Physics-Informed Hemispherical Mapping for Global Navigation Satellite System Multipath Mitigation in Mining Subsidence Monitoring.

Multipath remains a major limitation for global navigation satellite system (GNSS) precise point positioning (PPP)-based subsidence monitoring in mining areas. We propose a physics-informed multipath hemispherical mapping (PI-MHM) model for multifrequency, multi-GNSS PPP. The method combines single-difference-to-undifferenced residual preprocessing with a compact multilayer perceptron that models directional multipath from azimuth, elevation, and trigonometric features, while imposing orbital repeatability, spatial smoothness, and high-elevation attenuation as soft constraints. In a field validation using 11 days of observations from three mining-area monitoring stations, labeled as CR01, CR05, and CR07, PI-MHM achieved mean residual root-mean-square (RMS) reduction rates of 37.1%, 38.3%, and 40.1% at these stations, respectively, outperforming trend-surface MHM (T-MHM), congruent cells multipath central grid (C-MCG), and convolutional neural network-long short-term memory (CNN-LSTM). In the 1-h three-system PPP test, the mean horizontal and vertical RMS values decreased from 3.56 and 5.66 cm to 2.31 and 3.44 cm, respectively. At CR07, the post-convergence up-component RMS decreased from 2.72 to 1.99 cm. The results suggest that repeatability, smoothness, and elevation-dependent attenuation priors can improve multipath correction under complex mining-area conditions.