Study on soil moisture estimation using a three-frequency combination of observations integrated with robust estimation and machine learning

This study introduces two innovative methods-Three-frequency pseudorange combination (TFPC) and Three-frequency carrier phase combination (TFCPC)-for estimating soil moisture using GNSS-IR technology. Unlike traditional methods that require separating direct and reflected signals, these approaches leverage carrier phase and pseudorange multipath errors to improve accuracy. The new methods eliminate the impact of geometrical factors and atmospheric delays. By applying minimum covariance determinant (MCD) and moving average filter (MAF), the study effectively detects and corrects outliers in delay phases, enhancing the quality of the data. Using data from the Plate Boundary Observatory (PBO) H2O project, the study finds that combining corrected delay phases from multiple satellites improves correlations between estimated and actual soil moisture values. The TFPC method achieves correlation coefficients of 0.82 and 0.87 with multivariate linear regression (MLR) and radial basis function neural network (RBFNN) models, while the TFCPC method yields even better results at 0.85 and 0.91, respectively. These findings represent a significant advancement in high-precision soil moisture estimation, offering valuable implications for applications in agriculture, weather forecasting, and environmental monitoring.