Partitioning method of GNSS reference station and electronic equipment

Abstract

The invention relates to the technical field of satellite navigation and positioning, and discloses a GNSS reference station partitioning method and electronic equipment. The method comprises the following steps: acquiring space coordinate data of a plurality of GNSS reference stations in a preset space coordinate system; according to the total number N of the multiple GNSS reference stations, a clustering algorithm is determined, the number K of clustering partitions is set, K is larger than or equal to 1, and N is larger than or equal to 2; according to the space coordinate data of the GNSS reference stations, adopting the clustering algorithm to divide the plurality of GNSS reference stations into K clustering partitions, and outputting a partition result; wherein when the total number N is greater than a first threshold value, the determined clustering algorithm is a clustering algorithm based on K-means, and when the total number N is less than the first threshold value, the determined clustering algorithm is a clustering algorithm based on spectral clustering. By means of the method, automatic partitioning of the GNSS base station is achieved.

Description

Technical Field

[0001] This application relates to the field of satellite navigation and positioning technology, and in particular to a GNSS reference station partitioning method and electronic equipment. Background Technology

[0002] With the rapid development of GNSS technology, a large number of GNSS reference stations have been deployed globally, capable of providing positioning results at the millimeter or even sub-millimeter level, significantly improving the accuracy and reliability of location information. These GNSS reference stations provide reliable data support for fields such as crustal deformation monitoring, earth science research, and engineering practice, and have promoted the development of precision measurement technology, becoming a fundamental data source for research in multiple disciplines.

[0003] In large-scale GNSS reference station post-processing, the sheer number of GNSS reference stations means that directly processing all of them would consume enormous computing resources, significantly reducing operational efficiency. To address this issue, the industry commonly employs a GNSS reference station partitioning method, dividing the entire GNSS network into multiple subnets (i.e., different partitions) to improve processing efficiency and ensure high-precision results.

[0004] In practice, GNSS reference station partitioning typically follows two core principles: spacing partitioning and area partitioning. Spacing partitioning allocates GNSS reference stations based on their ground distances, sparsely distributing densely packed stations to ensure uniform station distribution and consistent baseline lengths within each partition, effectively reducing computational burden and guaranteeing solution accuracy. Area partitioning, on the other hand, divides GNSS reference stations based on their geographical location, assigning geographically proximate stations to the same subnet. Because adjacent GNSS reference stations have high data correlation, this method better eliminates errors and is widely used in fields such as crustal deformation monitoring and geodynamics research.

[0005] Currently, most GNSS reference station partitioning relies on manual operation, which not only leads to low partitioning efficiency and poor scalability but also easily introduces significant uncertainties in complex areas. Especially in fields such as crustal deformation, where massive amounts of GNSS data from multiple consecutive days of observation are frequently encountered, the conventional approach is to manually partition the data once, and then use the same fixed partitioning method for each subsequent day's calculations. However, because GNSS reference station data is affected by factors such as network latency, equipment failure, and data quality, daily observation data may dynamically change. Adopting a fixed partitioning strategy is clearly unreasonable and will lead to a significant reduction in computational efficiency. Summary of the Invention

[0006] The purpose of this application is to provide a GNSS reference station partitioning method and electronic device, which aims to achieve automated partitioning of GNSS reference stations.

[0007] To address the aforementioned technical problems, embodiments of this application provide a GNSS reference station partitioning method. The method includes: acquiring spatial coordinate data of multiple GNSS reference stations in a preset spatial coordinate system; determining a clustering algorithm based on the total number N of the multiple GNSS reference stations, and setting the number of clustering partitions K, wherein K is greater than or equal to 1, and N is greater than or equal to 2; dividing the multiple GNSS reference stations into K clustering partitions using the clustering algorithm based on the spatial coordinate data of the GNSS reference stations, and outputting the partitioning results; wherein, when the total number N is greater than a first threshold, the determined clustering algorithm is a K-means-based clustering algorithm, and when the total number N is less than the first threshold, the determined clustering algorithm is a spectral clustering-based clustering algorithm.

[0008] Embodiments of this application also provide an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a GNSS reference station partitioning method as described above.

[0009] In the technical solution provided in this application embodiment, the server acquires spatial coordinate data of multiple GNSS reference stations in a preset spatial coordinate system. The server determines a clustering algorithm and sets the number of clustering partitions K based on the total number N of the multiple GNSS reference stations, where K is greater than or equal to 1 and N is greater than or equal to 2. When the total number N is greater than a first threshold, the determined clustering algorithm is a K-means-based clustering algorithm; when the total number N is less than the first threshold, the determined clustering algorithm is a spectral clustering-based clustering algorithm. In this way, by quantitatively judging the total number N and the first threshold, the appropriate algorithm is automatically matched, replacing the subjective judgment of manual algorithm selection and avoiding the uncertainty caused by experience errors in complex areas. At the same time, the number of partitions K is automatically derived from the total number N, solving the inefficiency problem of manual partitioning, while ensuring that the value of K matches the number of stations and avoiding partition imbalance. Finally, based on the spatial coordinate data of the GNSS reference stations, a clustering algorithm is used to divide multiple GNSS reference stations into K clustering partitions, and the partitioning results are output. Based on the clustering algorithm, through automated calculations (such as K-means calculation of station-center distance, spectral clustering based on graph correlation), all stations are directly assigned to the corresponding partitions without the need for manual station-by-station judgment, thus solving the inefficiency of manual allocation. At the same time, the consistency of the algorithm avoids the uncertainty caused by omissions or misclassifications. The partitioning results can be directly generated into standardized formats such as tables or map annotations by the program, replacing manual processing and further improving efficiency. Moreover, when adding a new GNSS reference station, only the number of GNSS reference stations N and the spatial coordinate data need to be re-entered, and the algorithm can automatically recalculate the partitions, solving the problem of poor scalability of manual adjustments.

[0010] Furthermore, the K-means-based clustering algorithm includes: setting K cluster centers and corresponding cluster partitions in the spatial coordinate system; for each GNSS reference station, determining the nearest neighbor cluster center from the K cluster centers; sequentially assigning each GNSS reference station to the nearest neighbor cluster partition corresponding to the nearest neighbor cluster center; and after dividing each GNSS reference station into corresponding nearest neighbor cluster partitions, determining the partition center for each cluster partition. In this way, through automated center setting, station allocation, and partition center determination, manual intervention is completely replaced, achieving automated GNSS reference station partitioning.

[0011] Furthermore, the K-means-based clustering algorithm further includes: after setting K cluster centers and corresponding cluster partitions, setting a capacity for GNSS reference stations for each cluster partition, the capacity being determined based on the previous partitioning results; for each GNSS reference station, if the number of GNSS reference stations already allocated in the nearest neighbor cluster partition exceeds the capacity, then the GNSS reference station is allocated to the next nearest neighbor cluster partition. In this way, setting the capacity based on the previous partitioning results avoids capacity imbalance. When the nearest neighbor partition exceeds the capacity, the algorithm automatically distributes the GNSS reference stations to the next nearest neighbor partition, ensuring that GNSS reference stations still belong to geographically proximate partitions while avoiding excessive clustering in a single partition.

[0012] In addition, determining the partition center of the current cluster partition for each cluster partition includes: for each cluster partition, calculating the average coordinate value of the spatial coordinate data of all GNSS reference stations within the current cluster partition, and using the average coordinate value as the partition center of the current cluster partition.

[0013] Furthermore, after determining the partition center for each of the clustering partitions, the K-means-based clustering algorithm further includes: if the distance between the partition center and the nearest neighboring cluster center of the current clustering partition is greater than a second threshold, then setting K new cluster centers in the spatial coordinate system, and determining the nearest neighboring cluster center of each GNSS reference station in the spatial coordinate system, as well as the nearest neighboring clustering partition corresponding to the nearest neighboring cluster center. In this way, by forcibly requiring that the distance between any partition center and its nearest neighboring center is no greater than the second threshold, the problem of some partition centers being too far from adjacent partition centers, resulting in large geographical spans and spatial fragmentation of GNSS reference stations within the same partition, is avoided after controlling the number of clustering partitions.

[0014] Furthermore, the clustering algorithm based on spectral clustering includes: establishing a nearest neighbor graph, where the nodes of the nearest neighbor graph are the GNSS reference stations; calculating the graph Laplacian matrix corresponding to the nearest neighbor graph, where the graph Laplacian matrix is ​​an N×N dimensional matrix, and N is the number of the GNSS reference stations; performing eigenvalue decomposition on the graph Laplacian matrix and selecting K eigenvectors from the decomposition results; constructing an embedding subspace based on the K eigenvectors, where the embedding subspace represents the K-dimensional coordinates of the N GNSS reference stations; and performing a clustering operation on the N GNSS reference stations within the embedding subspace based on the K-dimensional coordinates, assigning the N GNSS reference stations to K clustering partitions. In this way, through automated center setting, station allocation, and partition center determination, manual intervention is completely replaced, achieving automated GNSS reference station partitioning.

[0015] In addition, the establishment of the nearest neighbor graph includes: treating each GNSS reference station as a node; determining the edges connecting each node to the K nearest nodes using a nearest neighbor algorithm; calculating the positional distance between each node and the K nearest nodes, and setting the weight of the edges based on the positional distance.

[0016] In addition, the step of performing eigenvalue decomposition on the graph Laplacian matrix and selecting K eigenvectors from the decomposition results includes: performing eigenvalue decomposition on the graph Laplacian matrix to obtain N eigenvectors; and selecting eigenvectors corresponding to the first K non-zero smallest eigenvalues ​​from the N eigenvectors. Attached Figure Description

[0017] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0018] Figure 1 This is a flowchart illustrating a GNSS reference station partitioning method according to some embodiments of this application; Figure 2 This is a flowchart of a K-means-based clustering algorithm according to some embodiments of this application; Figure 3 This is another flowchart of a K-means-based clustering algorithm according to some embodiments of this application; Figure 4 This is a flowchart of a clustering algorithm based on spectral clustering according to some embodiments of this application; Figure 5 This is a schematic diagram of the structure of an electronic device according to some embodiments of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this application to help readers better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments. The division of the various embodiments below is for the convenience of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0020] It should be understood that the terms "system," "device," "unit," and / or "module" used in this specification are a method of distinguishing different components, elements, parts, sections, or assemblies at different levels. However, if other words can achieve the same purpose, they may be replaced by other expressions.

[0021] Unless otherwise specified, the technical terms used to describe components, elements, etc. in this specification are not singular but may include plural. Generally speaking, terms such as "comprising" or "including" only indicate that explicitly identified steps, elements, or components are included, and these steps, elements, and components do not constitute an exclusive list, as the described method or apparatus may also include other steps or components.

[0022] This specification uses flowcharts to illustrate the operational steps performed by the apparatus or system of related embodiments. However, unless otherwise specified, the order in which these steps are described should not be construed as a limitation on the order of execution. Those skilled in the art can adjust the order of these steps based on the knowledge and information conveyed by the embodiments in this specification. Adjustments include, but are not limited to, reversing the order of steps, merging multiple steps, and splitting a step.

[0023] As the background technology indicates, the partitioning of most GNSS (Global Navigation Satellite System) reference stations relies on manual operation. This not only leads to low partitioning efficiency and poor scalability but also easily introduces significant uncertainties in complex areas. Especially in fields such as crustal deformation, where massive amounts of GNSS data from continuous observations over multiple days are frequently encountered, the conventional approach is to manually partition the data once, and then use the same fixed partitioning method for each subsequent day's calculations. However, because GNSS reference station data is affected by factors such as network latency, equipment failure, and data quality, daily observation data may dynamically change. Adopting a fixed partitioning strategy is clearly unreasonable and will lead to a significant reduction in computational efficiency.

[0024] To address the aforementioned technical problems, some embodiments of this application provide a GNSS reference station partitioning method. This method is applied to a server, which acquires spatial coordinate data of multiple GNSS reference stations in a preset spatial coordinate system. The server determines a clustering algorithm and sets the number of clustering partitions K based on the total number N of the multiple GNSS reference stations, where K is greater than or equal to 1 and N is greater than or equal to 2. When the total number N is greater than a first threshold, the determined clustering algorithm is a K-means-based clustering algorithm; when the total number N is less than the first threshold, the determined clustering algorithm is a spectral clustering algorithm. Thus, by quantitatively judging the total number N and the first threshold, an appropriate algorithm is automatically matched. For example, when N is large, K-means is used to balance efficiency; when N is small, spectral clustering is used to ensure spatial compactness, completely replacing the subjective judgment of manual algorithm selection and avoiding uncertainty caused by experience errors in complex areas. Simultaneously, the number of partitions K is automatically derived from the total number N, solving the inefficiency problem of manual partitioning and ensuring that the value of K matches the number of stations, avoiding partition imbalance. Finally, based on the spatial coordinate data of the GNSS reference stations, a clustering algorithm is used to divide multiple GNSS reference stations into K clustering partitions, and the partitioning results are output. Based on the clustering algorithm, through automated calculations (such as K-means calculation of station-center distance, spectral clustering based on graph correlation), all stations are directly assigned to the corresponding partitions without the need for manual station-by-station judgment, completely solving the inefficiency of manual allocation. At the same time, the consistency of the algorithm avoids the uncertainty caused by omissions and misclassifications. The partitioning results can be directly generated into standardized formats such as tables or map annotations by the program, replacing manual processing and further improving efficiency. Moreover, when adding a new GNSS reference station, it is only necessary to re-enter the number of GNSS reference stations N and the spatial coordinate data, and the algorithm can automatically recalculate the partitions, solving the problem of poor scalability of manual adjustments.

[0025] Figure 1 This is a flowchart illustrating a GNSS reference station partitioning method according to some embodiments of this application. This method can be executed by a computer device or a dedicated data processing system capable of GNSS data processing. In some embodiments, Figure 1 The process shown may include the following steps.

[0026] Step 101: Obtain spatial coordinate data of multiple GNSS reference stations in a preset spatial coordinate system.

[0027] The spatial coordinate data includes longitude, latitude, and altitude.

[0028] Step 102: Based on the total number N of multiple GNSS reference stations, determine the clustering algorithm and set the number of clustering partitions K. K is greater than or equal to 1, and N is greater than or equal to 2.

[0029] In some embodiments, when the total number N is greater than a first threshold, the determined clustering algorithm is a K-means-based clustering algorithm; when the total number N is less than the first threshold, the determined clustering algorithm is a spectral clustering-based clustering algorithm.

[0030] Step 103: Based on the spatial coordinate data of the GNSS reference stations, a clustering algorithm is used to divide the multiple GNSS reference stations into K clustering partitions, and the partitioning results are output.

[0031] In the above steps, the server processing system automatically matches and adapts the algorithm based on the number N of GNSS reference stations. For example, when N is large, K-means clustering is used, and when N is small, spectral clustering is used to avoid uncertainty caused by empirical errors in complex areas. The number of partitions K is automatically derived from the total number N, solving the inefficiency of manual partitioning, while ensuring that the value of K matches the number of stations to avoid partition imbalance. Based on the determined clustering algorithm, all GNSS reference stations are directly assigned to the corresponding partitions through automated partition calculation, without the need for manual judgment of each station, solving the inefficiency of manual allocation. The partitioning results can be directly generated into standardized formats such as tables or map annotations by the program, replacing manual processing and further improving efficiency. Moreover, when adding a new GNSS reference station, only the number N and spatial coordinate data of the GNSS reference station need to be re-entered, and the algorithm can automatically recalculate the partitions, solving the problem of poor scalability of manual adjustments.

[0032] For scenarios with a large number of GNSS reference stations that are concentrated in one location, some embodiments of this application provide a K-means-based clustering algorithm. Figure 2 This is a flowchart illustrating a K-means-based clustering algorithm according to some embodiments of this application. In some embodiments, Figure 2 The process shown may include the following steps.

[0033] Step 201: In the spatial coordinate system, set K cluster centers and cluster partitions that correspond one-to-one with the K cluster centers.

[0034] In one example, the number of partitions K is calculated based on the total number of GNSS reference stations N. Considering computational efficiency, the calculation rule for the number of partitions K in this embodiment is "K=N / 50". Here, N is the total number of GNSS reference stations, and every 50 GNSS reference stations are divided into one clustering partition, ensuring a moderate computational load per partition. After determining the number of partitions, i.e., the number of cluster centers, initial cluster centers are selected within the spatial coordinate system of the GNSS reference stations, either randomly or using the k-means++ method. In this way, by pre-setting K initial cluster centers and their corresponding clustering partitions, the subjectivity of manual partitioning is avoided.

[0035] Step 202: For each GNSS reference station, determine the nearest cluster center from the K cluster centers.

[0036] In one example, for each GNSS reference station, its distance to all cluster centers is calculated. Specifically, based on coordinate data within the spatial coordinate system—namely, the longitude, latitude, and optional altitude of the GNSS reference station—the spatial distance from each GNSS reference station to the K cluster centers is calculated using geographic distance formulas (such as Haversine distance, applicable to longitude and latitude) or Euclidean distance. The cluster center with the smallest distance is the "nearest neighbor cluster center" of that GNSS reference station. For example, if GNSS reference station A is 5 km from cluster center 1 and 8 km from cluster center 2, then cluster center 1 is the nearest neighbor center of A. In this step, quantified distances replace manual judgment of GNSS reference station affiliation, ensuring the objectivity of the zoning and thus reducing the human error rate.

[0037] Step 203: Assign each GNSS reference station to the nearest neighbor cluster partition corresponding to the nearest neighbor cluster center in sequence.

[0038] In one example, each GNSS reference station is preferentially assigned to the partition corresponding to its nearest cluster center. For instance, in step 202, if the nearest center of GNSS reference station A is cluster center 1, it will be preferentially assigned to cluster partition 1. In this way, by prioritizing nearby areas, GNSS reference stations are ensured to belong to geographically proximate partitions as much as possible, thereby improving the solution efficiency.

[0039] Step 204: After dividing each GNSS reference station into corresponding nearest neighbor clustering partitions, determine the partition center of the current clustering partition for each clustering partition.

[0040] In one example, for all assigned GNSS reference stations within each cluster partition, the arithmetic mean of their spatial coordinates (longitude, latitude, and optional altitude) is calculated. This average value is the partition center of the current cluster partition. For instance, if cluster partition 1 has 10 GNSS reference stations, the average longitude and average latitude of these 10 stations are calculated to form the new center coordinates. In this way, through automated center setting, station allocation, and partition center determination, manual intervention is completely replaced, achieving automated GNSS reference station partitioning.

[0041] Steps 201 to 204 complete one iteration of the K-means algorithm. The entire process requires no manual intervention (automatic calculation of the number of partitions, automatic selection of centers, automatic allocation, and automatic recentering), realizing automated partitioning of GNSS reference stations and directly solving the technical problems of low efficiency and high uncertainty of manual partitioning.

[0042] To avoid a surge in computational load due to excessively large partitions, and to prevent excessive clustering of individual partitions, in some embodiments, a partition balancing constraint is introduced based on the K-means-based clustering algorithm shown in steps 201 to 204. This ensures that the number of GNSS reference stations contained in each partition is relatively uniform, thereby reducing the surge in computational load caused by some partitions being too large, and the waste of resources or decrease in accuracy caused by partitions being too small. Figure 3 This is another flowchart of a K-means-based clustering algorithm according to some embodiments of this application. In some embodiments, Figure 3 The process shown may include the following steps.

[0043] like Figure 2 and Figure 3 As shown, steps 301, 303, and 306 are similar to steps 201, 202, and 204, respectively, and will not be described again here.

[0044] In step 302, the number of GNSS reference stations to be accommodated is set for each cluster partition.

[0045] In one example, to ensure relatively balanced partitioning, a capacity limit is set for each cluster partition, i.e., the maximum number of GNSS reference stations each cluster partition can support. This prevents a surge in computational load due to an excessive number of GNSS reference stations in a partition. The K-means algorithm is an iterative convergence process (requiring multiple updates and reallocations of centers). Therefore, the previous partitioning result has already adapted to the GNSS reference station distribution at that time (e.g., if a partitioning result stably accommodates 55 stations, it indicates that the spatial range and computational resources of that partition are suitable for that number). Setting the capacity limit based on this is more scientific than randomly setting an upper limit. This strategy avoids both excessively loose capacity (leading to overcapacity) and excessively tight capacity (leading to resource waste), further ensuring partition balance.

[0046] In step 304, each GNSS reference station is sequentially assigned to the nearest neighbor cluster partition corresponding to the nearest cluster center. If the number of GNSS reference stations already assigned in the corresponding nearest neighbor cluster partition is greater than the capacity, the GNSS reference station is assigned to the next nearest neighbor cluster partition.

[0047] In one example, for each GNSS reference station to be assigned, the partition containing the cluster center with the closest geographical distance is preferentially selected as the target candidate partition. If the current number of GNSS reference stations in the candidate partition has not reached the preset capacity threshold (e.g., 60 stations), the GNSS reference station is directly assigned to that partition. If the candidate partition has reached the capacity threshold, a second-nearest partition search is performed, and the GNSS reference station is dynamically assigned to the second-nearest geographically located partition that has not yet reached capacity saturation. Through this rule-based dynamic allocation process, the problem of a surge in computational load caused by a single partition exceeding the limit for the number of GNSS reference stations (e.g., more than 60 stations) is effectively avoided. Furthermore, by allocating to the second-nearest partition, geographical proximity is maintained to the greatest extent, thus effectively preserving the high correlation of GNSS reference station data within the partition. Finally, through the constraint of the preset capacity threshold, the number of GNSS reference stations accommodated in each partition is ensured to be relatively balanced, significantly optimizing the overall system efficiency. This avoids computational resource bottlenecks and efficiency declines caused by excessively large partition sizes, and also eliminates the defects such as resource idleness or impaired positioning accuracy that may result from excessively small partition sizes.

[0048] In step 306, it is determined whether the distance between the partition center and its nearest cluster center is greater than a second threshold. If the distance is greater than the second threshold, the initial cluster center reset process is triggered, i.e., the process returns to step 301. The purpose of this verification process is that while relying solely on partition capacity constraints can balance the computational load, it may lead to excessively sparse spatial distribution of cluster centers, resulting in some partition centers having excessively large spatial intervals with their neighboring centers. This excessive discretization of centers leads to an overly wide geographical distribution and insufficient spatial clustering of GNSS reference stations assigned to the same partition, thereby weakening the spatial correlation of GNSS reference station data within the partition and ultimately impairing the crucial common-mode error suppression capability in high-precision calculations. By forcibly limiting the spatial distance between any partition center and its nearest neighbor center to no more than a second threshold, this step effectively constrains the overall distribution density of cluster centers, ensuring that: 1) the spatial coverage of each partition remains relatively compact; and 2) GNSS reference stations within the same partition are closely distributed around its partition center, meeting the core requirement of high geographical proximity. This mechanism precisely compensates for the potential spatial discretization risk under a single capacity constraint, further guaranteeing the final solution accuracy from the perspective of spatial compactness.

[0049] Furthermore, to control computational complexity and prevent the process from falling into an endless loop, this method further incorporates an iteration termination mechanism: each time an initial cluster center reset operation is triggered (i.e., step 301) due to a failed partition center distance check (i.e., the distance is greater than the second threshold in step 306), the system accumulates an iteration count. When this accumulated iteration count reaches a preset iteration tolerance threshold, regardless of the current partition center distribution density check result, the subsequent initial cluster center reset process is immediately terminated, and the currently generated cluster partitioning result is used as the final output (i.e., step 307 is executed to output the partitioning result). This mechanism effectively avoids the ineffective consumption of computational resources caused by repeated resets by imposing a limit on the number of reset operations, providing a crucial guarantee for computational efficiency while ensuring algorithm convergence.

[0050] For scenarios where the number of GNSS reference stations is small and their distribution is loose, some embodiments of this application provide a clustering algorithm based on spectral clustering. Figure 4 This is a flowchart illustrating a spectral clustering-based clustering algorithm according to some embodiments of this application. In some embodiments, Figure 4 The process shown may include the following steps.

[0051] Step 401: Build the nearest neighbor graph and calculate the graph Laplacian matrix corresponding to the nearest neighbor graph.

[0052] In some examples, the nearest neighbor graph is constructed through the following steps: treating each GNSS reference station as a node; using the nearest neighbor algorithm, determining the edges connecting each node to its K nearest neighbors; calculating the location distance between each node and its K nearest neighbors, and setting the weight of the edges based on the location distance. Specifically, each GNSS reference station is considered a node in the graph, with N nodes being the total number of GNSS reference stations. In this step, two methods are used to determine whether nodes are connected: Method 1, finding the K nearest neighbors for each node (GNSS reference station) and connecting only to these K neighbors; Method 2, setting a distance threshold (e.g., 10km), connecting only when the geographical distance between two nodes is less than this threshold. The weight of the edges is determined by geographical distance or other similarity; for example, the closer the geographical distance, the greater the weight, indicating a higher correlation between the two station data. The nearest neighbor graph generated in this way is a sparse graph, meaning that most nodes are connected to only a few neighbors, thus reducing the computational burden of subsequent spectral clustering on large-scale data.

[0053] In one example, the Graph Laplacian is an N×N matrix, consistent with the number of GNSS reference stations. Each row and column corresponds to a node. Essentially, this matrix transforms the topological relationships of the graph into a mathematical matrix. The purpose is to extract the core relationships between nodes through matrix factorization; for example, geographically proximate nodes with higher weights will exhibit stronger relationships in the matrix. This allows for the automatic association of geographically proximate GNSS reference stations through the nearest neighbor graph, replacing manual subjective judgment of station proximity. Furthermore, the Graph Laplacian quantifies these relationships, providing a foundation for subsequent clustering and thus addressing the issue of significant uncertainty in manually partitioning complex regions.

[0054] Step 402: Perform eigenvalue decomposition on the graph Laplacian matrix and select K eigenvectors from the decomposition results.

[0055] In one example, the number of eigenvectors is determined by the preset number of cluster partitions K. The essence of eigenvalue decomposition is to decompose a high-dimensional N×N matrix into eigenvalues ​​and eigenvectors.

[0056] In some embodiments, selecting K eigenvectors can be achieved as follows: Eigenvalue decomposition is performed on the graph Laplacian matrix to obtain N eigenvectors; from these N eigenvectors, the eigenvectors corresponding to the K smallest non-zero eigenvalues ​​are selected. Specifically, the K smallest eigenvectors contain the main information of the node association structure in the nearest neighbor graph, representing geographically close and closely related GNSS reference stations. Eigenvalue decomposition reduces the dimensionality of high-dimensional GNSS reference station association information to K dimensions, reducing subsequent computation while preserving core geographical proximity information, thus avoiding the inefficiency of manually processing high-dimensional data.

[0057] Step 403: Construct an embedding subspace based on K feature vectors. Within the embedding subspace, perform a clustering operation on the N GNSS reference stations based on K-dimensional coordinates, and assign the N GNSS reference stations to K clustering partitions.

[0058] In one example, each GNSS reference station (node) corresponds to a K-dimensional coordinate in the embedding subspace. Specifically, the vector values ​​corresponding to the node in the K feature vectors selected in step 402 are combined sequentially into a K-dimensional vector (e.g., when K=3, the coordinates are (feature vector 1 value, feature vector 2 value, feature vector 3 value)). Geographically proximate and closely related GNSS reference stations will have "close" K-dimensional coordinates (because their values ​​in the feature vectors are similar), while the opposite is true for less geographically related stations. The embedding subspace essentially transforms the geographical relationships of GNSS reference stations into coordinate distances, making clustering easier to implement. Finally, the nodes are processed using subsequent K-means or other clustering algorithms in this embedding subspace, assigning each node to one of the clusters and outputting the partition label for each GNSS reference station (e.g., GNSS reference station A belongs to partition 1, GNSS reference station B belongs to partition 2), completing the automated partitioning.

[0059] In one or more of the above embodiments, to address the problems of low efficiency, poor scalability, and inability of fixed partitions to adapt to dynamic data changes in the processing of high-precision data from massive GNSS reference stations, two automated partitioning methods are proposed: First, a balanced K-means method with added constraints, which calculates the number of partitions by dividing 50 GNSS reference stations into one partition (K=N / 50) and sets an upper limit for the number of partitions to achieve a balanced number of partitions; Second, a method based on spectral clustering and nearest neighbor graphs, which constructs a node graph of GNSS reference stations and a Laplace matrix of the decomposition graph to achieve spatially compact partitioning. Ultimately, these methods replace manual operations, improve the efficiency and accuracy of GNSS data processing, adapt to the massive data processing needs of scenarios such as crustal deformation monitoring, and solve the problem of partition imbalance.

[0060] The steps of the various methods described above are only for clarity. In implementation, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, but without changing the core design of the algorithm and process, are also within the scope of protection of this application.

[0061] Another embodiment of this application also relates to an electronic device, such as... Figure 5 As shown, it includes at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to perform the GNSS reference station partitioning method as described above.

[0062] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0063] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0064] Those skilled in the art will understand that the above embodiments are specific implementations of this application, and in practical applications, various changes can be made in form and detail without departing from the spirit and scope of this application.

Claims

1. A zoning method for GNSS reference stations, characterized in that, The method includes: Acquire spatial coordinate data of multiple GNSS reference stations in a preset spatial coordinate system; Based on the total number N of the multiple GNSS reference stations, a clustering algorithm is determined, and the number K of clustering partitions is set, wherein K is greater than or equal to 1 and N is greater than or equal to 2; Based on the spatial coordinate data of the GNSS reference stations, the clustering algorithm is used to divide the multiple GNSS reference stations into K clustering partitions, and the partitioning results are output. Wherein, if the total number N is greater than the first threshold, the determined clustering algorithm is a K-means-based clustering algorithm; if the total number N is less than the first threshold, the determined clustering algorithm is a spectral clustering-based clustering algorithm.

2. The zoning method for GNSS reference stations according to claim 1, characterized in that, The K-means-based clustering algorithm includes: In the spatial coordinate system, K cluster centers are set, and cluster partitions are set one-to-one with the K cluster centers; For each of the GNSS reference stations, the nearest neighbor cluster center is determined from the K cluster centers; Each GNSS reference station is sequentially assigned to the nearest neighbor cluster partition corresponding to the nearest neighbor cluster center; After dividing each GNSS reference station into its corresponding nearest neighbor clustering partition, the partition center of the current clustering partition is determined for each clustering partition.

3. The zoning method for GNSS reference stations according to claim 2, characterized in that, The K-means-based clustering algorithm further includes: After setting K cluster centers and cluster partitions corresponding to the K cluster centers, the number of GNSS reference stations to be accommodated in each cluster partition is set, and the number of GNSS reference stations to be accommodated is determined according to the previous partitioning results. For each GNSS reference station, if the number of GNSS reference stations already allocated in the corresponding nearest neighbor clustering partition is greater than the capacity, then the GNSS reference station is allocated to the next nearest neighbor clustering partition.

4. The zoning method for GNSS reference stations according to claim 2, characterized in that, Determining the partition center for each of the clustering partitions includes: For each cluster partition, calculate the average coordinate value of the spatial coordinate data of all GNSS reference stations within the current cluster partition, and use the average coordinate value as the partition center of the current cluster partition.

5. The zoning method for GNSS reference stations according to claim 2, characterized in that, After determining the partition center of each cluster partition, the K-means-based clustering algorithm further includes: If the distance between the partition center and the nearest cluster center of the current cluster partition is greater than the second threshold, then K cluster centers are set again in the spatial coordinate system, and the nearest cluster center of each GNSS reference station in the spatial coordinate system and the nearest cluster partition corresponding to the nearest cluster center are determined.

6. The zoning method for GNSS reference stations according to claim 1, characterized in that, The clustering algorithm based on spectral clustering includes: Establish a nearest neighbor graph, wherein the nodes of the nearest neighbor graph are the GNSS reference stations; Calculate the graph Laplacian matrix corresponding to the nearest neighbor graph, wherein the graph Laplacian matrix is ​​an N×N dimensional matrix, and N is the number of GNSS reference stations; Perform eigenvalue decomposition on the graph Laplacian matrix and select K eigenvectors from the decomposition results; An embedding subspace is constructed based on the K feature vectors, and the embedding subspace represents the K-dimensional coordinates of the N GNSS reference stations; Within the embedded subspace, clustering operations are performed on the N GNSS reference stations based on the K-dimensional coordinates, and the N GNSS reference stations are assigned to K clustering partitions.

7. The zoning method for GNSS reference stations according to claim 6, characterized in that, The establishment of the nearest neighbor graph includes: Each of the aforementioned GNSS reference stations is treated as a node; The nearest neighbor algorithm is used to determine the edges connecting each node to the K nearest other nodes; Calculate the positional distance between each node and the K nearest nodes, and set the weight of the connecting edge based on the positional distance.

8. The zoning method for GNSS reference stations according to claim 6, characterized in that, The eigenvalue decomposition of the graph Laplacian matrix, and the selection of K eigenvectors from the decomposition results, includes: The graph Laplacian matrix is ​​subjected to eigenvalue decomposition to obtain N eigenvectors; From the N feature vectors, select the feature vector corresponding to the first K non-zero smallest feature values.

9. The zoning method for GNSS reference stations according to claim 1, characterized in that, The spatial coordinate data includes longitude, latitude, and altitude.

10. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the partitioning method of the GNSS reference station as described in any one of claims 1 to 9.

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