A two-step method for precisely correcting abnormal phases of the SNR modulation terms in GNSS-IR

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) retrieves soil moisture (SM) by calculating the phase of the signal-to-noise ratio (SNR) modulation term induced by ground reflection. The nonlinear least squares (NLS) algorithm is commonly adopted to extract the phase. However, the limitation of NLS algorithm leads to phase jump in different periods. To enhance the reliability of phase retrieval, we propose a two-step abnormal phase correction approach according to the analyzed phase error characteristics. Firstly, the SNR period method is developed to correct phase jump caused by NLS limitations, including entire-period and half-period shifts. Subsequently, residual errors induced by multipath effects are identified through the standard score (Z-score) and repaired via the Savitzky-Golay filter (SGF). The proposed technique significantly improves the correlation of the reconstructed phase time series with ground-truth SM. This two-step method effectively solves abnormal phase correction for GNSS-IR based SM retrieval.