Estimation of snow depth using pseudorange and carrier phase observations of GNSS single-frequency signal

A new method is proposed to estimate snow depth by using observations of the GNSS single-frequency signal collected by a ground-based receiver. The proposed method utilizes the pseudorange and carrier phase observations to form the geometry-free combination. Based on mathematical formulas of the amplitude attenuation factor, the pseudorange multipath error, and the carrier phase multipath error, a function is derived serving as the theoretical model that describes the relationship between the antenna height and the peak frequency of a series of function values associated with the range of satellite elevation angles. In the observation data processing stage, the moving average filtering method is used to remove the ionospheric delay from the combined observation series, followed by spectrum analysis to obtain the peak frequency, which is used to determine the antenna height and hence snow depth based on the theoretical model. A weighting method is proposed to combine individual snow depth estimates related to the use of signals of individual satellites to enhance the estimation accuracy. Each weighting coefficient is proportional to the maximum of the power spectral density of the combined observation series. The proposed method is substantiated by simulations and observations from geodetic-grade receivers, which can process multi-constellations and multi-frequency GNSS signals. Two field GNSS data sets collected in Heilongjing, China, and Colorado, USA, were used to evaluate the method. The results show that the root-mean-square error of GPS, BDS, and Galileo-based snow depth estimations is in the range of 2-6 cm when the topography around the GNSS receiver is flat.