The Global Navigation Satellite System-Reflections (GNSS-R) signal has been confirmed to be useful for retrieving sea level height. At present, the GNSS-Interferometric Reflectometry (GNSS-IR) technology based on the least square method to process signal-to-noise ratio (SNR) data is restricted by the satellite elevation angle in terms of accuracy and stability. This paper proposes a new GNSS-IR model combining variational mode decomposition (VMD) for sea level height estimation. VMD is used to decompose the SNR data into intrinsic mode functions (IMF) of layers with different frequencies, remove the IMF representing the trend item of the SNR data, and reconstruct the remaining IMF components to obtain the SNR oscillation item. In order to verify the validity of the new GNSS-IR model, the measurement data provided by the Onsala Space Observatory in Sweden is used to evaluate the performance of the algorithm and its stability in high elevation range. The experimental results show that the VMD method has good results in terms of accuracy and stability, and has advantages compared to other methods. For the half-year GNSS SNR data, the root mean square error (RMSE) and correlation coefficient of the new model based on the VMD method are 4.86 cm and 0.97, respectively.

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The signal-to-noise ratio (SNR) is important observations in global navigation satellite system-reflectometry (GNSS-R) technology. The oscillation frequency in the SNR arc is sensitive to different reflecting surfaces and can be used to build height model to track the variation of snow depth. However, it is difficult to obtain retrieval results with snow depth of zero in the actual snow depth retrieval experiments based on GNSS-R technology, which indicates that the classical model has nonnegligible retrieval errors in the snow-free state. This study aims to realize the detection of ground truth information before snow depth retrieval, i.e., classification of snow-free state and snow-covered state. Machine learning was introduced to achieve the aforementioned purpose and the SNR arc was used as the input data. Compared with the current mainstream topography correction algorithms, the algorithm proposed in this study does not rely on any priori ground measured data and has theoretical universality. The detection results can constrain the retrieval snow depth in the snow-free state and, thus, improve the retrieval accuracy. The experimental results for the 2014 seasonal snowpack at P351 station in Idaho, USA, show that the detection results obtained based on support vector machines agree well with the measured snow depth provided by the SNOTEL network, and the overall detection accuracy can reach about 96%. The daily snowpack state is determined by the majority of SNR arcs detected during the day and is only considered reliable if the percentage exceeds 75%. Only one day of the detection results was inaccurate and only 8 days (8/365) did not reach the set threshold of 75%. With the help of the detection results, the root-mean-square error of snow depth retrieval can be reduced from 20 cm in the classical algorithm to 15 cm, which results in a 25% improvement in retrieval accuracy. Moreover, this study broadens the application value of GNSS signals and provides a reference for the application of SNR in the detection field.

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