Abstract: As an emerging remote sensing technology, GNSS-MR utilizes the multipath effect of GNSS signals during propagation to retrieve surface parameters. It has been widely applied in the field of tidal inversion in recent years. However, traditional GNSS-MR techniques, when extracting the SNR residual sequence using low-order polynomials, often employ a coarse extraction method that does not fully consider the characteristics of GNSS interference signals. As a result, when the satellite elevation angle is large, the extracted SNR residual sequence contains non-interference components, leading to false peak phenomena during LSP frequency spectrum analysis and resulting in inversion distortion. In this study, we leverage the advantages of the variational mode decomposition (VMD) algorithm to adaptively decompose the synthesized signal into a series of intrinsic mode functions (IMFs) with specific physical meanings. We propose an improved GNSS-MR tidal inversion method based on VMD. The tidal inversion results from the SC02 station in Washington State over a period of 100 days indicate that among the three tidal inversion methods based on VMD proposed in this paper, the inversion accuracy and stability are highest when the number of IMFs obtained from VMD decomposition is set to 5 (referred to as VMD-5). Its RMSE is 33.74 cm, correlation coefficient is 0.920 5, and the number of anomalous inversion points is 40. Compared with the traditional inversion method, VMD-4 inversion method, and VMD-6 inversion method, the RMSE is reduced by 89.80%, 10.81% and 48.48% respectively. The correlation coefficients are increased by 305.40%, 2.30% and 25.99%, respectively. And the number of anomalous inversion points is reduced by 83.67%, 6.98% and 14.89%, respectively. The proposed VMD-5-based improved GNSS-MR tidal inversion method effectively reduces the number of anomalous inversion points in traditional inversion methods, significantly improves the accuracy and temporal resolution of inversions, and enables long-term, high-precision, high-stability, and high-temporal-resolution tidal inversion even at large satellite elevation angles.

Key words: GNSS-MR, inversion distortion, VMD, SNR