational scenarios.