A method for GNSS vertical displacement prediction, storage medium and electronic device

Abstract

This application relates to the field of data prediction technology, specifically providing a method, storage medium, and electronic device for GNSS vertical displacement prediction. The method may include: obtaining training samples from a sample set that are most similar to test samples of a site to be predicted; determining a target vertical displacement prediction model that matches the training samples from multiple pre-trained vertical displacement prediction models; and using the prediction result of the target vertical displacement prediction model for the test samples as the vertical displacement time series of the site to be predicted. The embodiments of this application can achieve dynamic selection of the vertical displacement prediction model, improving the prediction accuracy of the vertical displacement time series.

Description

Technical Field

[0001] This application relates to the field of data prediction technology, and more specifically, to a method, storage medium, and electronic device for predicting GNSS vertical displacement. Background Technology

[0002] GNSS, or Global Navigation Satellite System, is a space-based radio navigation and positioning system that provides users with all-weather, three-dimensional coordinates, velocity, and time information from any location on the Earth's surface or in near-Earth space. GNSS vertical displacement refers to the change in position of a monitoring point in the vertical direction (elevation direction), obtained through GNSS observation technology. It is one of the core observation indicators in fields such as GNSS deformation monitoring and crustal deformation monitoring.

[0003] Currently, traditional GNSS vertical displacement prediction methods mainly employ interpolation algorithms such as inverse distance weighted interpolation (IDW) and Kriging, or globally unified machine learning models. However, these methods have significant limitations in practical applications: traditional methods rely primarily on geometric location coordinates for deduction, often neglecting the periodic influence of environmental factors on vertical displacement; existing technologies, when measuring spatial proximity between stations, typically only calculate two-dimensional planar distances based on latitude and longitude, ignoring the crucial impact of altitude differences on vertical displacement patterns, resulting in an inability to accurately measure true proximity relationships in three-dimensional space; using a single algorithm or global model to predict all areas makes it difficult to consider the significant spatial heterogeneity and deformation pattern differences under different terrains, leading to low accuracy in GNSS vertical displacement prediction in complex scenarios.

[0004] Therefore, how to provide a more accurate method for predicting vertical displacement in GNSS has become an urgent technical problem to be solved. Summary of the Invention

[0005] The purpose of some embodiments of this application is to provide a method, storage medium, and electronic device for predicting GNSS vertical displacement. The technical solutions of the embodiments of this application can realize the dynamic selection of the vertical displacement prediction model, adapt to spatial heterogeneity, and improve the prediction accuracy of GNSS vertical displacement.

[0006] In a first aspect, some embodiments of this application provide a method for predicting GNSS vertical displacement, comprising: obtaining a training sample most similar to a test sample of a site to be predicted from a sample set; determining a target vertical displacement prediction model that matches the training sample from a plurality of pre-trained vertical displacement prediction models; and using the prediction result of the target vertical displacement prediction model for the test sample as the vertical displacement time series of the site to be predicted.

[0007] Some embodiments of this application determine a target vertical displacement prediction model from multiple vertical displacement prediction models using training samples similar to the test samples of the site to be predicted. The prediction results of the target vertical displacement prediction model for the test samples are then used as a vertical displacement time series. These embodiments allow for dynamic selection of the vertical displacement prediction model based on the test samples of the site to be predicted, adapting to spatial heterogeneity and improving the prediction accuracy of GNSS vertical displacement.

[0008] In some embodiments, determining the target vertical displacement prediction model that matches the training sample from a plurality of pre-trained vertical displacement prediction models includes: if a locally optimal model that matches the training sample exists in the model mapping table, then the locally optimal model is used as the target vertical displacement prediction model; wherein, the model mapping table includes the correspondence between different training samples in the sample set and the plurality of vertical displacement prediction models; the locally optimal model is one of the plurality of vertical displacement prediction models; if no locally optimal model that matches the training sample exists in the model mapping table, then the globally optimal model among the plurality of vertical displacement prediction models is used as the target vertical displacement prediction model.

[0009] Some embodiments of this application determine the acquisition method of the target vertical displacement prediction model by judging whether there is a locally optimal model in the model mapping table that matches the training samples, thereby achieving dynamic and accurate selection of the vertical displacement prediction model.

[0010] In some embodiments, the model mapping table is obtained through the following steps: obtaining multiple neighboring stations similar to any training station in the sample set; merging the time series samples of each of the multiple neighboring stations to obtain a training sample set; using the multiple vertical displacement prediction models to predict the training sample set respectively to obtain multiple vertical displacement prediction values; selecting the local optimal model from the multiple vertical displacement prediction models based on the multiple vertical displacement prediction values ​​and the corresponding true vertical displacement values ​​of the training sample set; and constructing the model mapping table using the training sample set and the local optimal model.

[0011] Some embodiments of this application obtain a training sample set by merging time-series samples from multiple neighboring sites of any training site, and then determine a locally optimal model by combining multiple vertical displacement prediction values ​​output by multiple vertical displacement prediction models with the actual vertical displacement values, thereby constructing a model mapping table. These embodiments provide effective support for the subsequent dynamic selection of vertical displacement prediction models.

[0012] In some embodiments, obtaining multiple neighboring sites similar to any training site includes: obtaining the site coordinates of the training site in the geocentric coordinate system; constructing a neighboring site index table using the three-dimensional coordinates of other sites in the geocentric coordinate system; and filtering the multiple neighboring sites from the neighboring site index table using the similarity between the training site and each of the other sites.

[0013] Some embodiments of this application determine the similarity between stations by using the station coordinates of any training station in the geocentric-fixed coordinate system and the three-dimensional coordinates of other stations, thereby filtering out multiple neighboring stations. The use of coordinates in the geocentric-fixed coordinate system in this application allows for the evaluation of the relationship between stations from three perspectives: latitude, longitude, and altitude. This improves the accuracy of spatial distance calculation, thereby enhancing the accuracy of similarity calculation and enabling precise identification of similar samples.

[0014] In some embodiments, the step of selecting the plurality of neighboring sites from the neighboring site index table using the similarity between any training site and each of the other sites includes: calculating the geographical similarity and pattern similarity between any training site and each site; fusing the geographical similarity and the pattern similarity to obtain the similarity; and selecting the plurality of neighboring sites from the neighboring site index table whose similarity meets preset conditions.

[0015] Some embodiments of this application obtain similarity by fusing geographical similarity and pattern similarity between sites, and then filter out multiple neighboring sites that meet the requirements from the neighboring site index table, providing effective support for subsequent model selection.

[0016] In some embodiments, selecting the locally optimal model from the plurality of vertical displacement prediction models based on the plurality of vertical displacement prediction values ​​and the actual vertical displacement values ​​corresponding to the training sample set includes: calculating the average absolute error between each of the plurality of vertical displacement prediction values ​​and the actual vertical displacement value; and selecting the model corresponding to the minimum value of the average absolute error as the locally optimal model.

[0017] Some embodiments of this application determine the local optimal model by means of the average absolute error between the predicted vertical displacement value and the actual vertical displacement value, thereby achieving efficient and accurate model selection.

[0018] In some embodiments, the plurality of vertical displacement prediction models are obtained by the following steps: constructing a training dataset; wherein the training dataset includes a feature matrix and vertical displacement values ​​corresponding to the feature matrix; the feature matrix includes temporal features, environmental features and spatial features; and training a plurality of initial models using the training dataset to obtain the plurality of vertical displacement prediction models.

[0019] Some embodiments of this application train multiple initial models using a training dataset to obtain multiple vertical displacement prediction models, providing a basis for dynamic selection of subsequent models.

[0020] In some embodiments, the feature matrix is ​​obtained through the following steps: acquiring vertical displacement time series data, environmental variable data, and location data of all GNSS stations; wherein the location data includes longitude, latitude, and altitude; extracting the time information from the vertical displacement time series data and encoding the time information to obtain the time feature; performing feature calculation on the environmental variable data to obtain the environmental feature; and encoding the location data to obtain the spatial feature.

[0021] Some embodiments of this application extract relevant features from vertical displacement time series data, environmental variable data, and location data to construct a feature matrix, which can fully explore the correlation between data and provide effective basic data support for subsequent vertical displacement prediction.

[0022] Secondly, some embodiments of this application provide a GNSS vertical displacement prediction apparatus, comprising: an acquisition module for acquiring a training sample most similar to a test sample from a sample set; a matching module for determining a target vertical displacement prediction model that matches the training sample from a plurality of pre-trained vertical displacement prediction models; and a prediction module for using the prediction result of the target vertical displacement prediction model for the test sample as the vertical displacement time series of the station to be predicted.

[0023] Thirdly, some embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can implement the method described in any embodiment of the first aspect.

[0024] Fourthly, some embodiments of this application provide an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, can implement the method as described in any embodiment of the first aspect.

[0025] Fifthly, some embodiments of this application provide a computer program product, the computer program product including a computer program, wherein the computer program, when executed by a processor, can implement the method described in any embodiment of the first aspect. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of some embodiments of this application, the accompanying drawings used in some embodiments of this application will be briefly described below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 System diagrams for GNSS vertical displacement prediction provided for some embodiments of this application; Figure 2 Flowchart of a method for obtaining a vertical displacement prediction model provided for some embodiments of this application; Figure 3 One of the flowcharts for a method of predicting vertical displacement in GNSS provided for some embodiments of this application; Figure 4 Flowchart 2 of the GNSS vertical displacement prediction method provided for some embodiments of this application; Figure 5 A block diagram of a GNSS vertical displacement prediction apparatus provided for some embodiments of this application; Figure 6 A schematic diagram of an electronic device provided for some embodiments of this application. Detailed Implementation

[0028] The technical solutions of some embodiments of this application will now be described with reference to the accompanying drawings.

[0029] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this application, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0030] In related technologies, GNSS vertical displacement prediction methods mainly employ a single interpolation algorithm. Their implementation uses only one interpolation algorithm (such as IDW or Kriging) and does not involve the fusion of multiple methods. Furthermore, it only requires known location coordinates (latitude and longitude) and GNSS values ​​of the GNSS station, without needing environmental data, time characteristics, or other data. When calculating distance, the Haversine distance formula is used, considering only latitude and longitude (two-dimensional) and completely ignoring altitude information. All locations to be predicted use the same algorithm parameters, disregarding spatial differences. GNSS variation patterns may differ in different regions (plains, mountains), but this interpolation method treats all locations uniformly. Another prediction method employs a machine learning model for prediction. This GNSS vertical displacement prediction method trains and uses only one machine learning model, without involving multi-model fusion or selection; it uses only basic features (such as year, month, day, current values ​​of environmental variables, latitude and longitude), without performing complex feature engineering such as periodic encoding, hysteresis feature extraction, or sliding statistics; it trains a unified model on the entire training set, and uses the same model for all test locations, without considering the characteristics of different locations; it uses default or empirical parameters, without adjusting parameters for different regions; the GNSS change patterns may differ in different geographical locations, but the single machine learning method uses the same model for all locations.

[0031] As can be seen from the above-mentioned related technologies, the existing GNSS vertical displacement prediction methods have the following defects: 1) They cannot adapt to spatial heterogeneity, resulting in low prediction accuracy. This is because GNSS vertical displacement is significantly affected by geographical location, and the GNSS variation patterns of different regions (plains, mountains, basins) are significantly different; the spatial correlation of plains is strong, and IDW interpolation has a good effect; the spatial correlation of mountainous / isolated stations is weak, and machine learning models (such as XGBoost) perform better. However, the single algorithm in the current traditional technology uses the same algorithm or model for all locations, which cannot adapt to this spatial heterogeneity. 2) The spatial distance calculation is inaccurate, affecting the identification of similar samples; this is because traditional methods usually use Haversine distance to calculate spatial distance, only considering latitude and longitude (two-dimensional), completely ignoring altitude information; however, for GNSS vertical displacement prediction, altitude is a key factor. Stations at different altitudes, even if their latitude and longitude are similar, may have different GNSS variation patterns; for example, a station at an altitude of 500m and a station at an altitude of 2000m, even if their latitude and longitude are the same, have significantly different GNSS displacement patterns. 3) Feature engineering is not systematic and cannot fully tap the potential of data. This is because traditional methods usually only use basic time-series features (year, month, day) and environmental features (current value), lacking systematic feature engineering. For example, time features lack periodic encoding (sin / cos) and cannot capture the periodicity of time series; environmental features lack lag features and moving statistics features and cannot capture time-series dependencies; spatial features lack systematic spatial feature extraction (such as distance from reference station, altitude stratification, etc.).

[0032] In view of this, some embodiments of this application provide a method for predicting GNSS vertical displacement. This method involves selecting training samples from a sample set that are most similar to pre-constructed test samples, and then determining a target vertical displacement prediction model that matches these training samples from multiple pre-trained vertical displacement prediction models. Subsequently, the prediction results of the test samples using this target vertical displacement prediction model are used as the vertical displacement time series. The embodiments of this application can achieve dynamic selection of the vertical displacement prediction model, improving the prediction accuracy of the vertical displacement time series.

[0033] The following is in conjunction with the appendix Figure 1 The overall structure of a GNSS vertical displacement prediction system provided by some embodiments of this application is illustrated by way of example.

[0034] like Figure 1As shown, some embodiments of this application provide a system diagram for GNSS vertical displacement prediction. This GNSS vertical displacement prediction system may include a terminal 100 and a prediction server 200. The terminal 100 can send test samples collected from the site to be predicted to the prediction server 200. The prediction server 200 can search for the most similar training sample from the sample set; using the training sample, it can determine a target vertical displacement prediction model from multiple vertical displacement prediction models; then, the prediction result of the target vertical displacement prediction model for the test sample is used as the vertical displacement time series of the site to be predicted.

[0035] In some embodiments of this application, terminal 100 can be a mobile terminal or a non-portable computer terminal; no specific limitation is made here. Furthermore, the multiple vertical displacement prediction models in the prediction server 200 are deployed after pre-training. The specific training process can be found in the method embodiments described below.

[0036] The following is in conjunction with the appendix Figure 2 The present application provides an exemplary embodiment of the process by which a prediction server 200 performs the acquisition of a vertical displacement prediction model.

[0037] Please see the appendix Figure 2 , Figure 2 A flowchart illustrating a method for obtaining a vertical displacement prediction model is provided for some embodiments of this application. The method for obtaining the vertical displacement prediction model may include: S210, Construct a training dataset; wherein the training dataset includes a feature matrix and the vertical displacement values ​​corresponding to the feature matrix; the feature matrix includes time features, environmental features and spatial features.

[0038] For example, in a specific embodiment of this application, GNSS data, environmental data, and station coordinate data are automatically loaded and integrated from multiple data sources, and a training dataset is constructed after data verification and preprocessing. For example, the vertical displacement values ​​corresponding to the vertical displacement time series data of all GNSS stations are loaded from a specified directory.

[0039] In some embodiments of this application, S210 may include: S211, acquire vertical displacement time series data, environmental variable data, and location data of all GNSS stations; wherein, the location data includes longitude, latitude, and altitude.

[0040] For example, in a specific embodiment of this application, time series data of vertical displacement of all GNSS stations (or GNSS data) is loaded from a specified directory, while interpolation identifiers are supported to distinguish between real data and interpolated data. Time series data of various environmental variables such as surface temperature, air pressure, and precipitation (as a specific example of environmental variable data) are loaded from a specified directory and aligned according to the GNSS stations. The latitude, longitude, and altitude information of all GNSS stations are loaded from relevant files to obtain the location data of all GNSS stations.

[0041] GNSS data, environmental variable data, and station coordinates (i.e., location data) are aligned by station and time to generate a unified data structure. The above data is then checked to ensure data integrity and identify missing values, resulting in an integrated GNSS data dictionary, environmental data dictionary, and station coordinate dictionary, which prepares for subsequent feature extraction.

[0042] S212, extract the time information of the vertical displacement time series data and encode the time information to obtain the time feature.

[0043] For example, in a specific embodiment of this application, the basic features of the time information include year, month, day, day of year, and day of week. Periodic encoding is applied to these basic features to obtain the time features.

[0044] Specifically, the monthly periodicity encoding involves converting months into sine and cosine values ​​using the following formulas: sin_month = sin(2π × month / 12), cos_month = cos(2π × month / 12); where month represents the months (1-12), used to capture the periodic changes in months, enabling the model to learn seasonal patterns.

[0045] The annual periodicity encoding converts the day of the year into sine and cosine values. The conversion formulas are: sin_dayofyear = sin(2π × dayofyear / 365), cos_dayofyear = cos(2π × dayofyear / 365); where dayofyear is the day of the year (1-365), used to capture the periodic changes of the year, enabling the model to learn annual periodic patterns.

[0046] S213, Perform feature calculations on the environmental variable data to obtain the environmental features.

[0047] For example, in a specific embodiment of this application, the following data is obtained for each environmental variable (i.e., surface temperature, air pressure, and rainfall) in the environmental variable data: current value (i.e., current temperature value, current air pressure value, and current rainfall value) and lag features. Three lag features are extracted for each environmental variable: the environmental variable value of the previous day (i.e., the value of the environmental variable yesterday); the environmental variable value of the previous 7 days (i.e., the value of the environmental variable 7 days ago); and the environmental variable value of the previous 30 days (i.e., the value of the environmental variable 30 days ago).

[0048] Four moving statistical features are extracted for each environmental variable: the arithmetic mean of the past 7 days (calculated over the past 7 days to capture short-term environmental trends); the arithmetic mean of the past 30 days (calculated over the past 30 days to capture medium-term environmental trends); the arithmetic mean of the past 90 days (calculated over the past 90 days to capture long-term environmental trends (quarterly level); and the standard deviation of the past 30 days (calculated over the past 30 days to capture the volatility of environmental changes). These four extracted moving statistical features are used as environmental features. Furthermore, to avoid data leakage, this embodiment uses a data shift operation to ensure that feature values ​​only use historical data.

[0049] S214, the location data is encoded to obtain the spatial features.

[0050] For example, in a specific embodiment of this application, the basic features in the location data include latitude, longitude, and altitude; latitude and longitude are periodically encoded to obtain latitude sine, latitude cosine, longitude sine, and longitude cosine values; altitude is hierarchically encoded to obtain low-altitude markers (less than 500 meters), medium-altitude markers (500-2000 meters), or high-altitude markers (greater than 2000 meters). Spatial features are obtained through the above methods.

[0051] This yields a feature matrix containing temporal, environmental, and spatial characteristics.

[0052] S220, the training dataset is used to train multiple initial models to obtain the multiple vertical displacement prediction models.

[0053] For example, in a specific embodiment of this application, multiple different types of base models are trained using the training dataset constructed above. These models (i.e., multiple vertical displacement prediction models) will serve as candidate models for the system. Subsequently, the most suitable vertical displacement prediction model will be dynamically selected by the local optimal model selection module to predict the vertical displacement of the site to be predicted.

[0054] Specifically, using the feature matrix and corresponding GNSS vertical displacement values ​​in the training dataset, the LightGBM model (as a specific example of the initial model) is trained using the Gradient Boosting Decision Tree (GBDT) algorithm. The prediction performance is gradually optimized through multiple iterations to obtain the trained LightGBM model (as a specific example of the vertical displacement prediction model).

[0055] Using the feature matrix and corresponding GNSS vertical displacement values ​​from the training dataset, the XGBoost model (as a specific example of the initial model) is trained using the extreme gradient boosting algorithm. Regularization techniques are then used to improve the robustness of the model, resulting in a trained XGBoost model (as a specific example of a vertical displacement prediction model).

[0056] Using the feature matrix and corresponding GNSS vertical displacement values ​​from the training dataset, the RandomForest model (as a specific example of the initial model) is subjected to the RandomForest algorithm. By integrating multiple decision trees, the prediction stability is improved, resulting in a trained RandomForest model (as a specific example of a vertical displacement prediction model).

[0057] Then, predictions are made using the aforementioned trained models on another training set, the root mean square error (RMSE) is calculated, and the model with the smallest RMSE is selected as the global optimal model.

[0058] It is understood that although only three types of models are listed above, the types of models can be flexibly extended and replaced in practical applications, and the embodiments of this application are not limited to this. In addition to using RMSE for evaluation, other indicators can also be used for evaluation when selecting the globally optimal model, and the embodiments of this application do not make specific limitations here.

[0059] The following is in conjunction with the appendix Figure 3 The present application provides an exemplary embodiment of the implementation process of GNSS vertical displacement prediction performed by the prediction server 200.

[0060] Please see the appendix Figure 3 , Figure 3 A flowchart of a GNSS vertical displacement prediction method is provided for some embodiments of this application. The GNSS vertical displacement prediction method may include: S310: Obtain the training sample from the sample set that is most similar to the test sample of the site to be predicted.

[0061] For example, in a specific embodiment of this application, based on the three-dimensional distance of the location data in the test sample in the Earth-Centered, Earth-Fixed (ECEF) coordinate system, the most similar training sample is found from the sample set. This can be achieved by calculating the similarity of the three-dimensional distance between the test sample and different training samples in the sample set using a similarity algorithm, thereby selecting the training samples. The test sample is a feature matrix generated by obtaining the latitude, longitude, and altitude of the site to be predicted, as well as environmental data (such as temperature and air pressure) for the time period to be predicted, and performing feature extraction and encoding according to the methods described in S212-S214.

[0062] It should be noted that, in addition to using the three-dimensional distance provided in this application for similarity calculation, other algorithms can also be used to achieve the same function, and the embodiments of this application are not specifically limited here.

[0063] S320, determine the target vertical displacement prediction model that matches the training sample from multiple pre-trained vertical displacement prediction models.

[0064] For example, in a specific embodiment of this application, a target vertical displacement prediction model that matches the training samples is selected from the above-trained LightGBM model, XGBoost model, and RandomForest model.

[0065] In some embodiments of this application, S320 may include: if a locally optimal model exists in the model mapping table that matches the training sample, then the locally optimal model is used as the target vertical displacement prediction model; wherein, the model mapping table includes the correspondence between different training samples in the sample set and the plurality of vertical displacement prediction models; the locally optimal model is one of the plurality of vertical displacement prediction models.

[0066] For example, in a specific embodiment of this application, the model mapping table is a pre-constructed correspondence table between different training samples and multiple vertical displacement prediction models, with one training sample corresponding to one vertical displacement prediction model. If the most similar training sample has a locally optimal model that matches it, then that model is used as the target vertical displacement prediction model.

[0067] In some other embodiments of this application, S320 may include: if there is no locally optimal model matching the training sample in the model mapping table, then the globally optimal model among the plurality of vertical displacement prediction models shall be used as the target vertical displacement prediction model.

[0068] For example, in a specific embodiment of this application, if the most similar training sample does not match the optimal model in the model mapping table, then the globally optimal model obtained after training is used as the target vertical displacement prediction model.

[0069] In other words, this application prioritizes the use of locally optimal models to achieve dynamic model selection at the sample level, adapting to the characteristic differences of different spatial locations. When a locally optimal model cannot be found, a globally optimal model is used as a fallback to ensure that the system can produce prediction results under any circumstances, thereby improving the system's robustness.

[0070] In some embodiments of this application, the model mapping table is obtained through the following steps: S1, Obtain multiple neighboring sites in the sample set that are similar to any training site; Specifically, S1 may include: S11, Obtain the station coordinates of any training station in the geocentric coordinate system.

[0071] For example, in a specific embodiment of this application, the location data of any training station is extracted from the location coordinates of the sample set. The geographic coordinates of the Earth's surface of any training station (i.e., latitude, longitude, and altitude in the location data) are converted into three-dimensional Cartesian coordinates in the geocentric coordinate system (as a specific example of station coordinates). By simultaneously considering differences in latitude and longitude and differences in altitude, three-dimensional spatial distances are measured more accurately. The specific conversion process is as follows: Set the parameters of the Earth ellipsoid model (such as the WGS-84 model), or in simplified calculations, set the Earth's average radius R to 6,371,000 meters (a constant). Convert latitude to radians: lat_rad = latitude × π / 180; convert longitude to radians: lon_rad = longitude × π / 180; altitude h is in meters; distance from the station to the Earth's center: r = R + h. The formula for calculating the three-dimensional Cartesian coordinates of ECEF is: x = r × cos(φ) × cos(λ), y = r × cos(φ) × sin(λ), z = r × sin(φ), where φ is latitude (radians) and λ is longitude (radians).

[0072] ECEF 3D Distance d The calculation formula is: ,in, and These are the ECEF three-dimensional Cartesian coordinates of the two stations, respectively.

[0073] S12, construct a neighboring station index table using the three-dimensional coordinates of other stations in the geocentric-geofixed coordinate system.

[0074] For example, in a specific embodiment of this application, to quickly find neighboring sites of any training site, a nearest neighbor index structure is pre-established to avoid recalculating all distances for each search. Based on the ECEF 3D coordinates of all sites in the sample set (any training site is one of all sites), the NearestNeighbors algorithm is used to construct the nearest neighbor structure (as a specific example of a neighboring site index table).

[0075] Specifically, the number of neighbors k for each site is dynamically calculated based on the total number of sites N, where k = max(5, min( N × 0.1 , N - 1); that is, calculate N × 0.1 and round down to obtain the candidate value k_candidate = N × 0.1 Take the larger value of k_candidate and 5 to ensure that there are at least 5 neighbors for model evaluation; take the smaller value of this value and (N - 1) to ensure that it does not exceed the total number of available neighbors.

[0076] The above method can be used to determine the nearest neighbor structure for each site.

[0077] S13, using the similarity between any training site and each of the other sites, filter out the multiple neighboring sites from the neighboring site index table.

[0078] For example, in a specific embodiment of this application, based on the similarity between any training site and other sites, multiple neighboring sites that are closest to it are selected from the nearest neighbor structure.

[0079] In some embodiments of this application, S13 may include: calculating the geographical similarity and pattern similarity between any training site and each site; fusing the geographical similarity and the pattern similarity to obtain the similarity; and filtering out the plurality of neighboring sites whose similarity meets preset conditions from the neighboring site index table.

[0080] For example, in a specific embodiment of this application, the geographical similarity_geo is calculated based on the ECFF distance, and its formula is: similarity_geo = 1.0 / (1.0 + distance / scale); where distance is the ECFF three-dimensional distance, and scale is the distance scale parameter (usually taken as the 25th percentile of the distance). This formula converts the distance into a similarity value between 0 and 1, accurately measuring the degree of similarity between two sites in three-dimensional spatial location.

[0081] Pattern similarity calculation is based on the cosine similarity of feature vectors. The formula for pattern similarity_pattern is: similarity_pattern = (X1·X2) / (||X1|| × ||X2||); where X1 and X2 are the feature vectors of the two sites (after normalization), · represents the vector dot product, and ||·|| represents the vector magnitude. This formula measures the degree of similarity between the two sites in the feature space, capturing similarities other than spatial location.

[0082] Geographic similarity and pattern similarity are combined according to their weights to obtain the combined similarity score, similarity_combined. similarity_combined = α × similarity_geo + (1-α) × similarity_pattern In this model, α represents the weighting coefficient. Geographical similarity is a crucial factor in GNSS vertical displacement prediction, thus it can be given a higher weight, such as 0.6. Pattern similarity, as supplementary information, can be given a lower weight, such as 0.4. The resulting similarity fusion considers both spatial location similarity and feature pattern similarity, providing a more comprehensive similarity measurement.

[0083] The combined similarity can be used to select sites with a similarity greater than a preset threshold (as a specific example of the preset condition) from the nearest neighbor structure, or the sites with the first few similarity values ​​(as another specific example of the preset condition) can be selected as multiple neighbor sites after sorting the similarity values ​​in descending order.

[0084] The similarity value of any training site is mapped to all training samples of that site, so that all time series samples of the same site share the same similarity value.

[0085] It is understandable that the above is an explanation based on any training site. In practical applications, it is necessary to obtain multiple neighboring sites for each site in the sample set in the same way.

[0086] S2, merge the time series samples of each of the multiple neighboring sites to obtain the training sample set; For example, in a specific embodiment of this application, based on the mapping relationship between each neighboring site and the site sample index in any training site, all time series samples of each neighboring site are obtained; the time series samples of all neighboring sites are merged to form a similar sample set (as a specific example of a training sample set). This similar sample set contains all training samples that are spatially closest to any current training site.

[0087] S3, the training sample set is predicted using the multiple vertical displacement prediction models respectively to obtain multiple vertical displacement prediction values; For example, in a specific embodiment of this application, similar sample sets are input into the trained LightGBM model, XGBoost model, and RandomForest model respectively to obtain the vertical displacement prediction value output by each model.

[0088] S4, based on the multiple vertical displacement prediction values ​​and the true vertical displacement values ​​corresponding to the training sample set, select the local optimal model from the multiple vertical displacement prediction models; construct the model mapping table through the training sample set and the local optimal model.

[0089] For example, in a specific embodiment of this application, after calculating the predicted vertical displacement value output by each model and the actual GNSS vertical displacement value (i.e., the actual vertical displacement value) corresponding to the similar sample set, the locally optimal model corresponding to the similar sample set is selected. This locally optimal model is used for the prediction of all time series samples at any training site.

[0090] After selecting the locally optimal model corresponding to the set of similar samples for each site using the above method, a model mapping table can be constructed, providing a foundation for subsequent intelligent model selection.

[0091] In some embodiments of this application, S4 may include: calculating the average absolute error between each of the plurality of vertical displacement prediction values ​​and the actual vertical displacement value; and taking the model corresponding to the minimum value of the average absolute error as the local optimal model.

[0092] For example, in a specific embodiment of this application, the mean absolute error (MAE) between the predicted vertical displacement value and the actual GNSS vertical displacement value output by each model is calculated: MAE = (1 / n) ×Σ|pred_i - true_i|; where n is the number of samples in the similar sample set, pred_i is the predicted value of the i-th sample, and true_i is the actual value of the i-th sample. The MAE value of each model is calculated in this way. The model corresponding to the minimum MAE value among all models is taken as the locally optimal model. If multiple models have the same MAE value (a very rare case), the first model encountered (in order of model name) is selected as the locally optimal model.

[0093] Besides using the MAE value, other evaluation metrics can also be used. The reason for choosing MAE in this embodiment is that: MAE is more stable for small samples and will not fluctuate significantly due to individual outliers; MAE is not sensitive to outliers and is more suitable for model evaluation in local areas (similar neighbors); the physical meaning of MAE (the absolute value of the average error) is more intuitive and easier to understand and compare.

[0094] S330, the prediction results of the target vertical displacement prediction model for the test sample are used as the vertical displacement time series of the station to be predicted.

[0095] For example, in a specific embodiment of this application, the test sample is input into the target vertical displacement prediction model to obtain the prediction result, i.e., the vertical displacement time series.

[0096] Alternatively, before executing S330, the test samples can be input into the trained LightGBM model, XGBoost model, and RandomForest model respectively to obtain the prediction results of each model. After selecting the target vertical displacement prediction model, its corresponding prediction results can be directly used as the vertical displacement time series of the site to be predicted.

[0097] Finally, the prediction results are encapsulated, including the final prediction results, the model name of the target vertical displacement prediction model, and the prediction results of each model (for analysis and debugging).

[0098] Detailed result files can be generated for each site, including prediction CSV files and prediction visualizations. The prediction performance of the system can be evaluated by calculating metrics such as RMSE, MAE, R², and PCC, and the model can be optimized in a timely manner.

[0099] The following is in conjunction with the appendix Figure 4 The present application provides an exemplary description of the specific process for GNSS vertical displacement prediction based on some embodiments.

[0100] Please see the appendix Figure 4 , Figure 4 A flowchart of a GNSS vertical displacement prediction method is provided for some embodiments of this application.

[0101] The above process is illustrated below by example.

[0102] S410 acquires vertical displacement time series data, environmental variable data, and location data for all GNSS stations.

[0103] S420 extracts features from the vertical displacement time series data, environmental variable data, and location data respectively to obtain the feature matrix.

[0104] S430: Construct a training dataset based on the feature matrix and the corresponding vertical displacement values ​​of the feature matrix.

[0105] S440: Train multiple initial models using the training dataset to obtain multiple vertical displacement prediction models; and determine the globally optimal model among the multiple vertical displacement prediction models.

[0106] S450 constructs a model mapping table based on the training sample set and the local optimal model for each site.

[0107] The training sample set of each site constitutes the overall sample set. The local optimum model is one of multiple vertical displacement prediction models.

[0108] S451, Obtain environmental variable data and location data of the site to be predicted, and construct test samples.

[0109] S460: Obtain the training sample that is most similar to the test sample of the site to be predicted from the sample set.

[0110] S470: Determine if the training sample has a matching model in the model mapping table. If so, execute S471; otherwise, execute S472.

[0111] S471, the local optimal model corresponding to the training sample is used as the target vertical displacement prediction model.

[0112] S472 uses the globally optimal model as the target vertical displacement prediction model.

[0113] S480 uses the prediction results of the target vertical displacement prediction model for the test sample as the vertical displacement time series of the site to be predicted.

[0114] It is understood that the specific implementation process of S410~S480 can be referred to the method implementation examples provided above. To avoid repetition, detailed descriptions are omitted here.

[0115] As can be seen from the embodiments described above, this application, through ECEF 3D distance calculation, multi-scale similarity fusion of geographic similarity and pattern similarity, systematic feature engineering, and a local optimal model selection mechanism, can dynamically select the most suitable model for different spatial locations, fully explore the potential of data, and thus significantly improve prediction accuracy. Through an intelligent fusion strategy, the most suitable model is dynamically selected based on the performance of local areas, avoiding the problem of the inferior model dragging down the traditional weighted fusion model, ensuring that the prediction accuracy is not lower than the best single model. Through a complete end-to-end automated system, the entire process from data loading to result output is automated, improving the system's practicality and ease of use.

[0116] Please refer to Figure 5 , Figure 5The diagram illustrates a block diagram of a GNSS vertical displacement prediction apparatus provided in some embodiments of this application. It should be understood that this GNSS vertical displacement prediction apparatus corresponds to the method embodiments described above and is capable of performing the various steps involved in the method embodiments. The specific functions of this GNSS vertical displacement prediction apparatus can be found in the description above; detailed descriptions are omitted here to avoid repetition.

[0117] Figure 5 The GNSS vertical displacement prediction device includes at least one software functional module that can be stored in a memory or embedded in the GNSS vertical displacement prediction device in the form of software or firmware. The GNSS vertical displacement prediction device includes: an acquisition module 510, used to acquire training samples that are most similar to test samples of the site to be predicted from a sample set; a matching module 520, used to determine a target vertical displacement prediction model that matches the training samples from a plurality of pre-trained vertical displacement prediction models; and a prediction module 530, used to use the prediction results of the target vertical displacement prediction model for the test samples as the vertical displacement time series of the site to be predicted.

[0118] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the aforementioned method, and will not be elaborated further here.

[0119] Some embodiments of this application also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can perform the operation of any of the methods corresponding to the methods provided in the above embodiments.

[0120] Some embodiments of this application also provide a computer program product, which includes a computer program, wherein when the computer program is executed by a processor, it can implement the operation of any of the methods corresponding to the above embodiments provided in the above embodiments.

[0121] like Figure 6 As shown, some embodiments of this application provide an electronic device 600, which includes a memory 610, a processor 620, and a computer program stored in the memory 610 and executable on the processor 620. When the processor 620 reads the program from the memory 610 via a bus 630 and executes the program, it can implement the methods of any of the above embodiments.

[0122] Processor 620 can process digital signals and can include various computing architectures. For example, it can be a complex instruction set computer architecture, a reduced instruction set computer architecture, or an architecture that implements multiple instruction set combinations. In some examples, processor 620 can be a microprocessor.

[0123] The memory 610 can be used to store instructions executed by the processor 620 or data related to the execution of instructions. These instructions and / or data may include code for implementing some or all of the functions of one or more modules described in the embodiments of this application. The processor 620 of this disclosure embodiment can be used to execute the instructions in the memory 610 to implement the methods shown above. The memory 610 includes dynamic random access memory, static random access memory, flash memory, optical memory, or other memories well known to those skilled in the art.

[0124] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application. It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0125] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0126] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A method for predicting vertical displacement using GNSS, characterized in that, include: Obtain the training sample from the sample set that is most similar to the test sample of the site to be predicted; Determine the target vertical displacement prediction model that matches the training sample from multiple pre-trained vertical displacement prediction models; The prediction results of the target vertical displacement prediction model for the test sample are used as the vertical displacement time series of the station to be predicted.

2. The method as described in claim 1, characterized in that, The step of determining the target vertical displacement prediction model that matches the training samples from multiple pre-trained vertical displacement prediction models includes: If a locally optimal model exists in the model mapping table that matches the training sample, then the locally optimal model is used as the target vertical displacement prediction model; wherein, the model mapping table includes the correspondence between different training samples in the sample set and the multiple vertical displacement prediction models; the locally optimal model is one of the multiple vertical displacement prediction models; If there is no locally optimal model matching the training sample in the model mapping table, then the globally optimal model among the multiple vertical displacement prediction models will be used as the target vertical displacement prediction model.

3. The method as described in claim 2, characterized in that, The model mapping table is obtained through the following steps: Obtain multiple neighboring sites in the sample set that are similar to any training site; The time series samples of each of the multiple neighboring sites are merged to obtain the training sample set; The training sample set is predicted using the multiple vertical displacement prediction models to obtain multiple vertical displacement prediction values. Based on the multiple vertical displacement prediction values ​​and the actual vertical displacement values ​​corresponding to the training sample set, the local optimal model is selected from the multiple vertical displacement prediction models; The model mapping table is constructed using the training sample set and the local optimal model.

4. The method as described in claim 3, characterized in that, The step of obtaining multiple neighboring sites similar to any training site includes: Obtain the coordinates of any of the training stations in the geocentric-geofixed coordinate system; A neighboring station index table is constructed using the three-dimensional coordinates of other stations in the geocentric-geofixed coordinate system. Using the similarity between any training site and each of the other sites, the multiple neighboring sites are selected from the neighboring site index table.

5. The method as described in claim 4, characterized in that, The step of filtering out the multiple neighboring sites from the neighboring site index table by utilizing the similarity between any training site and each of the other sites includes: Calculate the geographical similarity and pattern similarity between any training site and each other site; The similarity is obtained by fusing the geographical similarity and the pattern similarity. The neighboring sites that meet the preset similarity criteria are selected from the neighboring site index table.

6. The method according to any one of claims 3-5, characterized in that, The step of selecting the locally optimal model from the multiple vertical displacement prediction models based on the multiple vertical displacement prediction values ​​and the actual vertical displacement values ​​corresponding to the training sample set includes: Calculate the average absolute error between each of the multiple vertical displacement prediction values ​​and the actual vertical displacement value; The model corresponding to the minimum value of the mean absolute error is taken as the local optimal model.

7. The method according to any one of claims 1-5, characterized in that, The multiple vertical displacement prediction models were obtained through the following steps: Construct a training dataset; wherein the training dataset includes a feature matrix and the vertical displacement values ​​corresponding to the feature matrix; the feature matrix includes temporal features, environmental features, and spatial features; The training dataset is used to train multiple initial models to obtain the multiple vertical displacement prediction models.

8. The method as described in claim 7, characterized in that, The feature matrix was obtained through the following steps: Acquire vertical displacement time series data, environmental variable data, and location data for all GNSS stations; wherein the location data includes longitude, latitude, and altitude. The time information of the vertical displacement time series data is extracted and encoded to obtain the time feature; The environmental characteristics are obtained by performing feature calculations on the environmental variable data. The location data is encoded to obtain the spatial features.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, wherein the computer program is executed by a processor to perform the method as described in any one of claims 1-8.

10. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored on the memory and running on the processor, wherein the computer program is executed by the processor to perform the method as described in any one of claims 1-8.

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