A feature decomposition-based unsupervised learning method for identifying multipath signals in GNSS complex mountainous landslide monitoring

Abstract

The present application belongs to the technical field of satellite navigation and signal recognition, and particularly relates to a kind of GNSS complex mountainous area landslide monitoring multipath signal unsupervised learning identification method based on feature decomposition, the present application studies the signal-to-noise ratio of station, elevation angle, azimuth angle, double difference residual as characteristic value, and carries out feature decomposition, then utilizes K-means++ algorithm to carry out cluster analysis, by calculating the profile coefficient of cluster result, identification accuracy, the average value data of absolute value of multipath error of each cluster, based on this, the satellite data greatly influenced by multipath signal is eliminated, and then GNSS positioning calculation is carried out using the satellite data after elimination.The present application introduces the data processing method of feature decomposition, combines unsupervised learning K-means++ clustering algorithm, accurately identifies the multipath error in GNSS signal, the satellite data influenced by multipath error can be effectively eliminated by the method of the present application, the efficiency of multipath signal recognition is improved, and the GNSS positioning precision is significantly improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite navigation and signal recognition, and particularly relates to a GNSS complex mountainous area landslide monitoring multi-path signal unsupervised learning recognition method based on feature decomposition. BACKGROUND

[0002] Mountain landslide is one of the main types of geological disasters in the world, and the selection of monitoring methods and instruments is determined by different landslide types, geological characteristics, surrounding environment and inducing factors. Global navigation satellite system (GNSS) has become one of the most widely used technologies in three-dimensional deformation monitoring of landslide surface due to its advantages of wide coverage, all-weather operation, continuous monitoring and real-time feedback. In particular, the real-time dynamic relative positioning technology based on short baseline is widely used in three-dimensional deformation monitoring of the surface due to its rapid, efficient and real-time high-precision positioning capability. However, the observation environment of GNSS receiver installed in the mountain with potential landslide risk is usually poor, including the existence of surrounding mountains and various vegetation, and GNSS satellite signals often suffer from serious reflection, refraction and diffraction effects, resulting in large multi-path errors, which seriously affects the accuracy and reliability of the monitoring results.

[0003] In recent years, unsupervised classification algorithm has become one of the main methods for processing GNSS multi-path error recognition due to its high automation and environmental and data adaptability. In the unsupervised classification algorithm, the selection of eigenvalues is the key to determine the clustering effect. Since the dimensions and distributions of each eigenvalue are different, direct classification will affect the classification accuracy, so it is necessary to uniformly process the dimensions and distributions of each eigenvalue. The conventional processing method is to normalize each eigenvalue, but simple normalization ignores the correlation information between samples, and in addition, this method is easily affected by sample gross errors and has poor robustness. Such linear transformation only realizes the consistency of numerical range of each dimension, but ignores the potential coupling relationship between features. Simple normalization is highly sensitive to outliers, and when gross error samples cause the extreme value of a certain feature dimension to deviate, the normalization parameter will shift significantly, thereby distorting the overall feature distribution and causing large clustering center deviation error. Such defects make the robustness of the traditional method difficult to meet the data processing requirements of long time series and multiple interference sources in landslide monitoring scenarios. Therefore, it is urgent to research a technology for recognizing multi-path signals in complex mountainous area landslide monitoring. SUMMARY

[0004] To address the poor robustness of traditional multipath signal identification and processing methods, this invention aims to propose an unsupervised learning method for identifying multipath signals in GNSS landslide monitoring in complex mountainous areas. By selecting feature values, introducing feature decomposition data processing methods, and combining unsupervised learning K-means++ clustering algorithm, this method accurately identifies multipath errors in GNSS signals, effectively eliminates satellite data affected by multipath, and significantly improves ambiguity fixation rate and GNSS positioning accuracy.

[0005] Based on the above objectives, the technical solution adopted by the present invention is as follows:

[0006] In a first aspect, the present invention provides an unsupervised learning and recognition method for multipath signals in GNSS landslide monitoring in complex mountainous areas based on feature decomposition, comprising the following steps:

[0007] S1. Extract the signal-to-noise ratio, elevation angle, azimuth angle, and double-difference residual of the research station as feature values;

[0008] S2. Perform feature decomposition on the feature values ​​extracted in step S1 to obtain the scaled dataset;

[0009] S3. Cluster the scaled dataset from step S2 using the K-means++ algorithm;

[0010] S4. Using the contour coefficients, recognition accuracy, and average values ​​of the absolute values ​​of multipath errors of each cluster obtained after clustering in step S3, satellite data that is greatly affected by multipath signals is removed, and then GNSS positioning calculation is performed using the removed satellite data.

[0011] This invention selects four GNSS data points—signal-to-noise ratio, elevation angle, azimuth angle, and double-difference residual—as feature values. Considering the information loss and poor robustness that may occur in normalized feature values, this invention introduces a feature decomposition method to decompose the feature values, thereby obtaining more referential and usable feature information.

[0012] This invention uses the K-means++ unsupervised clustering algorithm for feature value clustering analysis. This method introduces a probability weighting mechanism to select initial cluster centers, which are more representative and dispersed, and effectively avoid the problem of excessively long algorithm convergence time. At the same time, the clustering results are evaluated using the contour coefficient, recognition accuracy, and the average value of the absolute value of the multipath error of each cluster. By filtering the data, objective, reliable, and reasonable raw data are provided for GNSS positioning.

[0013] This invention introduces a feature decomposition data processing method combined with the unsupervised learning K-means++ clustering algorithm to accurately identify multipath errors in GNSS signals. This method effectively eliminates satellite data affected by multipath errors, improving the efficiency of multipath signal identification and significantly enhancing GNSS positioning accuracy. This solves the accuracy reduction problem caused by the multipath effect of GNSS signals in complex geological environments, providing more reliable technical support for landslide monitoring.

[0014] Preferably, the feature decomposition includes the following steps:

[0015] Input the signal-to-noise ratio, elevation angle, azimuth angle, and double-difference residuals into the dataset matrix X. Calculate the correlation coefficient matrix R of matrix X. Solve for the fundamental solution set of matrix R and orthonormalize it to obtain the orthogonal matrix P. Multiply the dataset matrix X by the orthogonal matrix P to obtain the decorrelated matrix Y. Calculate the standard deviation σ for each dimension of the dataset matrix Y. i Form a diagonal matrix Λ, multiply the dataset by matrix Y by the diagonal matrix Λ, and obtain the scaled dataset Z.

[0016] Preferably, step 3 uses the K-means++ algorithm to cluster the scaled dataset Z, including the following steps:

[0017] The internal evaluation index CH value of the K-means++ algorithm is used as the index to obtain the number of optimal cluster centers for dataset Z. Based on the number of optimal cluster centers, each sample point is assigned to the cluster closest to the centroid. The cluster centers are iteratively updated using Euclidean distance and the algorithm is used until the objective function meets the requirements.

[0018] Preferably, the CH value is calculated based on the variance within clusters and the variance between clusters. The formula for calculating the CH value is as follows:

[0019]

[0020] In the formula, CH(k) is the CH exponent; B k W represents the covariance between clustered data. k tr(·) represents the covariance of the data within each cluster; tr(·) represents the trace of the matrix; n represents the total number of samples; and k represents the number of cluster centers.

[0021] The formula for calculating the Euclidean distance is as follows:

[0022]

[0023] The cluster centers are updated iteratively based on the following algorithm:

[0024]

[0025] The iteration stops when the objective function of the algorithm meets the requirement that the change in the sum of squared errors between samples and centroids within each cluster can be ignored. The expression for the objective function is:

[0026]

[0027] Preferably, the silhouette coefficient SC after clustering is:

[0028]

[0029] In the formula, S(i) represents the silhouette coefficient of a single sample, and its calculation formula is as follows:

[0030]

[0031] Where a(i) is smaller, it means that sample i is more closely related to its own cluster, and b(i) is larger, it means that sample i is more separated from other clusters. The closer the silhouette coefficient s(i) is to 1, the better the clustering effect of sample i is. The closer the value is to -1, the more suitable the sample is to be assigned to other clusters. The closer the value is to 0, the more the sample is on the boundary between two clusters.

[0032] Preferably, the formula for recognition accuracy is:

[0033]

[0034] Among them, S TP This is the result of the model correctly classifying the satellites; S TN This is the result of the model correctly classifying the poorly performing satellites; S FP This is an incorrect result from the model's classification of good satellites; S FN This is an incorrect result from the model's classification of poor satellites.

[0035] Preferably, the formula for calculating the average absolute value of the multipath error of each cluster is as follows:

[0036]

[0037] In the formula, Let M(i) be the average absolute value of the multipath error of the kth cluster, and M(i) be the multipath error of the kth cluster.

[0038] Secondly, this invention provides the application of the above-mentioned multipath signal unsupervised learning and recognition method in GNSS landslide monitoring in complex mountainous areas.

[0039] Accurate fixation of ambiguity is one of the key technologies for high-precision carrier phase positioning, while fixation rate is an important factor restricting the application of high-precision positioning in complex environments. The higher the fixation rate, the more accurate the landslide displacement monitoring results. This invention uses fixation rate as an evaluation index for the application effect of the above-mentioned multipath signal unsupervised learning and recognition method in GNSS complex mountain landslide monitoring. Experiments have shown that the multipath signal unsupervised learning and recognition method provided by this invention can improve the fixation rate to over 99%.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] This invention introduces a feature decomposition data processing method and combines it with the unsupervised learning K-means++ clustering algorithm to accurately identify multipath errors in GNSS signals. This method effectively eliminates satellite data affected by multipath errors, significantly improves GNSS positioning accuracy, and achieves a fixation rate of no less than 99%. It solves the problem of accuracy reduction caused by the multipath effect of GNSS signals in complex geological environments and provides more reliable technical support for landslide monitoring. Attached Figure Description

[0042] Figure 1 This is a flowchart of multipath signal identification for landslide monitoring in complex mountainous areas, as shown in Example 1.

[0043] Figure 2 This is a map showing the specific location of the survey area;

[0044] Figure 3 This is a topographic and environmental map of the station in Example 1;

[0045] Figure 4 A sky map of the station based on observation satellites;

[0046] Figure 5 The distribution map of each cluster class after K-means++ multipath recognition following normalization and feature decomposition;

[0047] Figure 6 A graph showing PDOP values ​​at the monitoring station;

[0048] Figure 7 A graph showing the relationship between the signal-to-noise ratio and elevation angle of the monitoring station;

[0049] Figure 8 Plot of CH values ​​for different cluster numbers;

[0050] Figure 9 The histograms show the ambiguity fixation rates for the three schemes. Detailed Implementation

[0051] To better illustrate the objectives, technical solutions, and advantages of this invention, the invention will be further described below with reference to specific embodiments. Those skilled in the art should understand that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0052] Example 1

[0053] This embodiment provides an unsupervised learning and recognition method for multipath signals in GNSS landslide monitoring in complex mountainous areas based on feature decomposition, such as... Figure 1 As shown, it includes the following steps:

[0054] S1. Extract characteristic values ​​such as signal-to-noise ratio, elevation angle, azimuth angle, and double-difference residuals of the research station.

[0055] The signal-to-noise ratio data can be obtained directly from the station's observation files. The acquisition of azimuth and elevation angles requires iterative calculation of the satellite position to obtain the satellite's precise position, followed by Earth rotation correction. Then, the satellite coordinates are converted from ECEF coordinates to station-centered ENU coordinates, and finally the satellite's azimuth and elevation angles are calculated.

[0056] Extracting the double-difference residual requires first performing inter-station single-difference to eliminate satellite clock errors and satellite orbit errors, and then performing inter-satellite single-difference to eliminate receiver clock errors, receiver hardware delays, and receiver antenna phase center errors, resulting in the double-difference formula:

[0057]

[0058] In the formula, assume there are stations p and q, and satellites j and k. In the formula, Δ▽ is the double difference operator. These are pseudorange observations. These are phase observations. It is the geometric distance after double difference, where λ is the wavelength. It's the blurriness throughout the week. It is ionospheric error. It is a tropospheric error. It is residual error (including multipath effects, etc.).

[0059] Due to the short baseline, the ionospheric and tropospheric errors are negligible, and the double-difference residuals can be directly extracted using the above formula.

[0060] S2. Perform feature decomposition on the feature values ​​extracted in step S1.

[0061] Because the eigenvalues ​​differ in dimension and distribution, direct classification may affect classification accuracy. Therefore, it is necessary to unify the dimension and distribution of the eigenvalues. A common method is to normalize the eigenvalues, but this method suffers from information loss and poor robustness. This invention introduces an eigenvalue decomposition method to decompose the eigenvalues. The method involves inputting the eigenvalues ​​signal-to-noise ratio S, elevation angle α, double-difference residual υ, and azimuth angle AZ into the dataset matrix X; calculating the correlation coefficient matrix R; solving the fundamental solution set of matrix R and orthonormalizing it to obtain the orthogonal matrix P; dot-multiplying the dataset matrix X by the orthogonal matrix P to obtain the decorrelated matrix Y; and calculating the standard deviation σ for each dimension of the dataset matrix Y. i Form a diagonal matrix Λ, multiply the dataset by matrix Y, and then multiply the diagonal matrix Λ, i.e., Z = Y·Λ to obtain the scaled dataset Z.

[0062] The specific process is as follows:

[0063] The eigenvalue signal-to-noise ratio S, elevation angle α, double-difference residual υ, and azimuth angle AZ are input into the dataset matrix X = [x1, x2, ..., x]. m ] T =(x ij ) n×m Where n is the number of satellites and m is the number of eigenvalues, in this paper m = 4, then the expression for matrix X is:

[0064]

[0065] Next, we can obtain the correlation coefficient matrix R of matrix X:

[0066]

[0067] In the formula, r ij Let r be the correlation coefficient between the i-th and j-th dimensions of the dataset. ij =r ji Solve the characteristic equation |R-λI| for the correlation coefficient matrix R. m If |=0, the eigenvalue can be obtained: λ i (i = 1, 2, ..., m), and find the fundamental solution set of matrix R: α = [α1, α2, ..., αm]. m ], and the fundamental solution set according to λ i Arrange the matrices in ascending order, and then perform orthogonalization on matrix α to obtain an orthogonal matrix P = [η1, η2, ..., η]. m ].

[0068] Multiply the dataset matrix X by an orthogonal matrix P, i.e., Y = X·P, to obtain the dataset matrix Y after eliminating correlation; calculate the standard deviation σ for each dimension of the dataset matrix Y. i (i = 1, 2, ..., m):

[0069]

[0070] Form a diagonal matrix Λ:

[0071]

[0072] Multiplying the dataset matrix Y by the diagonal matrix A yields the scaled dataset Z, i.e., Z = Y·Λ, thus completing the eigenvalue decomposition.

[0073] S3. Use the K-means++ algorithm to cluster the dataset obtained from the feature decomposition in step S2.

[0074] In the face of complex environments, in order to ensure the optimal number of signal classifications (i.e. the optimal number of clusters), this paper uses the CH value index, an internal evaluation index of the clustering algorithm, to obtain the optimal number of clusters k. After determining the number of cluster centers, each sample point is assigned to the cluster closest to the centroid, and the Euclidean distance is used for calculation. Then, the cluster centers are iteratively updated until the objective function meets the requirements, so as to improve the accuracy and reliability of the classification results.

[0075] The CH value is calculated based on the variance within each cluster and the variance between clusters. It considers both the dispersion of data points within each cluster and the distance between different clusters. The formula for calculating the CH value is:

[0076]

[0077] In the formula, CH(k) is the CH exponent; B k W represents the covariance between clustered data. k Let be the covariance of the data within each cluster; tr(·) be the trace of the matrix; n be the total number of samples; and k be the number of cluster centers. When the total number of samples and the number of cluster centers are fixed, the more densely the data points within a category are clustered, the better the clustering effect will be. With sufficient samples, as long as we reasonably select the feature vectors in the GNSS data, we can obtain accurate results by using the CH value for evaluation.

[0078] k-means++ introduces a probability weighting mechanism to select initial cluster centers, making the selected cluster centers more representative and dispersed. Its basic principle in the initialization process is to maximize the distance between the initial cluster centers. Then, each sample point is assigned to the cluster closest to its centroid, calculated using Euclidean distance, as shown in the formula:

[0079]

[0080] Because the centroid parameter may have a large error, resulting in poor clustering results, iterative calculations and updates to the cluster centers are required, i.e.:

[0081]

[0082] The iteration stops when the objective function of the algorithm meets the requirement that the sum of squared errors between samples and centroids within each cluster can be ignored. The objective function expression is:

[0083]

[0084] S4. Use the clustering results from step S3 to remove satellite data that are significantly affected by multipath signals.

[0085] After performing K-means++ clustering, the clustering effect is evaluated by the silhouette coefficient, recognition accuracy, and the average value of the absolute value of the multipath error of each cluster. This clearly distinguishes the extent to which each cluster is affected by the multipath error. After removing the worst-performing cluster, the optimized observation data is used for localization, and the fixation rate and localization accuracy are significantly improved.

[0086] The specific evaluation indicators are as follows:

[0087] ① Profile coefficient:

[0088] The contour coefficient is calculated based on the following two factors:

[0089] a(i): The average distance from sample i to other samples in its cluster, used to measure the closeness of a sample to its own cluster.

[0090] b(i): The average distance from sample i to samples in the nearest neighboring different clusters, used to measure the separation degree of the sample from other clusters.

[0091] The formula for calculating the profile coefficient is:

[0092]

[0093] Where a(i) is smaller, it means that sample i is more closely related to its own cluster, and b(i) is larger, it means that sample i is more separated from other clusters. The closer the silhouette coefficient s(i) is to 1, the better the clustering effect of sample i is; the closer the value is to -1, the more suitable the sample is to be assigned to other clusters; the closer the value is to 0, the more the sample is on the boundary between two clusters.

[0094] By calculating the silhouette coefficients of all samples and taking the average, the silhouette coefficient of the entire clustering result can be obtained; the total silhouette coefficient SC of the clustering is:

[0095]

[0096] ② Recognition accuracy:

[0097] This invention uses satellites with a pseudorange multipath error exceeding three times the mean error as correctly labeled results, and uses this as an external indicator to evaluate the accuracy of multipath identification. The identification accuracy formula is as follows:

[0098]

[0099] Among them, S TP This is the result of the model correctly classifying the satellites. TN This is the result of the model correctly classifying poorly classified satellites. FP This is an incorrect result from the model's classification of good satellites. FN This is an incorrect result from the model's classification of poor satellites.

[0100] ③ The average absolute value of the multipath error for each cluster:

[0101] To more intuitively reflect the quality of multipath error identification, this invention uses the average absolute value of the multipath error of each cluster as the quality evaluation index reflecting the multipath error identification result. The formula is as follows:

[0102]

[0103] In the formula, Let M(i) be the average absolute value of the multipath error of the kth cluster, and M(i) be the multipath error of the kth cluster.

[0104] Example 2

[0105] This embodiment uses the Tengqing Coal Mine in Huale Town, Shuicheng District, Liupanshui City as the test area. The landslide was monitored using the method described in Example 1. Base station TQ01 was set up in an open area with sparse vegetation and a wide field of vision, facilitating observation. Monitoring stations TQ02, TQ03, and TQ04 were all located at the upper edge of the landslide, surrounded by dense vegetation, resulting in severe satellite signal obstruction. The dynamic monitoring distance was 1.8 km, a short baseline. All monitoring points used dual-system, multi-frequency GNSS receivers to collect landslide monitoring data in complex landslide environments. The experiment was implemented using self-developed Monitor software. Data processing and analysis were performed using point TQ04 as an example. The positioning and processing strategy is shown in Table 1. Figure 3 This is a topographic map of the survey area and the environment of the survey stations. Figure 4 This is a sky map based on satellite observations. As can be seen from the topographic map of the survey area and the station environment map, there is significant tree obstruction around the monitoring station. The topographic sky map shows that the eastern side of the station is almost completely obscured by trees, and there is also partial obstruction to the northwest. Therefore, the availability and continuity of data from the northwest and east sides are poor.

[0106] Table 1 Location Processing Strategy

[0107] Treatment regimen Treatment strategy Use system GPS, BDS Frequency point GPS L1 & L2 BDS B1 & B2 Ambiguity fixing strategy Lambda Ratio value 3.0

[0108] The signal-to-noise ratio, elevation angle, double-difference residual, and azimuth angle, obtained from the 259th monitoring data of 2021, were used as samples for machine learning, with a total sample size of 102,287 (the sum of the number of visible satellites for each epoch). The CH value was used to obtain the optimal k value; the CH value index is as follows... Figure 5 As shown. By Figure 5 It can be seen that when k=5, the CH value is the largest and the optimal number of clusters is obtained. Then, the results obtained after feature decomposition of the sample data and the results after conventional normalization are used to perform multipath identification using K-means++. Figure 6 This is a distribution map of each cluster class after K-means++ multipath identification, following normalization and feature decomposition processing. Figure 6 The distribution of clusters after K-means++ multipath identification, after normalization, shows that the azimuth angle effectively anchored the satellites, successfully identifying those severely obstructed by a continuous section to the east of the monitoring station. However, while introducing azimuth angle as a feature variable effectively identifies severely obstructed satellites, it also introduces a problem: if the azimuth angles of two satellites equally affected by severe obstacles differ significantly, the distance difference will also increase when calculating the Euclidean distance between them. Ultimately, they will be assigned to different clusters during multipath identification, leading to the failure of the multipath identification process. From... Figure 6 The distribution of clusters after K-means++ multipath identification following feature decomposition shows that this problem can be overcome to some extent. Feature decomposition successfully identified not only satellites severely obstructed by continuous sections to the east of the monitoring station, but also satellites severely affected by obstructions in the northwest direction. The identification results of feature decomposition are more consistent with the real-world environment.

[0109] Next, using the two multipath recognition results, through the formula... The total silhouette coefficient and recognition accuracy of the two multipath identification results were calculated separately. After feature decomposition, the total silhouette coefficient of the multipath identification result was 0.539, and the recognition accuracy was 93.6%. After normalization, the total silhouette coefficient of the multipath identification result was 0.317, and the recognition accuracy was 86.1%. Then, for each cluster, the average absolute value of the multipath error of each cluster after multipath identification under the two data processing schemes was calculated using the formula. The results are shown in Table 2. Table 2 shows that the average absolute value of the multipath error of each cluster after feature decomposition is better than that after normalization. In particular, cluster 2, which is a satellite severely affected by multipath error, shows that its average absolute value after feature decomposition is greater than that after normalization, indicating that the multipath identification effect after feature decomposition is better than that of the conventional processing method.

[0110] Table 2 shows the average absolute value of multipath error for each cluster in multipath identification using two data processing schemes.

[0111]

[0112] Next, to verify the feasibility of the K-means++ GNSS signal classification and identification method based on feature decomposition, TQ04 measured data was used for identification verification. The data acquisition frequency was 15s, the observation duration was 24h, and the observation period was from 00:00:00 to 23:59:45 on the 259th day of 2021. Three identification schemes were designed: Scheme 1, no classification processing; Scheme 2, after the sample data was normalized, K-means++ classification processing was used to remove satellites severely affected by multipath errors; Scheme 3, after the sample data was feature decomposition processing, K-means++ classification processing was used to remove satellites severely affected by multipath errors.

[0113] The accuracy of three landslide monitoring schemes was evaluated using the fixation rate, the standard deviation of floating-point solution residuals, and the standard deviation of fixed-solution residuals. The fixation rate, in GNSS (Global Navigation Satellite System) positioning, is an indicator of the success rate of ambiguity resolution and is used to assess the reliability of the positioning algorithm. Its core meaning is the proportion of times the ambiguity is successfully fixed to an integer solution out of the total number of solutions within a certain period. The floating-point solution residual is the difference between GNSS observations and model predictions based on floating-point solutions when the integer ambiguity is not fixed. The floating-point solution residual reflects the degree of model fit to the observations; the smaller the residual, the closer the model is to the actual signal. The fixed-solution residual is the difference between the observations and model predictions based on fixed solutions (integer solutions) after the ambiguity is fixed to integers. The smaller the fixed-solution residual, the higher the consistency between the integer solutions and the actual observations, and the more reliable the positioning accuracy.

[0114] The results are as follows Figure 7As shown in Table 3, Scheme 3 exhibits significantly better fixed-point accuracy and floating-point solution precision than Schemes 1 and 2. Compared to Scheme 1, in the E, N, and U directions, the floating-point solution precision is improved by 55.3%, 30%, and 15%, respectively, while the fixed-point accuracy is improved by 8.8%. Compared to Scheme 2, the floating-point solution precision is improved by 15.2%, 11.5%, and 3.8%, respectively, while the fixed-point accuracy is improved by 5.4%. This is mainly because Scheme 3 effectively identifies satellite signals that are more susceptible to environmental interference, significantly reducing the impact of multipath diffraction errors at the edges of obstacles around the monitoring station. Furthermore, from... Figure 6 The distribution maps of each cluster show that, after feature decomposition, the multipath signals in the environment can be identified relatively well. From... Figure 4 As can be seen, the obstructions are distributed on the east and northwest sides of the station, which corresponds exactly to the identification area of ​​cluster 5 in Scheme 3. It can be seen that Scheme 3 better reflects the actual terrain of the station. Therefore, compared with Scheme 2, its accuracy and fixation rate in the E, N, and U directions are all improved. Correct fixation of ambiguity is one of the key technologies for high-precision carrier phase positioning, and the fixation rate is an important factor restricting the application of high-precision positioning in complex environments. The higher the fixation rate, the more accurate the landslide displacement monitoring results. The above results show that Scheme 3 has higher accuracy in landslide monitoring.

[0115] Table 3. Statistics on the Fixed Rate and Standard Deviation of the Three Schemes

[0116]

[0117] To further verify the recognition accuracy of the proposed algorithm, observation data from four consecutive days (days 259-262 of 2021) at monitoring point TQ04 were processed. Correlation analysis was performed on signal clusters severely affected by multipath errors. The results are as follows: Figure 8 As shown, the identification results over the four consecutive days were largely similar. Each day, satellites severely obstructed by continuous intervals to the east and northwest of the monitoring point were successfully identified. This aligns with the previously identified cluster 2, indicating that satellite signals in these areas are significantly affected by multipath errors. The number of satellites severely affected by multipath errors reached 12,088, accounting for 11.8% of the total.

[0118] Finally, the ambiguity fixation rate of the settlement results of the observation data of monitoring station TQ04 for 7 consecutive days from day 260 to day 266 of 2021 was further statistically analyzed, and the results are as follows: Figure 9 As shown. From Figure 9It can be seen that: Scheme 1 has the lowest fixed solution ratio over 7 consecutive days, with an average fixed rate of 89.3%; Scheme 2 has an average fixed rate of 93.4% over 7 consecutive days, which is an improvement over Scheme 1; Scheme 3 has the highest ambiguity fixation rate, with an average fixed rate of 99.4% over 7 consecutive days, which is higher than Scheme 1 and Scheme 2.

[0119] The above-disclosed embodiments are merely a few specific examples of the present invention. Those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the present invention. However, the embodiments of the present invention are not limited thereto, and any changes that those skilled in the art can conceive of should fall within the protection scope of the present invention.

Claims

1. A method for unsupervised learning and recognition of multipath signals for GNSS landslide monitoring in complex mountainous areas based on feature decomposition, characterized in that, Includes the following steps: S1. Extract the signal-to-noise ratio, elevation angle, azimuth angle, and double-difference residual of the research station as feature values; S2. Perform feature decomposition on the feature values ​​extracted in step S1 to obtain the scaled dataset; S3. Cluster the scaled dataset from step S2 using the K-means++ algorithm; S4. Using the contour coefficients, recognition accuracy, and average values ​​of the absolute values ​​of multipath errors of each cluster obtained after clustering in step S3, satellite data that is greatly affected by multipath signals is removed, and then GNSS positioning calculation is performed using the removed satellite data. The feature decomposition includes the following steps: Input the signal-to-noise ratio, elevation angle, azimuth angle, and double-difference residuals into the dataset matrix X. Calculate the correlation coefficient matrix R of matrix X. Solve for the fundamental solution set of matrix R and orthonormalize it to obtain the orthogonal matrix P. Multiply the dataset matrix X by the orthogonal matrix P to obtain the decorrelated matrix Y. Calculate the standard deviation σ for each dimension of the dataset matrix Y. i Form a diagonal matrix Λ、 Multiply the dataset by matrix Y and then multiply the points by the diagonal matrix. Λ, The scaled dataset Z is obtained.

2. The method as described in claim 1, characterized in that, Step 3 uses the K-means++ algorithm to cluster the scaled dataset Z, including the following steps: The internal evaluation index CH value of the K-means++ algorithm is used as the index to obtain the number of optimal cluster centers for dataset Z. Based on the number of optimal cluster centers, each sample point is assigned to the cluster closest to the centroid. The cluster centers are iteratively updated using Euclidean distance and the algorithm is used until the objective function meets the requirements.

3. The method as described in claim 2, characterized in that, The CH value is calculated based on the variance within clusters and the variance between clusters. The formula for calculating the CH value is: In the formula, CH(k) is the CH exponent; B k W represents the covariance between clustered data. k The covariance of data within a cluster; tr() is the trace of the matrix; n is the total number of samples; k is the number of cluster centers; The formula for calculating the Euclidean distance is as follows: The cluster centers are updated iteratively based on the following algorithm: The iteration stops when the objective function of the algorithm meets the requirement that the change in the sum of squared errors between samples and centroids within each cluster can be ignored. The expression for the objective function is: .

4. The method as described in claim 1, characterized in that, The clustered silhouette coefficient SC is: In the formula, S(i) represents the silhouette coefficient of a single sample, and its calculation formula is: Where a(i) is smaller, it means that sample i is more closely related to its own cluster, and b(i) is larger, it means that sample i is more separated from other clusters. The closer the silhouette coefficient s(i) is to 1, the better the clustering effect of sample i is. The closer the value is to -1, the more suitable the sample is to be assigned to other clusters. The closer the value is to 0, the more the sample is on the boundary between two clusters.

5. The method as described in claim 1, characterized in that, The formula for the recognition accuracy is: Among them, S TP This is the result of the model correctly classifying the satellites; S TN This is the result of the model correctly classifying the poorly performing satellites; S FP This is an incorrect result from the model's classification of good satellites; S FN This is an incorrect result from the model's classification of poor satellites.

6. The method as described in claim 1, characterized in that, The formula for calculating the average absolute value of the multipath error of each cluster is as follows: In the formula, Let M(i) be the average absolute value of the multipath error of the kth cluster, and M(i) be the multipath error of the kth cluster.

Images