Adaptive SSA noise reduction method, device and computer-readable storage medium

Abstract

The present application relates to an adaptive SSA denoising method, device and computer-readable storage medium, wherein the adaptive SSA denoising method comprises: embedding the original GNSS time series data to obtain the trajectory matrix corresponding to the original GNSS time series data; performing singular value decomposition on the above trajectory matrix to obtain a set of singular values; determining the reconstruction components corresponding to at least part of the singular values ​​to obtain multiple reconstruction components; reconstructing using the above multiple reconstruction components to obtain multiple reconstructed signals; determining the root mean square error and smoothness of each reconstructed signal; linearly combining the root mean square error and smoothness of each reconstructed signal to obtain the composite evaluation index corresponding to each reconstructed signal; and determining the denoised signal according to the size of the composite evaluation index corresponding to each reconstructed signal. Through this method, a significant denoising effect is achieved.

Description

Technical Field

[0001] The present application relates to the field of Global Navigation Satellite System (GNSS) signal processing, and in particular to an adaptive singular spectrum analysis (SSA) noise reduction method, device and computer-readable storage medium. Background Art

[0002] GNSS deformation monitoring has the characteristics of high monitoring accuracy and small cumulative displacement. Its monitoring time series includes real displacement and observation noise. If the original time series is directly analyzed, it is often difficult to distinguish deformation variables, trend items, etc. In GNSS time series analysis, SSA is a non-parametric spectral estimation method. This method is gradually developed on the basis of the classic Karhunen-Loeve spectral decomposition and embedding theory, and is a principal component analysis method for periodic oscillations of one-dimensional time series.

[0003] SSA can decompose the GNSS deformation monitoring signal into several SSA components and select several meaningful components for reconstruction to reduce noise. The key step to achieve SSA denoising is to determine the effective rank of the Hankel matrix, that is, the number of effective singular values.

[0004] In response to the above problems, scholars at home and abroad have proposed many solutions. Existing research methods for determining the number of valid singular values ​​include: selecting the number of singular values ​​based on the matrix rank minimization theory; by presetting a percentage threshold, dividing the accumulated eigenvalue value by the sum of all eigenvalues ​​and comparing it with the threshold; using the number of main frequencies in the fast Fourier transform result to determine the order of the effective rank; using the eigenvalue mean method to determine the number of valid singular values; using the principal component decomposition method to determine the number of valid singular values. The above methods have achieved good results in practical applications, but there are also certain limitations. For example, when the useful signal is submerged by noise, the useful signal frequency and the noise frequency in the FFT method result are difficult to distinguish, and the method will fail; the noise reduction signal obtained by the eigenvalue mean method will produce a more serious blurring effect. Most of the methods judge the number of valid singular values ​​through qualitative analysis, which is often difficult to apply to signals under complex noise backgrounds. Summary of the invention

[0005] In order to solve the above technical problems or at least partially solve the above technical problems, the present application provides an adaptive SSA noise reduction method, device and computer-readable storage medium.

[0006] In the first aspect, the present application provides an adaptive SSA denoising method, comprising: performing an embedding operation on GNSS original time series data to obtain a trajectory matrix corresponding to the GNSS original time series data; performing singular value decomposition on the above trajectory matrix to obtain a set of singular values; determining reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components; using the above multiple reconstruction components to perform reconstruction to obtain multiple reconstructed signals; determining the root mean square error and smoothness of each reconstructed signal; linearly combining the root mean square error and smoothness of each reconstructed signal to obtain a composite evaluation index corresponding to each reconstructed signal; and determining the denoised signal according to the size of the composite evaluation index corresponding to each reconstructed signal.

[0007] In some embodiments, determining the signal after noise reduction according to the size of the composite evaluation index corresponding to each reconstructed signal includes: determining the signal after noise reduction to be the reconstructed signal with the smallest composite evaluation index.

[0008] In some embodiments, the root mean square error and smoothness of each reconstructed signal are linearly combined to obtain a composite evaluation index corresponding to each reconstructed signal, including: normalizing the root mean square error and smoothness of each reconstructed signal; weighting the normalized root mean square error and smoothness according to the coefficient of variation method to obtain the weight of the linear combination; weighting the normalized root mean square error and smoothness of each reconstructed signal according to the weight of the above-mentioned linear combination to obtain a composite evaluation index corresponding to each reconstructed signal.

[0009] In some embodiments, determining reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components includes: determining the first k singular values ​​in order from large to small, where k is the maximum number of singular values ​​that terminate the loop; determining the reconstruction components corresponding to the above-mentioned first k singular values ​​to obtain k reconstruction components.

[0010] In some embodiments, determining the reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components also includes: determining the average value of the above-mentioned multiple singular values; determining the number k1 of singular values ​​greater than the average value; and determining the maximum number k of singular values ​​for terminating the loop based on the number k1 of singular values ​​greater than the average value.

[0011] In some embodiments, determining the maximum number k of singular values ​​for terminating the loop based on the number k1 of singular values ​​greater than the average value includes: determining the maximum number k of singular values ​​for terminating the loop to be twice the number k1 of singular values ​​greater than the average value.

[0012] In some embodiments, the multiple reconstruction components are used to perform reconstruction in the following manner to obtain multiple reconstructed signals:

[0013]

[0014] Among them, S i represents the i-th reconstructed signal, RC j represents the reconstructed component corresponding to the jth singular value in descending order, 1≤i≤k, where k is the number of reconstructed components.

[0015] In the second aspect, the present application provides an adaptive SSA noise reduction device, comprising: an embedding module, used to perform an embedding operation on GNSS original time series data to obtain a trajectory matrix corresponding to the GNSS original time series data; a decomposition module, used to perform singular value decomposition on the above-mentioned trajectory matrix to obtain a set of singular values; a first determination module, used to determine the reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components; a reconstruction module, used to reconstruct the above-mentioned multiple reconstruction components to obtain multiple reconstructed signals; a second determination module, used to determine the root mean square error and smoothness of each reconstructed signal; a third determination module, used to linearly combine the root mean square error and smoothness of each reconstructed signal to obtain a composite evaluation index corresponding to each reconstructed signal; a fourth determination module, used to determine the denoised signal according to the size of the composite evaluation index corresponding to each reconstructed signal.

[0016] In a third aspect, the present application provides a computer device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor; when the computer program is executed by the processor, the steps of any of the above-mentioned adaptive SSA denoising methods are implemented.

[0017] In a fourth aspect, the present application provides a computer-readable storage medium, on which an adaptive SSA noise reduction program is stored. When the adaptive SSA noise reduction program is executed by a processor, the steps of any of the above-mentioned adaptive SSA noise reduction methods are implemented.

[0018] The above technical solution provided by the embodiment of the present application has the following advantages compared with the prior art:

[0019] The method provided in the embodiment of the present application no longer uses a qualitative analysis method, but instead adopts a quantitative analysis method to accurately determine the optimal number of reconstruction layers; in a complex noise background, for example, the signal is contaminated by both Gaussian noise and impulse noise, and an obvious denoising effect is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0022] Figure 1 A flowchart of an implementation of the adaptive SSA noise reduction method provided by the present application;

[0023] Figure 2 A flowchart of another implementation of the adaptive SSA noise reduction method provided by the present application;

[0024] Figure 3 A structural block diagram of an implementation of an adaptive SSA noise reduction device provided by the present application;

[0025] Figure 4 A hardware schematic diagram of an implementation of a computer device provided in an embodiment of the present application;

[0026] Figure 5 It is a comparison chart of the denoising results of simulated data using the adaptive SSA denoising method, the mean method, and the FFT method;

[0027] Figure 6 is the composite evaluation index T corresponding to each reconstruction layer number of the adaptive SSA denoising method in the simulated data;

[0028] Figure 7 This is a comparison chart of the denoising results of the ZIMM station using the adaptive SSA denoising method and the mean method;

[0029] Figure 8 This is a comparison chart of the denoising results of BZ03 station using the adaptive SSA denoising method and the mean method;

[0030] Fig. 9 It is a comparison chart of the denoising results of the adaptive SSA denoising method, EMD, and wavelet BZ03 station. DETAILED DESCRIPTION

[0031] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0032] In the subsequent description, the suffixes such as "module", "component" or "unit" used to represent elements are only used to facilitate the description of the present invention, and have no specific meanings. Therefore, "module", "component" or "unit" can be used in a mixed manner.

[0033] As a tool for signal decomposition, SSA can decompose GNSS time series into several SSA components, and select several meaningful components for reconstruction to reduce noise, and then the true trend and deformation law of GNSS time series can be discovered.

[0034] SSA principle

[0035] In GNSS time series analysis, SSA is a non-parametric spectral estimation method. This method is gradually developed on the basis of the classical Karhunen-Loeve spectral decomposition and embedding theory, and is a principal component analysis method for one-dimensional time series to perform periodic oscillations.

[0036] SSA includes four parts: embedding, singular value decomposition, grouping, and reconstruction. Let the length of the one-dimensional discrete-time series signal x(n) be N, and the signal vector be x = [x1, x2,..., x N T , where T is the transpose operator. Specifically, it is as follows:

[0037] Embedding (forming the trajectory matrix): The signal vector is evenly divided into several parts with overlap. Define the length of these segments (called the window length) as L, where 1 < L ≤ N / 2. Then the trajectory matrix X (trajectory matrix) can be defined as X = [x1,…, x N-L+1 , that is:

[0038]

[0039] As shown above, the trajectory matrix X is a Hankel matrix.

[0040] Singular value decomposition: Perform singular value decomposition on the trajectory matrix X to obtain:

[0041]

[0042] Among them, λ i is the singular value arranged in descending order, with λ1 ≥ λ2 ≥ … ≥ λ L ≥ 0, and U i , V i are the left and right singular vectors of X respectively.

[0043] Grouping: If noise reduction processing is performed on the original time series, then the grouping operation is to represent the trajectory matrix X constructed by the original sequence x(n) as the sum of the useful signal S and the noise E, that is, X = S + E. In this way, the grouping operation is to determine the appropriate value to achieve signal-noise separation.

[0044] ​Reconstruction: The purpose of reconstruction is to transform the matrix obtained by the above grouping into the required sequence of length N. Let x * u,p is the uth element of the pth one-dimensional SSA component. Let x a,b,p is the a-th row and b-th column element of the p-th group (1≤p≤M) matrix after grouping. Then the grouping matrix can be reconstructed and converted back to a one-dimensional signal. The reconstruction formula is:

[0045]

[0046] Among them, u=1,…,N, p=1,…,M.

[0047] Adaptive SSA noise reduction

[0048] The key step to achieve SSA denoising is to determine the effective rank of the Hankel matrix, that is, the number of effective singular values. In the embodiment of the present application, based on the principal component decomposition method and according to the GNSS timing characteristics, a composite evaluation index T is introduced to obtain an adaptive SSA method, which no longer uses a qualitative analysis method, but a quantitative analysis method to accurately determine the optimal number of reconstruction layers (corresponding to the number of effective singular values), so that SSA has adaptive denoising capabilities.

[0049] Implementation Method 1

[0050] Figure 1 A flowchart of an implementation of the adaptive SSA noise reduction method provided by the present application is shown in FIG. Figure 1 As shown, the adaptive SSA noise reduction method includes steps S102 to S114.

[0051] Step S102: performing an embedding operation on the original GNSS time series data to obtain a trajectory matrix corresponding to the original GNSS time series data.

[0052] Step S104, performing singular value decomposition on the trajectory matrix to obtain a set of singular values.

[0053] Step S106: determine the reconstruction components corresponding to at least some of the singular values ​​to obtain a plurality of reconstruction components.

[0054] Step S108: reconstruct using the multiple reconstruction components to obtain multiple reconstructed signals.

[0055] Step S110, determining the root mean square error and smoothness of each reconstructed signal.

[0056] Step S112, linearly combining the root mean square error and smoothness of each reconstructed signal to obtain a composite evaluation index corresponding to each reconstructed signal.

[0057] Step S114, determining the denoised signal according to the size of the composite evaluation index corresponding to each reconstructed signal.

[0058] In the embodiment of the present application, the smaller the composite evaluation index is, the better the denoising effect is, and the better the corresponding reconstruction layer number is. As an example, in the above step S114, the denoised signal is determined to be the reconstructed signal with the smallest composite evaluation index. It should be understood that the embodiment of the present application is not limited to this.

[0059] In some examples, the above step S112 includes: normalizing the root mean square error and smoothness of each reconstructed signal; weighting the normalized root mean square error and smoothness according to the coefficient of variation method to obtain the weight of the linear combination; and weighting the normalized root mean square error and smoothness of each reconstructed signal according to the weight of the linear combination to obtain the composite evaluation index corresponding to each reconstructed signal. In this way, the proportion of signal detail information and approximation information can be better determined.

[0060] Since the useful signal components in the GNSS time series data often correspond to the reconstruction components of larger singular values, in some embodiments, the above step S106 includes: determining the first k singular values ​​in order from large to small, where k is the maximum number of singular values ​​that terminate the loop; determining the reconstruction components corresponding to the above first k singular values ​​to obtain k reconstruction components. In addition, determining the reconstruction components corresponding to the first k singular values ​​reduces the operation time and reduces data redundancy.

[0061] In some examples, determining the reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components also includes: determining the average value of the above multiple singular values; determining the number k1 of singular values ​​greater than the average value; and determining the maximum number k of singular values ​​for terminating the loop according to the number k1 of singular values ​​greater than the average value. As a result, the denoised signal obtained by the eigenvalue mean method has strong noise robustness and can better retain signal details. The denoising result is achieved in a better proportion of the two negatively correlated indicators of detail information and approximation information.

[0062] In some examples, determining the maximum number of singular values ​​k of the termination loop according to the number k1 of singular values ​​greater than the average value includes: determining the maximum number of singular values ​​k of the termination loop to be twice the number k1 of singular values ​​greater than the average value, that is, k=2k1. A better ratio of the two negatively correlated indicators of detail information and approximation information is achieved in the denoising result.

[0063] In some examples, in the above step S108, the above multiple reconstruction components are used to perform reconstruction in the following manner to obtain multiple reconstructed signals:

[0064]

[0065] Among them, S i represents the i-th reconstructed signal, RC j represents the reconstructed component corresponding to the jth singular value in descending order, 1≤i≤k, where k is the number of reconstructed components.

[0066] Implementation Method 2

[0067] In this embodiment, considering the inaccuracy of using noise evaluation criteria to judge noise in the principal component decomposition method and the complexity of using the Minka Bayesian model selection criteria to determine the maximum number of singular values, combined with the GNSS timing characteristics, the root mean square error and smoothness of the denoised signal, which are two negatively correlated indicators, are normalized, and then the coefficient of variation is used to determine the weights, and the root mean square error and smoothness are linearly combined to obtain a composite evaluation index T. Based on the principal component decomposition idea, the joint index T can directly determine the number of effective singular values ​​q. The smaller T is, the better the denoising effect is, and the better the corresponding reconstruction layer number is, so that the SSA method has adaptive denoising ability.

[0068] This method no longer relies on qualitative analysis, but instead uses quantitative analysis to accurately determine the optimal number of reconstruction layers. Through analysis of simulated data and measured GNSS timing data, it is concluded that its denoising results can achieve the optimal ratio of the two negatively correlated indicators, detail information and approximation information, and can be applied to GNSS timing under complex noise backgrounds.

[0069] Figure 2 A flowchart of another implementation of the adaptive SSA noise reduction method provided in an embodiment of the present application is shown in FIG. Figure 2 As shown, the adaptive SSA noise reduction method includes steps S202 to S214.

[0070] Step S202: perform embedding operation on the original time series x(n) to obtain a trajectory matrix X.

[0071] Specifically, let the original time series x(n) be embedded to obtain the trajectory matrix X:

[0072]

[0073] Among them, the original time series x(n)=[x1,x2,...,x N ] T , T is the transposition operator, N is the length of x(n), L is the length of the segment called the window length, and L=N / 3 is taken, but not limited to this.

[0074] Step S204: Perform singular value decomposition on the trajectory matrix X to obtain a set of singular values ​​λ1,…,λ arranged from large to small Land the left and right singular vectors U of X i 、V i .

[0075] Specifically, the trajectory matrix X is decomposed into singular values:

[0076]

[0077] Among them, λ i are the singular values ​​in descending order, with λ1≥λ2≥…≥λ L ≥ 0. U i 、V i are the left and right singular vectors of X respectively.

[0078] Step S206: Determine singular values ​​λ1,…,λ L The mean of λ1,…,λ L The number of singular values ​​k1 greater than or equal to the mean in the loop is taken as the maximum number of singular values ​​k=2*k1 that terminates the loop.

[0079] Step S208: Determine the reconstructed components RC1, ..., RC corresponding to the first k singular values k .

[0080] Specifically, the reconstruction component RC p The calculation formula is as follows:

[0081]

[0082] in, is the u-th element of the p-th one-dimensional SSA component; x a,b,p is the pth trajectory matrix X after singular value decomposition p The a-th row and b-th column element of ; u=1,…,N; p=1,…,k.

[0083] Step S210: Based on the reconstruction components RC1, ..., RC k Determine the reconstructed signal S1,…,S k .

[0084] in, Among them, S i To reconstruct the signal, 1≤i≤k.

[0085] Step S212, determine the reconstructed signals S1, ..., S k The corresponding composite evaluation index T1,…,T k .

[0086] Specifically, step S212 includes:

[0087] (1) Determine each reconstructed signal Where 1≤i≤k.

[0088] (2) Determine the reconstructed signal S i The root mean square error (RMSE) and smoothness (r) are calculated as follows:

[0089]

[0090]

[0091] Among them, s(n) is the denoised signal (reconstructed signal), and x(n) is the original signal.

[0092] (3) Normalize the RMSE and r indicators.

[0093] in:

[0094]

[0095]

[0096] (4) Use the coefficient of variation method to weight the normalized PRMSE and Pr:

[0097]

[0098]

[0099]

[0100]

[0101] Among them, σ and μ are standard deviation operation and mean operation respectively, CV represents the coefficient of variation, and W is the weight based on the coefficient of variation.

[0102] (5) Determine the reconstructed signal S i Composite evaluation index T i .

[0103] Among them, T i =W PRMSE ×PRMSE+W Pr ×Pr;

[0104] Take i = 1,…,k, and determine S1,…,S k The corresponding composite evaluation index T1,…,T k .

[0105] Step S214, determine T q =min(T1,…,T k )(1≤q≤k),T q The corresponding S qis the useful signal S after final noise reduction.

[0106] By comparing the adaptive SSA denoising results with the EMD and wavelet analysis methods, it is found that the GNSS time series denoising results obtained using adaptive SSA can extract deformation signals from the original time series more effectively and stably than EMD and wavelet.

[0107] Adaptive SSA noise reduction device

[0108] The embodiment of the present application also provides an adaptive SSA noise reduction device. Figure 3 A structural block diagram of an implementation of an adaptive SSA noise reduction device provided in an embodiment of the present application, such as Figure 3 As shown, the adaptive SSA denoising device comprises: an embedding module 310, which is used to perform an embedding operation on the original GNSS time series data to obtain a trajectory matrix corresponding to the original GNSS time series data; a decomposition module 320, which is connected to the embedding module 310, and is used to perform singular value decomposition on the above trajectory matrix to obtain a group of singular values; a first determination module 330, which is connected to the decomposition module 320, and is used to determine the reconstruction components corresponding to at least part of the singular values ​​to obtain multiple reconstruction components; a reconstruction module 340, which is connected to the first determination module 330, and is used to reconstruct the above multiple reconstruction components to obtain multiple reconstructed signals; a second determination module 350, which is connected to the reconstruction module 340, and is used to determine the root mean square error and smoothness of each reconstructed signal; a third determination module 360, which is connected to the second determination module 350, and is used to linearly combine the root mean square error and smoothness of each reconstructed signal to obtain a composite evaluation index corresponding to each reconstructed signal; a fourth determination module 370, which is connected to the third determination module 360, and is used to determine the denoised signal according to the size of the composite evaluation index corresponding to each reconstructed signal.

[0109] In the embodiment of the present application, the smaller the composite evaluation index is, the better the denoising effect is, and the better the corresponding reconstruction layer number is. As an example, the fourth determination module 370 is used to determine that the denoised signal is a reconstructed signal with the smallest composite evaluation index. It should be understood that the embodiment of the present application is not limited to this.

[0110] In some examples, the third determination module 360 ​​is used to normalize the root mean square error and smoothness of each reconstructed signal; weight the normalized root mean square error and smoothness according to the coefficient of variation method to obtain the weight of the linear combination; and weight the normalized root mean square error and smoothness of each reconstructed signal according to the weight of the linear combination to obtain the composite evaluation index corresponding to each reconstructed signal. In this way, the ratio of signal detail information and approximation information can be better determined.

[0111] Since the useful signal components in the GNSS time series data often correspond to the reconstruction components of the larger singular values, in some examples, the first determination module 330 is used to determine the first k singular values ​​in order from large to small, where k is the maximum number of singular values ​​that terminate the loop; determine the reconstruction components corresponding to the first k singular values, and obtain k reconstruction components. In addition, determining the reconstruction components corresponding to the first k singular values ​​reduces the operation time and reduces data redundancy.

[0112] In some examples, the first determination module 330 is further used to determine the average value of the above-mentioned multiple singular values; determine the number k1 of singular values ​​greater than the average value; and determine the maximum number k of singular values ​​for terminating the loop according to the number k1 of singular values ​​greater than the average value. As a result, the noise reduction signal obtained by the eigenvalue mean method has strong noise robustness and can better retain signal details. The noise reduction result is achieved in the two negatively correlated indicators of detail information and approximation information to achieve a better ratio.

[0113] In some examples, the first determination module 330 is used to determine that the maximum number of singular values ​​k of the termination loop is twice the number of singular values ​​k1 greater than the average value, that is, k=2k1. This achieves a better ratio of the two negatively correlated indicators of detail information and approximation information in the denoising result.

[0114] In some examples, the reconstruction module 340 is used to reconstruct using the above-mentioned multiple reconstruction components in the following manner to obtain multiple reconstructed signals:

[0115]

[0116] Among them, S i represents the i-th reconstructed signal, RC j represents the reconstructed component corresponding to the jth singular value in descending order, 1≤i≤k, where k is the number of reconstructed components.

[0117] The embodiment of the present application also provides a computer device. Figure 4 A hardware structure diagram of an implementation of a computer device provided in an embodiment of the present application is shown in FIG. Figure 4 As shown, the computer device 10 of the embodiment of the present application includes: at least including but not limited to: a memory 11 and a processor 12 that can be interconnected through a system bus. It should be noted that Figure 4 Computer device 10 is shown only with components 11 - 12 , but it should be understood that implementing all of the components shown is not a requirement, and more or fewer components may alternatively be implemented.

[0118] In this embodiment, the memory 11 (i.e., a readable storage medium) includes a flash memory, a hard disk, a multimedia card, a card-type memory (e.g., an SD or DX memory, etc.), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the memory 11 may be an internal storage unit of the computer device 10, such as a hard disk or a memory of the computer device 10. In other embodiments, the memory 11 may also be an external storage device of the computer device 10, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card, etc. equipped on the computer device 10. Of course, the memory 11 may also include both the internal storage unit of the computer device 10 and its external storage device. In this embodiment, the memory 11 is generally used to store an operating system and various software installed on the computer device 10. In addition, the memory 11 may also be used to temporarily store various data that have been output or are to be output.

[0119] The processor 12 may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chips in some embodiments. The processor 12 is generally used to control the overall operation of the computer device 10. In this embodiment, the processor 12 is used to run the program code stored in the memory 11 or process data, such as the adaptive SSA noise reduction method.

[0120] This embodiment also provides a computer-readable storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory (for example, an SD or DX memory, etc.), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a disk, an optical disk, a server, an App application store, etc., on which a computer program is stored, and the program is executed by a processor to implement a corresponding function. The computer-readable storage medium of this embodiment is used to store the program code of the adaptive SSA noise reduction method, and the adaptive SSA noise reduction is implemented when it is executed by the processor.

[0121] Analysis of Adaptive SSA Noise Reduction Example

[0122] Simulation data noise reduction analysis

[0123] GNSS time series generally consists of three parts: periodic term, trend term and noise. The simulation data model is constructed, which mainly consists of two periodic signals, a Gaussian white noise with a signal-to-noise ratio of 6dB and a random noise, and a low-frequency trend term is added. The sampling rate is 1s, and a total of 2000 sampling points are set. The expression is:

[0124]

[0125] Among them, wgn is Gaussian white noise and randn is random noise.

[0126] In order to verify the reliability of the adaptive method of this application, traditional evaluation indicators such as signal-to-noise ratio (SNR), root mean square error (RMSE), and smoothness (r) are used to quantitatively illustrate the denoising effect, and compared with the mean method (Wang Y Y. Mean value of eigenvalue-based SVD signal denoising algorithm [J]. Computer Applications and Software, 2012, 29 (05): 121-123 (Ch). Wang Yiyan. SVD signal denoising algorithm based on characteristic mean [J]. Computer Applications and Software, 2012, 29 (05): 121-123.) and FFT method (Qian Zhengwen, Cheng Li, Li Yinghong. Signal denoising method by means of SVD [J]. Journal of Vibration Measurement & Diagnosis, 2011, 31(4): 459-463 (Ch). Qian Zhengwen, Cheng Li, Li Yinghong. Signal denoising method using singular value decomposition [J]. Vibration. Test & Diagnosis, 2011, 31(04): 459-463.) is used for comparison. If the signal-to-noise ratio index of the signal after denoising is higher, the root mean square error and smoothness index are smaller, it means that the denoising effect is better.

[0127] like Figure 5 As shown in the figure, from top to bottom are: the original signal ("original signal" in the figure), the noisy signal ("noise signal" in the figure), the denoising results using the adaptive SSA denoising method ("self-adaption" in the figure), the mean method ("Mean" in the figure), and the FFT method ("FFT" in the figure), refer to Figure 5 As shown in the figure, all three methods can effectively remove noise, but the mean method does not eliminate noise completely; the FFT method fails to effectively retain the low-frequency trend term and there is an over-denoising phenomenon, which causes the result to deviate greatly from the original noise-free signal when the sampling point increases.

[0128] like Figure 6 As shown in the figure, the adaptive SSA denoising method is used to calculate the composite evaluation index T corresponding to each reconstruction layer of the analog signal. Figure 5 As shown in Figure 2, when the number of reconstruction layers is 5, the T value is the smallest, that is, the optimal number of reconstruction layers is 5.

[0129] In order to quantitatively illustrate the effectiveness of the adaptive method, the signal-to-noise ratio (SNR), root mean square error (RMSE), and smoothness (r) are used for quantitative analysis. As can be seen from Table 1, the r values ​​after denoising by the three methods are all small, indicating that the overall trend characteristics of the denoising results of the three methods are obvious. Among them, the adaptive method makes the best proportion distribution between RMSE and r value. Although the smoothness r is slightly larger than that of the FFT method, the RMSE is smaller than that of the FFT method, and the SNR value obtained by the adaptive method is the largest. All of the above show that the adaptive method is more superior.

[0130] Table 1. Quantitative analysis of the denoising results of simulated data using three methods

[0131] Denoising methods SNR RMSE r Adaptive SSA 24.163 0.189 0.000491 Mean method 15.730 0.498 0.0511 FFT Method 14.597 0.568 0.000489

[0132] GNSS elevation time series noise reduction analysis

[0133] Compared with simulation data, GNSS time series are often more complex in composition, and simulation data alone is not enough to explain the advantages and disadvantages of each method. In this paper, the TRACK module in the GAMIT software package and the IGU ephemeris are used to obtain two sets of measured data for comparative analysis: the elevation time series of the Swiss ZIMM station and the elevation time series of the BZ03 station in the measured deformation zone.

[0134] like Figure 7 As shown in the figure, from top to bottom, they are: the original time series, the adaptive SSA denoising results, the mean denoising results, and the composite evaluation index T value corresponding to each reconstruction layer of the adaptive SSA denoising method. When the FFT method is applied to this data, there are too many extreme points in the fast Fourier transform result, making it difficult to distinguish the main frequency, and the method fails. Figure 7 As shown, it can be seen that the adaptive SSA denoising method has better denoising effect and can better remove impulse noise.

[0135] like Figure 8As shown, from top to bottom are the denoising results of the BZ03 station: the original time series, adaptive SSA denoising, and the mean method, as well as the composite evaluation index T value corresponding to each reconstruction layer number of the adaptive SSA denoising. Among them, the number of reconstruction layers obtained by the FFT method is the same as that of the adaptive method of this application. It is worth noting that the first singular value λ1 of the trajectory matrix X of the BZ03 station obtained by SSA decomposition accounts for 92.8% of the sum of all singular values, and the sum of the first two singular values ​​accounts for 94.3% of the sum of all singular values. The number of reconstruction layers obtained by the method of this application and the FFT method is 2 layers, and the number of reconstruction layers obtained by the mean method is 4 layers. Table 2 shows the RMSE and r values ​​of the denoised data of the two stations obtained by the adaptive SSA denoising method of this application and the mean method. It can be seen that the adaptive SSA denoising method of this application makes the best proportional distribution between RMSE and r value, and the denoising result is more reliable.

[0136] Table 2. Quantitative analysis of station denoising results using two methods

[0137]

[0138] In order to fully illustrate the superiority of the SSA method in GNSS deformation monitoring data processing, Fig. 9 The comparison of the denoising results of time series using adaptive SSA, EMD, and small wavelet variable data is given. From top to bottom, the denoising results obtained by adaptive SSA, EMD, and wavelet are compared with the original time series of BZ03 station. The EMD result uses the mutual correlation coefficient method to determine the decomposed modal component IMF k , considering that the BZ03 station is a continuous monitoring data, the boundary layer IMF k The wavelet denoising adopts heuristic threshold and soft threshold function, and uses Debauchies wavelet (N=10 order vanishing moment). Fig. 9 It can be seen that the results obtained by using the proposed method can more effectively and stably extract deformation signals from the monitoring time series compared with EMD and wavelet.

[0139] This paper makes further improvements on the principal component decomposition method, normalizes the root mean square error and smoothness of the denoised signal, and obtains a composite evaluation index T. The number of reconstruction layers is determined according to the index T, so that the SSA method has adaptive denoising capabilities. The adaptive denoising method is compared with existing research using simulated data and measured GNSS time series. The results show that the adaptive SSA method has the following three characteristics: ① Instead of using qualitative analysis methods, quantitative analysis methods are used to accurately determine the optimal number of reconstruction layers; ② The denoising results can achieve the best ratio of the two negatively correlated indicators of detail information and approximation information; ③ Under complex noise backgrounds, when the signal is contaminated by both Gaussian noise and impulse noise, the measured results show that the GNSS time series denoising effect using the adaptive SSA method is obvious.

[0140] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0141] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0142] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, a magnetic disk, or an optical disk), and includes a number of instructions for enabling a terminal (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

[0143] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. An adaptive singular spectrum analysis (SSA) denoising method, characterized in that: include: Performing an embedding operation on the original time series data of the global navigation satellite system (GNSS) to obtain a trajectory matrix corresponding to the original time series data of the GNSS; Performing singular value decomposition on the trajectory matrix to obtain a set of singular values; Determine reconstruction components corresponding to at least some of the singular values ​​to obtain a plurality of reconstruction components; Reconstructing using the multiple reconstruction components to obtain multiple reconstructed signals; determining the root mean square error and smoothness of each reconstructed signal; The root mean square error and smoothness of each reconstructed signal are linearly combined to obtain a composite evaluation index corresponding to each reconstructed signal; Determine the signal after denoising according to the size of the composite evaluation index corresponding to each reconstructed signal; The root mean square error and smoothness of each reconstructed signal are linearly combined to obtain the composite evaluation index corresponding to each reconstructed signal, including: Normalize the root mean square error and smoothness of each reconstructed signal; The normalized root mean square error and smoothness are weighted according to the coefficient of variation method to obtain the weight of the linear combination; According to the weight of the linear combination, the normalized root mean square error and smoothness of each reconstructed signal are weighted to obtain a composite evaluation index corresponding to each reconstructed signal.

2. The adaptive SSA denoising method according to claim 1, characterized in that: The signal after noise reduction is determined according to the size of the composite evaluation index corresponding to each reconstructed signal, including: determining the signal after noise reduction to be the reconstructed signal with the smallest composite evaluation index.

3. The adaptive SSA denoising method according to claim 1, characterized in that: Determine reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components, including: Determine the first k singular values ​​in descending order, where k is the maximum number of singular values ​​that terminate the loop; Determine the reconstruction components corresponding to the first k singular values ​​to obtain k reconstruction components.

4. The adaptive SSA denoising method according to claim 3, characterized in that: Determining reconstruction components corresponding to at least some of the singular values ​​to obtain a plurality of reconstruction components also includes: determining an average value of the portion of singular values; determining the number k1 of singular values ​​greater than the mean; The maximum number k of singular values ​​for terminating the loop is determined according to the number k1 of singular values ​​greater than the average value.

5. The adaptive SSA denoising method according to claim 4, characterized in that: Determining the maximum number k of singular values ​​of the termination loop according to the number k1 of singular values ​​greater than the average value includes: determining the maximum number k of singular values ​​of the termination loop to be twice the number k1 of singular values ​​greater than the average value.

6. The adaptive SSA denoising method according to claim 1, characterized in that: Reconstruction is performed using the multiple reconstruction components in the following manner to obtain multiple reconstructed signals: Among them, S i represents the i-th reconstructed signal, RC j represents the reconstructed component corresponding to the jth singular value in descending order, 1≤i≤k, where k is the number of reconstructed components.

7. An adaptive singular spectrum analysis (SSA) noise reduction device, characterized in that: include: An embedding module, used for performing an embedding operation on the original time series data of the global navigation satellite system GNSS to obtain a trajectory matrix corresponding to the original time series data of the GNSS; A decomposition module, used for performing singular value decomposition on the trajectory matrix to obtain a set of singular values; A first determination module is used to determine reconstruction components corresponding to at least some of the singular values ​​to obtain multiple reconstruction components; A reconstruction module, used for performing reconstruction using the multiple reconstruction components to obtain multiple reconstructed signals; A second determination module is used to determine the root mean square error and smoothness of each reconstructed signal; The third determination module is used to linearly combine the root mean square error and smoothness of each reconstructed signal to obtain a composite evaluation index corresponding to each reconstructed signal, including: normalizing the root mean square error and smoothness of each reconstructed signal; weighting the normalized root mean square error and smoothness according to the coefficient of variation method to obtain the weight of the linear combination; weighting the normalized root mean square error and smoothness of each reconstructed signal according to the weight of the linear combination to obtain the composite evaluation index corresponding to each reconstructed signal; The fourth determination module is used to determine the denoised signal according to the size of the composite evaluation index corresponding to each reconstructed signal.

8. A computer device, characterized in that: The computer device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor; When the computer program is executed by the processor, the steps of the adaptive SSA denoising method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores an adaptive SSA noise reduction program, which, when executed by a processor, implements the steps of the adaptive SSA noise reduction method according to any one of claims 1 to 6.

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