A GNSS signal denoising method based on a CSS joint filtering algorithm

Abstract

The application discloses a GNSS signal denoising method based on a CSS joint filtering algorithm and belongs to the technical field of signal processing. The original GNSS signal is first decomposed into a plurality of IMF components by using a CEEMD method, and noise dominant IMFs and signal dominant IMFs are distinguished according to the cross-correlation coefficient variation between the IMFs and the original GNSS signal. Then, the noise dominant IMFs are iteratively weighted by using an SVD decomposition method, and effective information components in the noise IMFs are extracted. Finally, the extracted information components and the signal dominant IMFs are subjected to SG filtering and smoothing denoising, clean signal IMFs are obtained, and the denoising purpose is achieved. Through experiments on the U-direction time series of two stations, it is found that the method has obvious advantages, can restore the effective information in the noise dominant IMF components, and has high technical value and application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of signal processing, in particular to a GNSS signal denoising method based on CSS joint filtering algorithm. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) in the realization of precise positioning function, will be subject to different error sources of interference, including from satellite end error: such as satellite ephemeris deviation, satellite clock error, from the propagation path error: such as relativistic effect, ionospheric refraction and tropospheric delay deviation, from the receiver end error: such as receiver clock error, etc., the above error basically can be eliminated by real-time kinematic differential technology and the corresponding error correction model. But the random noise error generated by the receiver itself and the surrounding environment cannot be weakened and eliminated by such methods, so how to eliminate the interference of random noise error to GNSS signal has become a research hotspot in recent years. Common GNSS signal denoising technology includes EMD denoising, EEMD denoising, CEEMD denoising, SVD decomposition algorithm, SG filtering, etc. EMD noise reduction method has the defects of modal aliasing, end effect, etc., so the EEMD and CEEMD noise reduction method is proposed subsequently, which solves the problem of modal aliasing and makes the decomposition result more thorough. Although CEEMD denoising method overcomes the problem of modal aliasing of the decomposed IMF component, it cannot be properly processed, so the denoising effect is not good. SVD decomposition uses a small data set to represent the effective component of the original signal, which actually plays the effect of removing noise component, but only local optimization can be carried out. SG filtering is based on the least square method, which has good smoothing effect on signals containing weak noise, but cannot effectively eliminate noise interference under complex conditions. The noise contained in the original GNSS signal belongs to non-stationary noise, and it is difficult to achieve the best filtering by using the above method alone, and the optimal denoising effect can be achieved by joint filtering of multiple algorithms. Therefore, the present application provides a GNSS signal denoising method based on CSS joint filtering algorithm, which can effectively extract the real GNSS signal from random noise interference and provide a new idea for subsequent GNSS signal denoising algorithm, the steps are as follows: SUMMARY

[0003] The present application provides a GNSS signal denoising method based on CSS joint filtering algorithm, which can effectively extract the real GNSS signal from random noise interference and provide a new idea for subsequent GNSS signal denoising algorithm, the steps are as follows:

[0004] Step one, using CEEMD method to decompose the original GNSS signal into several IMF components;

[0005] Step two, statistics of the cross-correlation degree of each IMF component and the original GNSS signal, and using the change of cross-correlation coefficient to identify the demarcation point of noise dominant IMFs and signal dominant IMFs;

[0006] Step three, judging the threshold range through the demarcation point, which can detect the noise dominant IMFs and information dominant IMFs in the threshold range;

[0007] Step four, using SVD decomposition to iteratively weight the noise dominant IMFs, and then reconstructing the processed noise IMFs and signal IMFs after SG filtering and smoothing, so as to obtain the real GNSS signal.

[0008] Preferably, the original GNSS signal is decomposed into several IMF components by using the CEEMD method, specifically:

[0009] (1) adding n pairs of positive and negative auxiliary white noise with equal amplitude to the original GNSS signal, thereby obtaining two sets of GNSS signal sets: Wherein, y(t) is the original signal, n(t) is the positive and negative auxiliary white noise with equal amplitude, F1(t) and F2(t) are the GNSS signals after adding auxiliary white noise, thereby obtaining 2n sets of signal sets;

[0010] (2) CEEMD decomposition is performed on the 2n signals, and the corresponding IMF components are added and averaged to obtain the j-th IMF component, that is, Wherein, I jj (t) is the j-th IMF component, c ij (t) is the i-th signal and the j-th IMF component;

[0011] (3) after CEEMD method decomposition, the GNSS signal is equal to the sum of all IMF components and residual term, that is, Wherein, r(t) is the residual term, and the number of IMF components is n.

[0012] Preferably, the cross-correlation degree of each IMF component and the original GNSS signal is calculated, and the change of cross-correlation coefficient is used to identify the demarcation point of noise dominant IMFs and signal dominant IMFs, specifically: first, the cross-correlation degree of each IMF component and the original GNSS signal is calculated, and the formula is used for calculation, wherein, R iis the correlation coefficient between each IMF component and the original GNSS signal; then, the curvature L of the correlation coefficient between each IMF component and the original GNSS signal is calculated, Finally, the demarcation point is identified by the change of the curvature, and the minimum point of the curvature value is the demarcation point between the noise dominant IMFs and the signal dominant IMFs.

[0013] Preferably, the threshold range is determined by the demarcation point, and the noise dominant IMFs and the information dominant IMFs in the threshold range can be detected, which is specifically: the dominant nature of each IMF component is determined by the demarcation point. Since the CEEMD method has the property of decomposing the signal into several IMF components arranged in order from high frequency to low frequency, and the random noise has high frequency characteristics, it is considered that the noise dominant IMFs are before the demarcation point, and the information dominant IMFs are after the demarcation point.

[0014] Preferably, the noise dominant IMFs are iteratively weighted by SVD decomposition, and the processed noise IMFs and signal IMFs are smoothed by SG filtering and then reconstructed to obtain the real GNSS signal, which is specifically: the noise dominant IMFs are iteratively weighted by SVD decomposition until the noise dominant IMFs are converted into signal dominant IMFs, and then a small amount of residual noise in the signal is smoothed by SG filtering, so as to obtain clean IMFs; similarly, the signal dominant IMFs are smoothed by SG filtering, so as to obtain clean signal dominant IMFs; the two are reconstructed to obtain the real GNSS signal; wherein the fitting order of the SG filter is 3, the convolution frame is 11, and the smoothing number is 3. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a flow chart of the method of the present application;

[0016] Figure 2 is a correlation coefficient waveform diagram;

[0017] Figure 3 is the CEEMD decomposition result of the original GNSS signal;

[0018] Figure 4 is the result of the original GNSS signal after noise reduction;

[0019] Figure 5 is a residual sequence diagram of the original GNSS signal after noise reduction. DETAILED DESCRIPTION

[0020] The method of the present application will be described in detail below according to the drawings and specific embodiments:

[0021] The application firstly decomposes the original GNSS signal into several IMF components by using the CEEMD method, and distinguishes the noise dominant IMFs and the signal dominant IMFs according to the correlation coefficient variation between the IMFs and the original GNSS signal; then, the noise dominant IMFs are iteratively weighted by using the SVD decomposition method to extract the effective information components in the noise IMFs; finally, the extracted information components and the signal dominant IMFs are smoothed by SG filtering to obtain clean signal IMFs for reconstruction, so as to realize the noise reduction purpose.

[0022] As shown in the figure, a GNSS signal noise reduction method based on a CSS joint filtering algorithm, specifically comprising the following steps: Figure 1 As shown in the figure, a GNSS signal noise reduction method based on a CSS joint filtering algorithm, specifically comprising the following steps:

[0023] Step one, decompose the original GNSS signal into several IMF components by using the CEEMD method;

[0024] Step two, calculate the cross-correlation degree of each IMF component and the original GNSS signal, and use the variation of the cross-correlation coefficient to identify the demarcation point of the noise dominant IMFs and the signal dominant IMFs;

[0025] Step three, determine the threshold range by the demarcation point, and detect the IMFs dominated by noise and the IMFs dominated by information in the threshold range;

[0026] Step four, iteratively weight the noise dominant IMFs by using the SVD decomposition, and then reconstruct the processed noise IMFs and the signal IMFs after SG filtering and smoothing, so as to obtain the real GNSS signal.

[0027] Specifically, in the step one, it comprises:

[0028] Add n pairs of positive and negative auxiliary white noise with equal amplitude to the original GNSS signal, and then decompose the two sets of GNSS signals by using the EMD function to obtain each order intrinsic mode component, and then repeat the above process until the residual signal is monotonic, and then integrate all the intrinsic mode components to complete the empirical mode decomposition, which is as follows:

[0029] (1) Add n pairs of positive and negative auxiliary white noise with equal amplitude to the original GNSS signal, so as to obtain two sets of GNSS signal sets: Wherein, y(t) is the original signal, n(t) is the positive and negative auxiliary white noise with equal amplitude, F1(t) and F2(t) are the GNSS signals after adding the auxiliary white noise, so as to obtain 2n sets of signal sets;

[0030] (2) The CEEMD is decomposed for the 2n signals, and the corresponding IMF components are added and averaged to obtain the jth IMF component, that is where, I jj (t) is the jth IMF component, c ij (t) is the ith signal and the jth IMF component.

[0031] (3) After the CEEMD method is decomposed, the GNSS signal is equal to the sum of all IMF components and the residual term, that is where, r(t) is the residual term, and the number of IMF components is n.

[0032] where, the added auxiliary white noise in the CEEMD method is 100, and the amplitude is 0.01-0.10.

[0033] Specifically, in the step two, it includes:

[0034] The random noise error is generated due to the receiver itself or the change of the surrounding external environment, and has contingency and uncertainty. Therefore, the cross-correlation degree of the noise dominant IMFs and the original GNSS signal is obviously lower than that of the signal dominant IMFs and the original GNSS signal, and by statistically determining the change of the curvature of the cross-correlation coefficient of each IMF and the original GNSS signal, the demarcation point of the noise IMFs and the signal IMFs can be determined, as shown in the following formula: Figure 2

[0035] The calculation formula of the cross-correlation coefficient of the IMFs and the original GNSS signal is:

[0036]

[0037] The calculation formula of the curvature of the cross-correlation coefficient of the IMFs and the original GNSS signal is:

[0038]

[0039] where, R i is the cross-correlation coefficient of the ith IMF component and the original GNSS signal, and L is the curvature. The minimum point of the curvature value is the demarcation point of the noise dominant IMFs and the signal dominant IMFs.

[0040] Specifically, in the step three, it includes:

[0041] The demarcation point is used to determine the dominant nature of each IMF component. Since the CEEMD method has the property of decomposing the signal into several IMF components arranged in descending order from high frequency to low frequency, and the random noise has high frequency characteristics, it is considered that the noise dominant IMFs are before the demarcation point, and the information dominant IMFs are after the demarcation point, as shown in the following formula: Figure 3 ​shown.

[0042] Specifically, in the step four, comprising:

[0043] The iterative weighting strategy based on SVD decomposition is as follows:

[0044] (1) Assuming that the noise-dominant IMF set obtained by decomposing the original GNSS signal through the CEEMD method is imf1, imf2,..., imf k , where k is Figure 2 The demarcation point between the noise-dominant IMFs and the signal-dominant IMFs in the set imf

[0045] (2) The IMF set imf i is divided into k subsets, i.e., imf1, imf2,..., imf i , i = 1, 2,..., k, and an n x m order matrix A is constructed according to formula (3), and then A is subjected to SVD decomposition to obtain a singular value factor set s i in descending order, and u i , v T ;

[0046] A = USV n (3)

[0047] where U = [u1, u2,..., u n×n ] ∈ R n ; V = [v1, v2,..., v m×m ] ∈ R r ; S = [diag(σ1, σ2,..., σ1), 0] or its transpose, depending on whether n > m or n < m, r = min(n, m), 0 is a zero matrix, and σ1≥σ2≥…σ i1 ≥ 0 are singular value factors of the matrix A;

[0048] (3) The first i effective singular value factors are selected according to the SVD differential spectrum theory to reconstruct imf , i.e., the effective information imf i extracted by SVD decomposition;

[0049] (4) The imf i1 is subjected to weighting processing according to formula (4), and the purpose is to recover the part of the effective information lost after step (3);

[0050]

[0051] (5) The imf i1 is subjected to processing according to steps (2)-(4) to obtain imf i2 ;

[0052] (6) Steps (2)-(5) are repeated until imfim The cross-correlation coefficient of the original GNSS signal x i (t) is greater than or equal to Figure 2 The threshold point P in the IMF is greater than or equal to i After m times of weighted iterative processing, the signal component occupies the dominant position in the noise IMF.

[0053] The reasons for selecting SVD decomposition to establish the iterative weighting strategy are as follows:

[0054] (1) SVD decomposition has strong noise reduction capability in local signal area;

[0055] (2) SVD decomposition has the advantages of simple and fast calculation, small amount of operation data, etc.;

[0056] (3) The first few singular values representing effective information can be quickly selected by SVD difference spectrum method;

[0057] The SG filter smoothing algorithm strategy is as follows:

[0058] Regarding the original sequence points {x1, x2, x3, … x m}, the fitting curve equation is assumed to be:

[0059] x(t) = c0+ c1t + c2t 2 + … + c n t n , n∈z (5)

[0060] Where x(t) is the fitting point, t is the time, n is the fitting order, and c n is the fitting parameter.

[0061] The fitting residual of the least square algorithm is:

[0062]

[0063] Where [x(t)-c0-c1t-c2t 2 -…-c n t n ] is the fitting residual, and S r is the sum of squared residuals.

[0064] If the fitting parameters c i (i = 0, 1, 2, …, n) satisfy formula (6) minimum, the points of formula (5) are considered to be the best fitting points of the original sequence.

[0065] The noise-dominant IMFs are iteratively weighted by using SVD decomposition until the noise-dominant IMFs are converted into signal-dominant IMFs, and then a small amount of residual noise in the signal is smoothed by SG filtering, so that clean IMFs are obtained; similarly, the signal-dominant IMFs are smoothed by SG filtering, so that clean signal-dominant IMFs are obtained; reconstruction is performed on the two to obtain the real GNSS signal; wherein the fitting order of the SG filter is 3, the convolution framework is 11, and the smoothing number is 3.

[0066] The experimental results show that

[0067] In order to evaluate the effectiveness of the method of the application, the time series of the U direction of the Hennan University of Science and Technology and the HuaCes HNJZ station in the south 0001 are selected, and the CEEMD method and the method in the application are used to develop experiments, and the cross-correlation coefficient R, the root mean square error (RMSE), the signal-to-noise ratio (SNR) and the like are used as main evaluation indexes, and the evaluation formula is as follows:

[0068]

[0069]

[0070]

[0071] Wherein, n is the signal length, xt(i) is the signal after noise reduction, x(i) is the original signal, cov(x,x t ) is the covariance of x and x t , and sigma x and sigma xt are the standard deviations of x and x t .

[0072] As can be seen from Table 1, the root mean square error of the signal after noise reduction is significantly lower than that of the CEEMD method by using the CSS joint filtering algorithm to process the original GNSS signal of the station, and the cross-correlation coefficient and the signal-to-noise ratio are also further improved. This is because the CEEMD method directly discards the noise-dominant IMFs, so that the effective information contained in the noise IMFs is lost. As can be seen from Figure 4 , Figure 5 , the CSS joint filtering algorithm retains more effective signal components, and the amplitude of the residual sequence after noise reduction by the method of the application is smaller than that of the CEEMD method.

[0073] The average value of the accuracy evaluation indexes of the two stations is counted, and compared with the CEEMD method, and it is found that the cross-correlation coefficient of the denoised signal and the original GNSS signal after the original GNSS signal is processed by the CSS joint filtering algorithm is 0.99, the root mean square error is reduced by 0.12mm, and the signal-to-noise ratio is improved by 4.31dB. Through the above analysis, the denoising method based on the CSS joint filtering algorithm is better than the CEMMD method in denoising effect.

[0074] Table 1 Comparison of denoising effects of two methods

[0075]

Claims

1. A method for GNSS signal denoising based on a CSS joint filtering algorithm, characterized in that, It comprises the following steps: Step one, using CEEMD method, the original GNSS signal is decomposed into several IMF components; Step two, the correlation degree of each IMF component and the original GNSS signal is calculated, and the change of the correlation coefficient is used to identify the demarcation point between noise dominant IMFs and signal dominant IMFs; Step three, the threshold range is determined by the demarcation point, and the noise dominant IMFs and information dominant IMFs in the threshold range can be detected; Step four, the noise dominant IMFs are iteratively weighted using SVD decomposition, and the processed noise IMFs and signal IMFs are smoothed by SG filter and then reconstructed to obtain the real GNSS signal; In step two, the correlation degree of each IMF component and the original GNSS signal is calculated, and the change of the correlation coefficient is used to identify the demarcation point between noise dominant IMFs and signal dominant IMFs, the specific process is as follows: Firstly, the correlation degree between each IMF component and the original GNSS signal is calculated by the formula wherein R i is the correlation coefficient between each IMF component and the original GNSS signal; then, the curvature L of the correlation coefficient between each IMF component and the original GNSS signal is calculated, Finally, the demarcation point is identified by the change of the curvature, and the minimum point of the curvature value is the demarcation point between the noise dominant IMFs and the signal dominant IMFs. In step three, the threshold range is determined by the demarcation point, and the noise dominant IMFs and information dominant IMFs in the threshold range can be detected, the specific process is as follows: The demarcation point is used to determine the dominant nature of each IMF component, since the CEEMD method has the property of decomposing the signal into several IMF components arranged from high frequency to low frequency, and the random noise has high frequency characteristics, so it is considered that the noise dominant IMFs are before the demarcation point, and the information dominant IMFs are after the demarcation point; In step four, the noise dominant IMFs are iteratively weighted using SVD decomposition, and the processed noise IMFs and signal IMFs are smoothed by SG filter and then reconstructed to obtain the real GNSS signal, the specific process is as follows: The noise dominant IMFs are iteratively weighted using SVD decomposition until the noise dominant IMFs are converted to signal dominant IMFs, and then the remaining small amount of noise in the smoothed signal is removed by SG filter, so that clean IMFs are obtained; Similarly, the signal dominant IMFs are smoothed by SG filter to obtain clean signal dominant IMFs; The two are reconstructed to obtain the real GNSS signal; Wherein, the fitting order of the SG filter is 3, the convolution frame is 11, and the smoothing times is 3.

2. The GNSS signal denoising method based on the CSS joint filtering algorithm according to claim 1, characterized in that, In step one, the original GNSS signal is decomposed into several IMF components using CEEMD method, the specific process is as follows: (1) Adding n pairs of positive and negative auxiliary white noise with equal amplitude to the original GNSS signal to obtain two sets of GNSS signal sets: Wherein, y(t) is the original signal, n(t) is the positive and negative auxiliary white noise with equal amplitude, F1(t) and F2(t) are the GNSS signals after adding the auxiliary white noise, thereby obtaining 2n sets of signal sets; (2) CEEMD decomposition is performed on the 2n signals, and the corresponding IMF components are added and averaged to obtain the jth IMF component, i.e. where, I jj (t) is the jth IMF component, c ij (t) is the ith signal, the jth IMF component; (3) After the CEEMD method is decomposed, the GNSS signal is equal to the sum of all IMF components and the residual remainder, that is, wherein r(t) is the residual remainder, and the number of IMF components is n.

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