Multi-observation robust regression for continuous coastal sea surface height monitoring using GNSS multipath reflectometry

Global Navigation Satellite System Multipath Reflectometry (GNSS-MR) has substantial potential for coastal sea surface height (SSH) monitoring. Although signal-to-noise ratio (SNR), carrier phase, and pseudorange observations have been used for SSH retrieval, how to fully exploit their complementary information and determine an optimal retrieval strategy remains insufficiently understood. This study develops a multi-observation GNSS-MR framework for SSH retrieval by integrating SNR-based spectral analysis and inverse modeling, single-frequency code-minus-carrier retrieval, and dual- and triple-frequency combinations based on carrier phase and pseudorange observations. A Multi-Observation Robust Regression (MORR) method is further proposed to fuse heterogeneous retrievals within a sliding temporal window while accounting for the second-order dynamic variation of sea level. The results show that carrier-phase-based methods achieve accuracy comparable to SNR-based retrieval, with root mean square errors (RMSEs) below 17 cm and correlation coefficients (R) above 0.98, whereas pseudorange-based approaches yield lower accuracy, with RMSEs of 25.11 and 26.92 cm for dual- and triple-frequency strategies, respectively. The multi-observation strategy substantially enhances temporal coverage, providing an average of 354.66 retrieval timestamps per day and a median sampling interval of 0.038 h. More importantly, MORR achieves the best overall performance, with an RMSE of 2.51 cm against TG records. Ablation experiments further confirmed the contribution of multi-observation, reducing the RMSE from 4.30 to 2.51 cm at SC02 and from 5.21 to 3.47 cm at an independent station (NBFH). These results demonstrate that multi-observation GNSS-MR combined with MORR provides a high-accuracy and high-temporal-resolution remote-sensing solution for continuous coastal SSH monitoring.