Multi-constellation and multi-frequency GNSS-IR sea level retrieval using sliding-window and helmert variance component estimation

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) has emerged as an effective technique for nearshore sea surface height (SSH) retrieval. However, traditional single-system and single-frequency approaches are constrained by limited satellite coverage, resulting in low sampling rates and insufficient exploitation of the complementarity among multi-source observations. To address these limitations, this study utilizes multi-frequency signal-to-noise ratio (SNR) observations from four GNSS constellations, namely GPS, GLONASS, Galileo, and BeiDou, collected at two coastal stations, MAYG and HKQT. An integrated multi-constellation and multi-frequency GNSS-IR framework is developed by incorporating dynamic sea-surface correction, tropospheric delay compensation, a sliding-window strategy, and Helmert variance component estimation (HVCE). Experimental results demonstrate that, compared with the equal-weight fusion method, the proposed multi-GNSS combination scheme reduces the root mean square error (RMSE) of SSH retrievals by 38%–61%, while achieving Pearson correlation coefficients exceeding 0.93 with tide gauge observations. The HVCE strategy adaptively determines optimal weights for multi-source observations based on the statistical characteristics of their residuals, effectively mitigating the effects of heterogeneous observation precision and unbalanced weighting. Combined with a fixed-step sliding-window strategy, the proposed framework produces stable and continuous SSH time series at a uniform 10-min interval, achieving a balance between retrieval accuracy and temporal continuity. This study provides a robust and practical approach for high-quality nearshore sea-level monitoring using multi-GNSS SNR observations.