A GNSS coordinate series smoothing method and system based on least squares spectral analysis

Abstract

The application provides a GNSS coordinate sequence smoothing method and system based on least square spectrum analysis, and relates to the technical field of coordinate time sequence denoising, and comprises the following steps: acquiring and storing historical GNSS positioning coordinates and real-time GNSS positioning coordinates of a monitoring station; establishing a Gaussian model according to the historical GNSS positioning coordinates and the real-time GNSS positioning coordinates; performing preliminary smoothing on the real-time GNSS positioning coordinates by using the Gaussian model to obtain preliminary smoothed real-time GNSS positioning coordinates; and performing secondary smoothing processing on the preliminary smoothed real-time GNSS positioning coordinates by using a least square spectrum analysis method to obtain final smoothed real-time GNSS positioning coordinates. The application combines Gaussian model smoothing and least square spectrum analysis, can effectively eliminate high-frequency noise, outliers and periodic errors in the GNSS coordinate sequence in real time, and thus obtains clearer and more accurate GNSS coordinate sequences.

Description

Technical Field

[0001] This invention relates to the field of coordinate time series denoising technology, and in particular to a GNSS coordinate series smoothing method and system based on least squares spectral analysis. Background Technology

[0002] In the field of deformation monitoring, it is necessary to analyze GNSS coordinate time series to monitor the deformation of target points. However, due to multipath effects and GNSS observation noise, the accuracy of GNSS monitoring is limited. To obtain smoother and more accurate GNSS coordinate sequences for better monitoring and analysis of target point deformation, it is necessary to reasonably reduce the impact of multipath effects on the coordinate sequences. Existing research mainly uses methods such as mode decomposition, wavelet transform, harmonic function model fitting, and sidereal filtering for analysis. Among them, mode decomposition and wavelet transform mainly decompose the signal, process each decomposed component, and finally reconstruct a new time series. They mainly deal with high-frequency noise, while low-frequency noise is the main factor affecting the accuracy of GNSS monitoring. Traditional harmonic function model fitting constructs a coordinate time series model and uses the maximum likelihood method for fitting; however, it is only suitable for post-event modeling and analysis and cannot meet the needs of real-time monitoring. Summary of the Invention

[0003] To overcome the limitations of real-time analysis and insufficient smoothing accuracy mentioned above, this invention provides a GNSS coordinate sequence smoothing method and system based on least squares spectral analysis.

[0004] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: This invention provides a GNSS coordinate sequence smoothing method based on least squares spectral analysis, comprising: Acquire and store historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model is established based on the historical GNSS positioning coordinates; The real-time GNSS positioning coordinates are smoothed and preprocessed using the Gaussian model to obtain the preprocessed real-time GNSS positioning coordinates. Based on the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates, an updated Gaussian model is established; Using the updated Gaussian model, the real-time GNSS positioning coordinates are initially smoothed to obtain initially smoothed real-time GNSS positioning coordinates; The preliminary smoothed real-time GNSS positioning coordinates are then subjected to a second smoothing process using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

[0005] Preferably, establishing a Gaussian model based on the historical GNSS positioning coordinates includes: After storing the historical GNSS positioning coordinates in chronological order into the first preset template length, the first template window data is obtained; Outlier handling was performed on the first template window data using the quartile method and z-fraction method, resulting in the processed first template window data: (1) in, The z-score statistic is... Represents coordinate data values. This represents the mean of a time series statistical analysis. The standard deviation of time series statistics The coefficient term for the z-score threshold. and These are the lower and upper quartiles of the time series. Interquartile range, The threshold coefficient for the quartile method; A Gaussian model is established based on the processed first template window data: (2) in, Components representing GNSS coordinates and These represent the standard deviation and mean of the processed data in the first template window, respectively. Pi Represents the natural constant.

[0006] Preferably, the real-time GNSS positioning coordinates are subjected to Gaussian model weighted smoothing using the Gaussian model to obtain preprocessed real-time GNSS positioning coordinates, including: The real-time GNSS positioning coordinates are filtered for outliers using the quartile method and z-fraction method to obtain the filtered real-time GNSS positioning coordinates. The filtered real-time GNSS positioning coordinates are then subjected to Gaussian model weighted smoothing to obtain preprocessed real-time GNSS positioning coordinates. The expression for the Gaussian model weighted smoothing is as follows: (3) in, Indicates the first before smoothing GNSS coordinates, , It is a Gaussian model. The preprocessed real-time GNSS positioning coordinates.

[0007] Preferably, an updated Gaussian model is established based on the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates, including: After storing the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates in chronological order into the second preset template length, the second template window data is obtained; Outlier processing is performed on the second template window data based on the quartile method and z-fraction method to obtain the processed second template window data; An updated Gaussian model is built based on the processed second template window data.

[0008] Preferably, the initially smoothed real-time GNSS positioning coordinates are subjected to a second smoothing process using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates, including: Once the initially smoothed real-time GNSS positioning coordinates meet the third preset template length, a fitting model is constructed for the initially smoothed real-time GNSS positioning coordinates. Solve for each frequency of the fitted model to construct a least-squares solution model. The parameters of the least squares solution model are solved using the least squares method, and then the estimated value of the fitted model is obtained. Based on the frequency analysis of the preliminarily smoothed real-time GNSS positioning coordinates using the fitted model estimates, significant periodic terms are searched and removed to obtain the final real-time GNSS positioning coordinates.

[0009] Preferably, after the initially smoothed real-time GNSS positioning coordinates meet the third preset template length, a fitting model is constructed for the initially smoothed real-time GNSS positioning coordinates, including: The fitting model is as follows: (4) (5) in, This represents a set of frequency spectra that cover all periods of the analyzed data. Indicates the corresponding frequency number. Indicates the corresponding frequency. Indicates frequency as The fitting trigonometric function at time; , Indicates frequency as The parameters to be estimated at that time; A time vector representing the data, containing the time corresponding to each data point. , This indicates the preset length.

[0010] Preferably, the least squares solution model is constructed by solving for each frequency of the fitted model, including: For each frequency Solve for the parameters to be estimated separately, and iteratively construct the least squares solution model: (6) (7) (8) (9) in, This represents the fitted residual vector at this point. Represents the coefficient matrix. Represents the vector of parameters to be estimated. This represents the time series of real-time GNSS data after initial smoothing.

[0011] Preferably, the least squares method is used to solve for the parameters of the least squares solution model, thereby obtaining the estimated value of the fitted model, including: The frequency can be obtained using the least squares method. The parameter vector to be estimated at time for: (10) in, The variance matrix representing the time series; Indicates matrix transpose; Based on the solved parameters to be estimated To obtain the fitted model Estimated value.

[0012] Preferably, based on the frequency analysis of the initially smoothed real-time GNSS positioning coordinates using the fitted model estimates, significant periodic terms are searched and removed to obtain the final real-time GNSS positioning coordinates, including: Using the fitting model Estimates for each frequency Analysis shows that: (11) according to The search is performed on statistically significant frequencies, with the following search criteria: (12) in, Indicates degrees of freedom. Indicates having and 2 degrees of freedom with a significance level of The critical value of the F-distribution; Calculate and verify the corresponding frequency in a loop. Then, periodic signals that meet the conditions are removed to obtain the final smooth real-time GNSS positioning coordinates.

[0013] This invention also provides a GNSS coordinate sequence smoothing system based on least squares spectral analysis, comprising: The coordinate acquisition module is used to acquire and store the historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model construction module is used to build a Gaussian model based on the historical GNSS positioning coordinates; The preliminary smoothing module is used to perform preliminary smoothing on the real-time GNSS positioning coordinates using the Gaussian model to obtain the preliminary smoothed real-time GNSS positioning coordinates. The Gaussian model update module is used to establish an updated Gaussian model based on the historical GNSS positioning coordinates and the initially smoothed real-time GNSS positioning coordinates. The secondary smoothing module is used to perform secondary smoothing on the initially smoothed real-time GNSS positioning coordinates using the updated Gaussian model, so as to obtain the secondary smoothed real-time GNSS positioning coordinates. The final smoothing module is used to perform a third smoothing process on the second-smoothed real-time GNSS positioning coordinates using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

[0014] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention combines Gaussian model smoothing and least squares spectral analysis to eliminate high-frequency noise, outliers, and periodic errors in GNSS coordinate sequences in real time and effectively, thereby obtaining clearer and more accurate GNSS coordinate sequences. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a GNSS coordinate sequence smoothing method based on least squares spectral analysis in Example 1. Figure 2 This is a schematic diagram of the structure of a GNSS coordinate sequence smoothing system based on least squares spectral analysis in Example 3. Detailed Implementation

[0016] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions; It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] Example 1 This embodiment provides a GNSS coordinate sequence smoothing method based on least squares spectral analysis, such as... Figure 1 As shown, it includes: Acquire and store historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model is established based on the historical GNSS positioning coordinates; The real-time GNSS positioning coordinates are smoothed and preprocessed using the Gaussian model to obtain the preprocessed real-time GNSS positioning coordinates. Based on the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates, an updated Gaussian model is established; Using the updated Gaussian model, the real-time GNSS positioning coordinates are initially smoothed to obtain initially smoothed real-time GNSS positioning coordinates; The preliminary smoothed real-time GNSS positioning coordinates are then subjected to a second smoothing process using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

[0019] In the specific implementation process, firstly, historical and real-time GNSS positioning coordinates of the monitoring station are acquired and stored; then, a Gaussian model is established based on the historical GNSS positioning coordinates; next, the real-time GNSS positioning coordinates are smoothed using the Gaussian model to obtain pre-processed real-time GNSS positioning coordinates; subsequently, an updated Gaussian model is established based on the historical and pre-processed real-time GNSS positioning coordinates; the real-time GNSS positioning coordinates are initially smoothed using the updated Gaussian model to obtain initially smoothed real-time GNSS positioning coordinates; finally, the initially smoothed real-time GNSS positioning coordinates are further smoothed using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

[0020] This invention employs a two-step smoothing strategy to process GNSS coordinate sequences: First, a Gaussian model is used for preliminary smoothing, effectively suppressing most high-frequency noise; then, based on this, least squares spectral analysis is used for secondary fine smoothing, further eliminating residual outliers and periodic errors in the sequence, thereby obtaining a clearer and more accurate coordinate sequence.

[0021] Example 2 This embodiment provides a sensor deployment and protection method based on network locality, including: Acquire and store historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model is established based on the historical GNSS positioning coordinates; The real-time GNSS positioning coordinates are smoothed and preprocessed using the Gaussian model to obtain the preprocessed real-time GNSS positioning coordinates. Based on the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates, an updated Gaussian model is established; Using the updated Gaussian model, the real-time GNSS positioning coordinates are initially smoothed to obtain initially smoothed real-time GNSS positioning coordinates; The preliminary smoothed real-time GNSS positioning coordinates are then subjected to a second smoothing process using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

[0022] It should be noted that, in this embodiment, establishing a Gaussian model based on the historical GNSS positioning coordinates includes: After storing the historical GNSS positioning coordinates in chronological order into the first preset template length, the first template window data is obtained; the reference coordinates of the monitoring points are analyzed from the first template window data and used as a reference benchmark for deformation monitoring variables to calculate the initial and final deformation differences.

[0023] Outlier handling was performed on the first template window data using the quartile method and z-fraction method, resulting in the processed first template window data: (1) in, The z-score statistic is... Represents coordinate data values. This represents the mean of a time series statistical analysis. The standard deviation of time series statistics The coefficient term for the z-score threshold. and These are the lower and upper quartiles of the time series. Interquartile range, The threshold coefficient for the quartile method; If a large number of outliers are removed, the data in the first template window is supplemented by extrapolation based on historical data. Since the first template window contains a sufficient amount of data, the data can be considered to follow a normal distribution.

[0024] A Gaussian model is established based on the processed first template window data: (2) in, Components representing GNSS coordinates and These represent the standard deviation and mean of the processed data in the first template window, respectively. Pi Represents the natural constant.

[0025] It should be noted that, in this embodiment, the real-time GNSS positioning coordinates are subjected to Gaussian model weighted smoothing using the Gaussian model to obtain preprocessed real-time GNSS positioning coordinates, including: The real-time GNSS positioning coordinates are filtered for outliers using the quartile method and z-fraction method to obtain the filtered real-time GNSS positioning coordinates. The filtered real-time GNSS positioning coordinates are then subjected to Gaussian model weighted smoothing to obtain preprocessed real-time GNSS positioning coordinates. The expression for the Gaussian model weighted smoothing is as follows: (3) in, Indicates the first before smoothing GNSS coordinates, , It is a Gaussian model. The preprocessed real-time GNSS positioning coordinates.

[0026] It should be noted that, in this embodiment, an updated Gaussian model is established based on the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates, including: After storing the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates in chronological order into the second preset template length, the second template window data is obtained; Outlier processing is performed on the second template window data based on the quartile method and z-fraction method to obtain the processed second template window data; An updated Gaussian model is built based on the processed second template window data.

[0027] It should be noted that, in this embodiment, the initially smoothed real-time GNSS positioning coordinates are subjected to a second smoothing process using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates, including: Once the initially smoothed real-time GNSS positioning coordinates meet the third preset template length, a fitting model is constructed for the initially smoothed real-time GNSS positioning coordinates. Solve for each frequency of the fitted model to construct a least-squares solution model. The parameters of the least squares solution model are solved using the least squares method, and then the estimated value of the fitted model is obtained. Based on the frequency analysis of the preliminarily smoothed real-time GNSS positioning coordinates using the fitted model estimates, significant periodic terms are searched and removed to obtain the final real-time GNSS positioning coordinates.

[0028] For example, real-time GNSS coordinate data with a 5-second interval, after being smoothed by weighted moving average using an updated Gaussian model, yields a smoothed result with a 5-minute interval. This effectively smooths high-frequency noise, eliminates the influence of outliers, and preserves the actual characteristics of the GNSS coordinate sequence, ensuring real-time performance.

[0029] It should be noted that, in this embodiment, after the initially smoothed real-time GNSS positioning coordinates meet the third preset template length, a fitting model is constructed for the initially smoothed real-time GNSS positioning coordinates, including: The fitting model is as follows: (4) (5) in, This represents a set of frequency spectra that cover all periods of the analyzed data. Indicates the corresponding frequency number. Indicates the corresponding frequency. Indicates frequency as The fitting trigonometric function at time; , Indicates frequency as The parameters to be estimated at that time; A time vector representing the data, containing the time corresponding to each data point. , This indicates the preset length.

[0030] It should be noted that in this embodiment, the least squares solution model is constructed by solving for each frequency of the fitted model, including: For each frequency Solve for the parameters to be estimated separately, and iteratively construct the least squares solution model: (6) (7) (8) (9) in, This represents the fitted residual vector at this point. Represents the coefficient matrix. Represents the vector of parameters to be estimated. This represents the time series of real-time GNSS data after initial smoothing.

[0031] It should be noted that, in this embodiment, the least squares method is used to solve for the parameters of the least squares solution model, thereby obtaining the estimated value of the fitted model, including: Least squares spectral analysis is a high-precision frequency estimation technique. Based on the least squares criterion, it fits a series of trigonometric functions to a discrete data sequence to identify statistically significant frequency components, thereby obtaining an accurate signal spectrum.

[0032] The frequency can be obtained using the least squares method. The parameter vector to be estimated at time for: (10) in, The variance matrix representing the time series; Indicates matrix transpose; Based on the solved parameters to be estimated To obtain the fitted model Estimated value.

[0033] It should be noted that, in this embodiment, based on the frequency analysis of the initially smoothed real-time GNSS positioning coordinates using the fitted model estimates, significant periodic terms are searched and removed to obtain the final real-time GNSS positioning coordinates, including: Using the fitting model Estimates for each frequency Analysis shows that: (11) according to The search is performed on statistically significant frequencies, with the following search criteria: (12) in, Indicates degrees of freedom. Indicates having and 2 degrees of freedom with a significance level of The critical value of the F-distribution; Calculate and verify the corresponding frequency in a loop. Then, periodic signals that meet the conditions are removed to obtain the final smooth real-time GNSS positioning coordinates.

[0034] Example 3 This embodiment provides a GNSS coordinate sequence smoothing system based on least squares spectral analysis, used to implement the GNSS coordinate sequence smoothing method based on least squares spectral analysis described in Embodiment 1 or 2, such as... Figure 2 As shown, it includes: The coordinate acquisition module is used to acquire and store the historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model construction module is used to build a Gaussian model based on the historical GNSS positioning coordinates; The preliminary smoothing module is used to perform preliminary smoothing on the real-time GNSS positioning coordinates using the Gaussian model to obtain the preliminary smoothed real-time GNSS positioning coordinates. The Gaussian model update module is used to establish an updated Gaussian model based on the historical GNSS positioning coordinates and the initially smoothed real-time GNSS positioning coordinates. The secondary smoothing module is used to perform secondary smoothing on the initially smoothed real-time GNSS positioning coordinates using the updated Gaussian model, so as to obtain the secondary smoothed real-time GNSS positioning coordinates. The final smoothing module is used to perform a third smoothing process on the second-smoothed real-time GNSS positioning coordinates using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

[0035] The same or similar labels correspond to the same or similar parts; The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A GNSS coordinate sequence smoothing method based on least squares spectral analysis, characterized in that, include: Acquire and store historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model is established based on the historical GNSS positioning coordinates, including: After storing the historical GNSS positioning coordinates in chronological order into the first preset template length, the first template window data is obtained; Outlier filtering is performed on the first template window data using the quartile method and z-fraction method to obtain the processed first template window data: The expressions for the quartile method and the z-fraction method are as follows: (1) in, The z-score statistic is... Represents coordinate data values. This represents the mean of a time series statistical analysis. The standard deviation of time series statistics The coefficient term for the z-score threshold. and These are the lower and upper quartiles of the time series. Interquartile range, The threshold coefficient for the quartile method; A Gaussian model is established based on the processed first template window data: (2) in, Components representing GNSS coordinates and These represent the standard deviation and mean of the processed data in the first template window, respectively. Pi Represents the natural constant; The real-time GNSS positioning coordinates are subjected to Gaussian model weighted smoothing using the Gaussian model to obtain preprocessed real-time GNSS positioning coordinates. Based on the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates, an updated Gaussian model is established, including: After storing the historical GNSS positioning coordinates and the preprocessed real-time GNSS positioning coordinates in chronological order into the second preset template length, the second template window data is obtained; Outlier processing is performed on the second template window data based on the quartile method and z-fraction method to obtain the processed second template window data; An updated Gaussian model is established based on the processed second template window data; Using the updated Gaussian model, the real-time GNSS positioning coordinates are initially smoothed to obtain initially smoothed real-time GNSS positioning coordinates; The initially smoothed real-time GNSS positioning coordinates are then subjected to a second smoothing process using least squares spectral analysis to obtain the final smoothed real-time GNSS positioning coordinates, including: Once the initially smoothed real-time GNSS positioning coordinates meet the third preset template length, a fitting model is constructed for the initially smoothed real-time GNSS positioning coordinates, including: The fitting model is as follows: (4) (5) in, This represents a set of frequency spectra that cover all periods of the analyzed data. Indicates the corresponding frequency number. Indicates the corresponding frequency. Indicates frequency as The fitting trigonometric function at time; , Indicates frequency as The parameters to be estimated at that time; A time vector representing the data, containing the time corresponding to each data point. , Indicates the preset length; Solve for each frequency of the fitted model to construct a least-squares solution model. The parameters of the least squares solution model are solved using the least squares method, and then the estimated value of the fitted model is obtained. Based on the frequency analysis of the preliminarily smoothed real-time GNSS positioning coordinates using the fitted model estimates, significant periodic terms are searched and removed to obtain the final real-time GNSS positioning coordinates.

2. The GNSS coordinate sequence smoothing method based on least squares spectral analysis according to claim 1, characterized in that, The real-time GNSS positioning coordinates are subjected to Gaussian model weighted smoothing using the Gaussian model to obtain preprocessed real-time GNSS positioning coordinates, including: The real-time GNSS positioning coordinates are filtered for outliers using the quartile method and z-fraction method to obtain the filtered real-time GNSS positioning coordinates. The filtered real-time GNSS positioning coordinates are then subjected to Gaussian model weighted smoothing to obtain preprocessed real-time GNSS positioning coordinates. The expression for the Gaussian model weighted smoothing is as follows: (3) in, Indicates the first before smoothing GNSS coordinates, , It is a Gaussian model. The preprocessed real-time GNSS positioning coordinates.

3. The GNSS coordinate sequence smoothing method based on least squares spectral analysis according to claim 1, characterized in that, Solve for each frequency of the fitted model to construct a least-squares solution model, including: For each frequency Solve for the parameters to be estimated separately, and iteratively construct the least squares solution model: (6) (7) (8) (9) in, This represents the fitted residual vector at this point. Represents the coefficient matrix. Represents the vector of parameters to be estimated. This represents the time series of real-time GNSS data after initial smoothing.

4. The GNSS coordinate sequence smoothing method based on least squares spectral analysis according to claim 1, characterized in that, The parameters of the least squares solution model are solved using the least squares method, thereby obtaining the estimated values ​​of the fitted model, including: The frequency can be obtained using the least squares method. The parameter vector to be estimated at time for: (10) in, The variance matrix representing the time series; Indicates matrix transpose; Based on the solved parameters to be estimated To obtain the fitted model Estimated value.

5. A GNSS coordinate sequence smoothing method based on least squares spectral analysis according to claim 1, characterized in that, Based on the frequency analysis of the initially smoothed real-time GNSS positioning coordinates using the fitted model estimates, significant periodic terms are searched for and removed to obtain the final real-time GNSS positioning coordinates, including: Using the fitting model Estimates for each frequency Analysis shows that: (11) according to The search is performed on statistically significant frequencies, with the following search criteria: (12) in, Indicates degrees of freedom. Indicates having and 2 degrees of freedom with a significance level of The critical value of the F-distribution; Calculate and verify the corresponding frequency in a loop. Then, periodic signals that meet the conditions are removed to obtain the final smooth real-time GNSS positioning coordinates.

6. A GNSS coordinate sequence smoothing system based on least squares spectral analysis, used to implement the GNSS coordinate sequence smoothing method based on least squares spectral analysis according to any one of claims 1-5, characterized in that, include: The coordinate acquisition module is used to acquire and store the historical and real-time GNSS positioning coordinates of the monitoring station; A Gaussian model construction module is used to build a Gaussian model based on the historical GNSS positioning coordinates; The preliminary smoothing module is used to perform preliminary smoothing on the real-time GNSS positioning coordinates using the Gaussian model to obtain the preliminary smoothed real-time GNSS positioning coordinates. The Gaussian model update module is used to establish an updated Gaussian model based on the historical GNSS positioning coordinates and the initially smoothed real-time GNSS positioning coordinates. The secondary smoothing module is used to perform secondary smoothing on the initially smoothed real-time GNSS positioning coordinates using the updated Gaussian model, so as to obtain the secondary smoothed real-time GNSS positioning coordinates. The final smoothing module is used to perform a third smoothing process on the second-smoothed real-time GNSS positioning coordinates using the least squares spectral analysis method to obtain the final smoothed real-time GNSS positioning coordinates.

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