Physically guided dual-antenna GNSS-R snow depth inversion based on ensemble learning

Global Navigation Satellite System Reflectometry (GNSS-R) is significant for snow cover monitoring. To address the issues of weak reflected signals, inaccurate feature extraction, and insufficient precision in traditional single-antenna GNSS-R snow depth inversion, a physically guided dual-antenna ensemble learning inversion method is proposed. Dual antennas are utilized to receive direct and reflected signals. variational mode decomposition (VMD) and Lomb-Scargle periodogram (LSP) are employed to process signals and extract physically meaningful primary and secondary frequency features. Subsequently, an ensemble classifier is constructed to establish a non-linear mapping model between features and snow depth. To verify the effectiveness of the method, experiments were conducted based on data from the Altay station in Xinjiang in 2025, and the inversion performance of multiple satellite combinations was analyzed. Experimental results demonstrate that the VMD algorithm exhibits superior decomposition and reconstruction capabilities for non-stationary GNSS signals, effectively mitigating environmental noise interference. Feature weight analysis based on Shapley additive explanations (SHAP) values clarifies the synergistic mechanism between physical and statistical features, establishing a physical basis for adaptive weight redistribution under varying observation conditions. Meanwhile, the voting-based ensemble learning strategy, through multi-model weighted fusion, effectively overcomes the overfitting risks associated with single models and significantly enhances system robustness, obtaining an inversion precision with a mean absolute error (MAE) of 0.364 cm and a maximum absolute error of 2 cm, which improves the accuracy by about 50% compared to the single random forest model. Overall, the proposed method maintains consistent performance across multiple satellite combinations, verifying its potential for engineering applications in snow monitoring within complex environments.