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PRELIMINARY STUDY ON WAVELET DENOISING METHOD FOR INVERSION OF SNOW DEPTH IN GNSS-MR

GNSS-MR technology inverts snow depth by using low-altitude SNR data. This information contains rich surface information. Due to the complex surface environment, the signal received by the receiver contains noise,during snow depth inversion, it is not possible to extract relatively "pure" snow information. Therefore, the wavelet denoising method is used to compare with the traditional polynomial. The results show that the snow depth RMSE of the polynomial inversion is 8cm and the error is 7cm. Wavelet denoising inversion The snow depth RMSE is 5cm and the error is 3cm. The experimental verification wavelet denoising method can better eliminate the systematic error and improve the inversion precision.


INTRODUCTION
The measurement of snow thickness is a key factor in estimating the moisture content of snow. In recent years, GNSS-MR technology has achieved a series of research results in the inversion of the surface environment [Ozeki, et al. 2012;Zhou et al. 2018;Ao et al. 2012;Larson et al. 2008;Cheng et al. 2014;Zhang et al. 2013]. However, the current inversion of snow depth using GNSS-R technology is mainly concentrated on the inversion method of each carrier or carrier combination.
The noise of the signal is not processed. Therefore, based on the GPS L2 carrier, the wavelet analysis method is used to denoise the signal-to-noise ratio of the L2 carrier to verify the feasibility of wavelet analysis in inversion of snow depth. .The GNSS-R technology inversion of snow depth mainly uses low-altitude SNR data, which is not only affected by the environment, but also by the receiver itself.
The receiving process contains more or less noise, so the observation data Denoising processing to obtain relatively "clean" snow information is beneficial to improve the accuracy of the inversion. The wavelet decomposition will produce the low frequency part and the high frequency part, and the original information is mainly concentrated in the low frequency part, so this paper only decomposes and reconstructs the low frequency part. In this paper, the principle of NSSS-MR technology inversion of snow depth is firstly described. Then the traditional quadratic polynomial and wavelet denoising method are used to carry out snow depth inversion. The advantages of wavelet denoising method are verified by comparison with measured data. Because in the experiment, it is found that the difference between the denoising and the quadratic polynomial inversion results is very small. Therefore, the wavelet experiment in this paper directly uses the two-layer decomposition and reconstruction signal to invert the snow depth. As shown in Fig. 1, it is a schematic diagram of the inversion of snow depth by GNSS-MR technology. It can be seen from the figure that the receiver receives the direct signal and the reflected signal of the satellite at the same time, and the reflected signal enters the ground surface and then has a reflection effect before entering the receiver. Therefore, this paper mainly extracts the snow depth inversion experiment of the reflected signal. In the figure, H is the vertical reflection distance from the phase center of the receiver antenna to the soil surface layer, which is the known amount of actual measurement; h is the vertical reflection distance from the antenna phase center to the snow surface layer; h snow is the snow thickness on the soil layer; θ is the satellite elevation angle, that is, the incident angle at which the direct signal is reflected by the surface.

GNSS-MR INVERSION SNOW DEPTH PRINCIPLE
For the geodetic GPS receiver antenna, the main function is to suppress the multipath observation error. The amplitude of the direct signal and the reflected signal have the following relationship:

≫
(1) From Figure 1, the SNR and signal amplitude are as follows [Dai et al. 2016]: Combining equation (1), the influence of multipath effect on signal-to-noise ratio is mainly due to the satellite elevation angle, that is, Ad and Ar differ greatly in numerical value, and low-order polynomial is usually used to eliminate trend term Ad. The research shows that the low-altitude multipath effect has the greatest influence on the SNR residual sequence, which provides important data for multi-path inversion of surface parameters. The amplitude of the multipath reflected signal can be expressed as: = cos ( 4 ℎ sin + ) As shown in Fig. 1, in equation (3), λ represents the carrier wavelength, θ represents the satellite elevation angle, h represents the vertical reflection distance, and t = t = sinθ, f = 2h / λ, then equation (3) can be simplified to The standard cosine function expression is: In the formula (4), the frequency f contains the vertical reflection distance parameter h. If the spectrum analysis is performed on the equation (4), the frequency f can be obtained.
Because the Lomb-Scargle algorithm (LS) [Cao et al. 1986] transform can not only effectively extract the weak periodic signal from the time domain sequence, but also can reduce the false signal generated by the uneven time domain sequence to some extent, so the LS spectrum is used in this paper.
Analytical method for spectrum analysis. By performing L-S spectrum analysis on the SNR residual sequence, the frequency f of the GPS multipath reflected signal can be obtained, and the vertical reflection distance h can be obtained by f=2h⁄λ.
Referring to Figure 1, the thickness of the snow can be calculated by the formula h snow =H-h. Thereby, snow depth measurement using SNR observations is achieved.

Wavelet Analysis Theory
The signal-to-noise ratio data is affected by various factors such as the condition of the measuring instrument and the surrounding environment of the tracking station, so that the signal received by the receiver will contain various noise effects and cover the actual situation. Therefore, the wavelet theory is introduced to reduce the signal. Noise processing. In

EXPERIMENT AND ANALYSIS
The GPS-MR technique mainly extracts the signal-to-noise ratio residual sequence in the reflected signal and performs L-S spectral analysis to obtain the inversion snow depth value.
Therefore, an important indicator for selecting a suitable wavelet base is the wavelet's ability to cancel. Wu Zhicheng [Wu et al.2013] and other four wavelet basis functions of sym10, coif3, bior3.5 and haar were selected to extract the trend term by comparing the ability of different wavelet basis functions. The results show that sym10 wavelet has the best ability to eliminate. Therefore, this paper uses sym10 wavelet base. Since the low frequency signal retains more original information, the high frequency part is seriously affected by noise. Therefore, this paper only decomposes and reconstructs the low frequency part.
The experimental data source of this paper is the L1 band data of the GPS continuous observation of the Yel2 (62°28′ 51.9′′N, 114°28′50.9′′W) station from January 1st to April 10th, 2016 provided by IGS. The measured snow depth data is provided by the National Climate Data Center (https://www.ncdc.noaa.gov/). The wavelet base used in this experiment is db4, and the number of denoising layers is 2. As shown in Figure 3 below, a and b are the signal-to-noise residual sequence and the corresponding LS spectrum of the No. 8 satellite using the quadratic polynomial to remove the trend term. In Figure 4, c and d are wavelets and the wavelet is analyzed. The low frequency signal (the signal to noise ratio residual sequence after the trend term is removed) and the corresponding LS spectrum.

CONCLUSION
From the experiments in this paper, the inversion accuracy of wavelet denoising method is better than polynomial.
Appropriate elimination of noise can improve the accuracy of inversion snow depth, but wavelet denoising will also eliminate some useful information of snow, so the number of wavelet decomposition layers is how much more appropriate, and still have to continue experimenting. In this paper, only the low-frequency signal is decomposed and reconstructed. In the following research, the high-frequency signal will be decomposed and reconstructed, and the snow depth will be combined with the low-frequency signal.