A method and system for fast generation of a regional tropospheric delay grid

Abstract

The present application belongs to the technical field of surveying and mapping, and discloses a regional troposphere delay grid fast generation method and system. In the present application, a regional troposphere delay grid fast generation model adaptive to terrain and GNSS station network is constructed, which includes three modules of GNSS station feature extraction, target grid point feature extraction and GNSS station to grid point mapping; by introducing a graph attention network and a multi-head cross attention mechanism, the local spatial correlation of different regional station network distribution can be dynamically described, and the global change characteristics of the troposphere delay can be captured at the same time; by further fusing the station position and the terrain attribute through geographical space feature embedding, the feature consistency expression under the condition of terrain difference is realized. While maintaining the local spatial dependence modeling capability, the present application enhances the capturing capability of global feature correlation, realizes the adaptive modeling of different GNSS station network distribution and terrain change, and improves the spatial continuity and prediction accuracy of the troposphere delay.

Description

Technical Field

[0001] This invention belongs to the field of surveying and mapping technology, and relates to a method and system for rapid generation of regional tropospheric delayed grids. Background Technology

[0002] Tropospheric delay is a significant source of error in precise positioning using Global Navigation Satellite Systems (GNSS). In high-precision positioning and navigation applications, this delay can lead to ranging errors of several meters to tens of meters, severely impacting positioning accuracy and reliability. Particularly under complex terrain and extreme weather conditions, the tropospheric delay varies dramatically with time and space, making accurate modeling extremely difficult.

[0003] To achieve centimeter-level high-precision positioning, accurate measurement and modeling of tropospheric delay errors are crucial, which helps improve the performance of GNSS applications in fields such as surveying, autonomous driving, and precision agriculture.

[0004] Related techniques can establish tropospheric delay models through empirical tropospheric delay models and by interpolating / fitting the tropospheric delay of continuously running GNSS reference stations. However, these methods currently have the following drawbacks:

[0005] (1) Traditional empirical tropospheric delay models are not accurate in capturing changes in wet delay and are generally based on standard atmospheric assumptions or empirical formulas, resulting in low accuracy and difficulty in meeting the requirements for high-precision positioning.

[0006] (2) Based on the tropospheric delay model of GNSS station, interpolation / fitting usually uses linear / low-order polynomial or kriging method, which makes it difficult to capture the nonlinear effect of complex terrain on tropospheric delay.

[0007] (3) The uneven distribution of GNSS stations leads to poor prediction results of traditional methods in areas with sparse stations; therefore, it is difficult to provide high-precision tropospheric delay correction models in complex terrain areas and areas with sparse stations.

[0008] Therefore, there is an urgent need to propose a method for rapid generation of regional tropospheric delay grids that adapts to terrain and GNSS station networks. Summary of the Invention

[0009] The purpose of this invention is to propose a method for rapid generation of regional tropospheric delay grids, so as to achieve adaptive modeling of different GNSS station network distributions and terrain changes, which is beneficial to significantly improve the spatial continuity and prediction accuracy of tropospheric delay.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A method for rapidly generating regional tropospheric delayed grids includes the following steps:

[0012] Step 1. Obtain zenith tropospheric delay and geospatial feature information of GNSS stations and target grid points within the target area to construct a training dataset for model training in Step 2 below;

[0013] Step 2. Construct a rapid generation model for regional tropospheric delayed grids that is adaptive to terrain and GNSS station network, which includes a GNSS station feature extraction module, a target grid point feature extraction module, and a GNSS station-to-grid point mapping module;

[0014] The GNSS station feature extraction module is used to realize a high-dimensional representation of the original GNSS station input data, including station coordinates, station topography, and station tropospheric delay data, to obtain node features.

[0015] The target grid point feature extraction module is used to perform geospatial feature embedding operations to obtain grid point features;

[0016] The GNSS station-to-grid point mapping module achieves the mapping from GNSS stations to grid points through cross attention. The grid point features are used as query Q, and information is learned from the node feature key K / value V to generate the zenith tropospheric delay information of the target grid point.

[0017] Step 3. Train the regional tropospheric delay grid rapid generation model based on the training dataset, and use the trained regional tropospheric delay grid rapid generation model to realize the rapid generation of zenith tropospheric delay information of target grid points;

[0018] During model training, the zenith tropospheric delay of GNSS stations in the training dataset, as well as the geospatial features of GNSS stations and target grid points, are used as inputs to the model, with the zenith tropospheric delay of the target grid points serving as the label.

[0019] Furthermore, based on the aforementioned method for rapid generation of regional tropospheric delayed grids, this invention also proposes a corresponding system for rapid generation of regional tropospheric delayed grids, which employs the following technical solution:

[0020] A system for rapidly generating regional tropospheric delayed grids includes a computer device; wherein the computer device includes a memory and a processor; a computer program is stored in the memory; when the processor executes the computer program, it implements the steps of the method for rapidly generating regional tropospheric delayed grids as described above.

[0021] The present invention has the following advantages:

[0022] As described above, this invention discloses a method for rapidly generating regional tropospheric delay grids. This method constructs a rapid generation model for regional tropospheric delay grids to achieve adaptive modeling of GNSS station distribution and terrain features. The model incorporates a graph attention network and a multi-head cross-attention mechanism. The graph attention network, based on a sparse spatial topology constructed from station latitude and longitude, adaptively aggregates node features within a neighborhood, dynamically characterizing the local spatial correlation of station network distributions in different regions. The multi-head cross-attention mechanism establishes a cross-domain feature mapping between the regular grid and station node features, capturing the global variation features of tropospheric delay through parallel attention calculations in multiple subspaces. Geospatial feature embedding further integrates station location and terrain attributes, achieving consistent feature expression under terrain variation conditions. Through this structural design, this invention enhances the ability to capture global feature correlations while maintaining the ability to model local spatial dependencies, achieving adaptive modeling of different GNSS station network distributions and terrain changes, and significantly improving the spatial continuity and prediction accuracy of tropospheric delay. This invention presents a high-precision regional tropospheric delay grid rapid generation model based on GNSS data, which can improve the tropospheric delay accuracy in complex terrain areas and is of great significance for enhancing real-time precision positioning performance in complex terrain. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the method for rapid generation of regional tropospheric delayed grids in an embodiment of the present invention.

[0024] Figure 2 This is a network structure diagram of the regional tropospheric delayed grid rapid generation model constructed in an embodiment of the present invention;

[0025] Figure 3 This is a network structure diagram of geospatial feature embedding in an embodiment of the present invention;

[0026] Figure 4 This is a network structure diagram of the cross-attention mechanism in an embodiment of the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0028] Example 1

[0029] like Figure 1 As shown in the figure, this embodiment describes a method for rapid generation of regional tropospheric delayed grids, which includes the following steps:

[0030] Step 1. Obtain zenith tropospheric delay and geospatial feature information of GNSS stations and target grid points within the target area to construct a training dataset for model training in Step 2 below.

[0031] The target area can be a selected geographical or administrative region, such as a province or a river basin. The boundary of the target area can be determined by latitude and longitude coordinates, but this embodiment of the invention does not limit this.

[0032] Geospatial feature information includes GNSS station coordinates (i.e., latitude and longitude), topography and target grid point coordinates (i.e., latitude and longitude), and topography. Topographic attributes include elevation, slope, aspect, surface roughness index, and normalized difference vegetation index (NDVI).

[0033] I. The process of obtaining the zenith tropospheric delay from a GNSS station is as follows:

[0034] First, an observation equation is constructed based on the phase and pseudorange observations of the GNSS station (the process is relatively conventional and will not be described in detail here). Then, using dual-frequency observations, the observations of the two frequencies are linearly combined to eliminate the first-order ionospheric delay term.

[0035] The static zenith delay in the tropospheric zenith can be accurately calculated by the model; however, the wet zenith delay is related to water vapor and is difficult to model accurately. Therefore, it is estimated as a parameter, and the Kalman filter method is used to estimate the wet zenith delay parameter.

[0036] The zenith wet delay is summed with the zenith static delay calculated by the model to obtain the zenith tropospheric delay information of the GNSS station.

[0037] II. The process of obtaining the zenith tropospheric delay information of the target grid point is as follows:

[0038] Based on EAR5 reanalysis data, meteorological elements such as temperature, air pressure, and specific humidity of the surface layer and each isobaric surface layer are obtained. Based on the meteorological elements, the zenith tropospheric delay information of the target grid point is calculated and used as the label data.

[0039] The zenith tropospheric delay information for this target grid point is a numerical model zenith tropospheric delay grid. The formula for calculating the zenith tropospheric delay grid based on meteorological elements is expressed as follows:

[0040] ;

[0041] in, The zenith tropospheric delay is defined as the altitude of the grid points above the Earth's surface. The zenith tropospheric delay is the distance between the surface elevation of the grid points and the elevation of the top isobaric surface. The zenith static delay is the zenith delay above the elevation of the isobaric surface at the top. Since the water vapor content is negligible above this elevation, only the zenith static delay is calculated here, while the zenith wet delay is ignored. The elevation of the top isobaric surface. The ground elevation of the target grid point. Let be the gas constant for dry air. is the gas constant for moist air; , and The refractive index coefficient; This refers to the atmospheric pressure at the top isobaric surface. This represents the gravitational acceleration at the top isobaric surface. Atmospheric temperature, For air pressure, For wetness, This indicates a false temperature.

[0042] It should be noted that the ERA5 reanalysis data is the latest generation of global meteorological reanalysis data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). Covering the period from 1979 to the present, EAR5 boasts high temporal (hourly) and high spatial (approximately 0.25° × 0.25°) resolution, encompassing various meteorological variables including atmospheric, surface, and radiation data. The data is generated by assimilating observations from satellites, ground-based systems, balloons, and numerical models, exhibiting global consistency and long-term series characteristics, and is widely used in meteorological research, climate analysis, and hydrological simulation.

[0043] ERA5 data is divided into surface layer data and isobaric surface layer data. The surface layer mainly includes surface variables such as surface temperature and humidity, while the isobaric surface layer data contains three-dimensional atmospheric fields of 37 standard pressure layers (from 1000 hPa to 1 hPa). The zenith tropospheric delay grid calculated from the above data has a time resolution of 1 hour and a spatial resolution of 0.25°×0.25°.

[0044] III. The process of obtaining the geospatial features of GNSS stations and target grid points is as follows:

[0045] The elevation, slope, aspect, surface roughness index, and normalized vegetation index of GNSS stations and target grid points are calculated based on high-resolution digital elevation model (DEM) data.

[0046] The calculation formulas for slope, aspect, and surface roughness are expressed as follows:

[0047] ;

[0048] Where Slope is the slope and Aspect is the slope aspect; Slope-related surface roughness; The elevation change rate in the x-direction; y represents the elevation change rate in the y direction; i represents the index, corresponding to a single sampling point or grid cell; N represents the total number of sampling points.

[0049] Simultaneously, the Normalized Difference Vegetation Index (NDVI) at GNSS stations and target grid points is acquired.

[0050] The normalized vegetation index (NDI) at GNSS stations and target grid points is derived from the NDI product of the Moderate Resolution Imaging Spectroradiometer (MODIS).

[0051] After obtaining the above data, a dataset containing GNSS station and target grid point zenith tropospheric delay and geospatial feature information is constructed. This dataset is used as a training dataset for training the model in step 2 below.

[0052] Step 2. Construct a rapid generation model for regional tropospheric delay grids that is adaptive to terrain and GNSS station network. This model includes a GNSS station feature extraction module, a target grid point feature extraction module, and a GNSS station-to-grid point mapping module.

[0053] The model's inputs are the zenith tropospheric delay of the GNSS station and the geospatial features of the GNSS station and the target grid point. The model's output is the zenith tropospheric delay of the target grid point (numerical model).

[0054] The GNSS station feature extraction module is used to realize a high-dimensional representation (node ​​feature representation) of the original GNSS station input data, including station coordinates, station topography, and station tropospheric delay data, to obtain node features.

[0055] like Figure 2 As shown, the GNSS station feature extraction module adopts a dual-branch feature extraction structure. Specifically, the dual-branch feature extraction structure includes a first feature extraction branch and a second feature extraction branch.

[0056] The input to the first feature extraction branch is the coordinates of the GNSS station and the terrain attributes.

[0057] The input to the first feature extraction branch is first processed by graph batching, and then the station coordinates and terrain attributes after graph batching are mapped into a high-dimensional geospatial feature vector through a neural network via geospatial feature embedding.

[0058] Graph batching does not directly extract features, but it acts as a bridge in the processing of station features. It transforms the features of stations (nodes) within a batch from a sparse splicing form into a dense aligned tensor.

[0059] Graph batching involves determining the batch size and the number of nodes per sample, finding the node count of the longest sample, cyclically filling each sample node and marking valid nodes using a mask, and finally generating aligned node features and node masks.

[0060] The batch processing steps for this image can:

[0061] A unified structure facilitates batch processing, transforming irregular node data into regular tensors, enabling the model to process the entire batch in parallel on the GPU at once;

[0062] Provide a mask marker to clearly distinguish which stations are real and which are filled, which can be directly used as the key-padding mask in the subsequent attention layer.

[0063] No information is lost; the true node features of each sample are preserved intact, with only zeros padded for alignment.

[0064] It supports dynamic sample node counts, does not require a fixed number of stations for each sample, and offers high data flexibility, making it the fundamental mechanism for achieving GNSS station network self-adaptation.

[0065] Geospatial feature embedding is a process that maps the station coordinates (latitude and longitude) and terrain attributes (elevation, slope, aspect, surface roughness, and NDVI) after batch processing of maps into a highly expressive vector representation through a neural network.

[0066] Among them, station latitude and longitude embedding can encode geographic coordinates into spatial location features, enabling the model to distinguish between "adjacent" and "far away" stations; terrain embedding enables the model to capture the environmental semantics of the surface at that location, such as mountainous areas, plains, NDVI differences, etc.; feature fusion is based on a gating mechanism to fuse station location and terrain information to form a comprehensive geospatial representation.

[0067] When the model migrates to a new region (with different GNSS station distributions and terrain environments), geospatial feature embedding enables the model to construct similar spatial semantics using geographical features, automatically adapting to the new spatial environment and achieving terrain adaptation and GNSS station network adaptation. For example... Figure 3 As shown, the geospatial feature embedding process is as follows:

[0068] The input for geospatial feature embedding is the station coordinates and terrain attributes after batch processing of the map; where the station coordinates are the station's latitude and longitude, and the station's terrain attributes include elevation, slope, aspect, surface roughness, and NDVI.

[0069] First, the station coordinates, i.e., the station's latitude and longitude information, are processed through a single-layer fully connected network to extract the station's latitude and longitude features. Then, the extracted station latitude and longitude features are encoded with location codes to obtain the location feature vector.

[0070] Simultaneously, the terrain attribute information of the measuring station is processed by a multilayer perceptron network to obtain a terrain feature vector;

[0071] By fusing the station location feature vector and the terrain feature vector based on the gating mechanism, a high-dimensional geospatial feature vector is obtained.

[0072] The second feature extraction branch is used to extract tropospheric delay features from the station. It includes neighborhood feature aggregation based on graph attention network, sparse node linear mapping, and graph batching to generate a high-dimensional tropospheric delay feature representation.

[0073] The input to the second feature extraction branch is the station's (node's) tropospheric delay and the sparse spatial graph topology (edge ​​index). The edge index is constructed using the k-nearest neighbor method based on the station's coordinates (latitude and longitude). Specifically:

[0074] For each station (node), calculate the geographical distance between the node and the other nodes (stations), and select the k stations closest to the current node as neighboring nodes. Add edges to each neighboring node to form a connection relationship.

[0075] Since each node is connected to only k neighbors, rather than having full connections with all nodes, the resulting graph topology is a sparse spatial graph topology. "Sparse" here refers to the sparseness of connections between nodes, meaning the number of edges is much smaller than the number of edges required for fully interconnected nodes, thus significantly reducing computational complexity and highlighting local spatial dependencies.

[0076] The information input to the second feature extraction branch first passes through a graph attention network, which is based on a sparse spatial graph topology constructed from the latitude and longitude of the station and adaptively aggregates node features within the neighborhood.

[0077] like Figure 2 As shown, the graph attention network further processes the sparse spatial topology by calculating the feature correlation between each node and its neighboring nodes (such as the similarity of tropospheric delay features) to obtain learnable attention weights, thereby achieving adaptive weighted aggregation of neighborhood features and extracting node representations that fuse local spatial dependencies.

[0078] Specifically, the processing steps of graph attention networks are as follows:

[0079] I. Apply a linear mapping to the tropospheric delay at the nodes, as shown in the following formula:

[0080] ;

[0081] in Represents each node, Represents the original features of the node. Indicates weight, This represents the features after projection.

[0082] II. Calculate the unnormalized attention score using the following formula:

[0083] ;

[0084] in Representative node Attention score for neighbor j;

[0085] Representative node Concatenation with the feature vector of neighbor j Represents a node The set of neighbors is determined by the k-nearest neighbor method. This is a learnable parameter vector used to calculate the attention score. It is a non-linear activation function.

[0086] III. Normalize the attention weights for neighbors, as shown in the following formula:

[0087] ;

[0088] in For normalized attention weights, node all The sum of the indexed scores of the neighbors.

[0089] IV. Weighted aggregation of neighbor features, as shown in the following formula:

[0090] ;

[0091] in Representative node Updated features Represents the characteristics of neighboring nodes.

[0092] After aggregation, to fuse the multi-head attention outputs and unify the feature dimensions, a sparse node linear mapping layer is applied to the sparse node features output by the graph attention network. This maps the high-dimensional features after multi-head concatenation to a fixed hidden dimension, achieving feature dimensionality reduction and representation compression. Subsequently, the features output after the sparse node linear mapping are processed by graph batching (graph batching fills the sparse node features of different samples within a batch into a dense tensor of a fixed size and generates a node validity mask so that subsequent cross-attention modules can align the input dimensions), resulting in the tropospheric delay feature vector.

[0093] The high-dimensional geospatial feature vector obtained above is added to the tropospheric delay feature vector to obtain node tokens. These node tokens are used as the key / value pairs in the cross-attention mechanism described below and are queried by the grid tokens to realize information propagation from nodes to grid points.

[0094] In the cross-attention mechanism, grid tokens are used as queries to "query" node tokens, which contain tropospheric delay information.

[0095] The target grid point feature extraction module is used to perform geospatial feature embedding operations to obtain grid point features.

[0096] Target grid point feature extraction only requires performing geospatial feature embedding to obtain grid point feature representations (grid tokens). The geospatial feature embedding process is the same as the geospatial feature embedding process described above, and will not be repeated here.

[0097] The GNSS station-to-grid point mapping module achieves the mapping from GNSS stations to grid points through cross-attention. The grid point features are used as query Q, and information is learned from the node feature keys K / values ​​V. Then, through nonlinear transformations such as residual connection, layer normalization, and feedforward network, the zenith tropospheric delay information of the target grid point is generated.

[0098] like Figure 4 As shown, in this embodiment, the inputs to the cross-attention mechanism are the node feature vector and the grid point feature vector obtained by the GNSS station feature extraction module and the target grid point feature extraction module, respectively. The processing procedure is as follows:

[0099] I. Generate queries, keys, and values.

[0100] Using grid point features as query input, a linear transformation is performed to generate the (Query, Q) required for attention calculation. Using node features as key / value input, a linear transformation is performed to generate the key (Key, K) and value (Value, V) required for attention calculation. Each attention head has an independent Q, K, and V linear mapping to capture feature correlations in different subspaces.

[0101] II. Calculate the attention score.

[0102] First, calculate the basic attention score, which is the dot product of Q and K for each head.

[0103] For the h-th attention head, given the query matrix Bond matrix The formula for calculating the basic attention score is as follows:

[0104] ;

[0105] in, For each dimension of attention head, The basic attention score matrix of the h-th attention head.

[0106] Next, the structural mask (bias) is calculated in the same way as the basic attention score, but the input is not Q and K, but the original node feature vector and grid point feature vector. This represents the prior correlation between the grid point and each station node, and serves as the prior attention weight to help the model pay more attention to locally related nodes. The formula is expressed as follows:

[0107] ;

[0108] in, For grid feature representation vectors, The node feature representation vector. This is a structural bias.

[0109] The node mask generated by graph batching is used again to directly overwrite the values ​​of the invalid nodes in the structural bias matrix with negative infinity, so as to ensure that these positions do not participate in attention weighting in subsequent softmax calculations.

[0110] Finally, the structural bias (effective nodes) is added to the basic attention score to obtain the final attention score matrix for each head.

[0111] ;

[0112] ;

[0113] in, For the structural bias after padding masking, the first The structural bias or structural mask value of each grid token relative to the j-th node token. The final attention score matrix for the h-th head.

[0114] III. Calculate the multi-head attention weights.

[0115] Perform softmax along the K-dimensional axis on the attention score matrix for each head to obtain the attention weights. This attention weight is used for weighted aggregation of node features, and its specific formula is as follows:

[0116] ;

[0117] The role of Softmax is to convert the "Q-K similarity" into a normalized "probability distribution of attention weights".

[0118] IV. Multi-headed attention output.

[0119] Each head uses the attention weight to perform a weighted summation on V to obtain its own head output. The outputs of all attention heads are concatenated and mapped back to the hidden dimension through the output linear layer to form the final multi-head cross-attention output.

[0120] ;

[0121] .

[0122] in, The weighted output of the h-th head The value of the h-th head. This means concatenating the outputs of all attention heads. The output is a linear transformation matrix, which is the linear mapping result after concatenating all the heads.

[0123] V. Feature enhancement.

[0124] The output of the multi-head attention is processed through residual connections, layer normalization, and feedforward network nonlinear transformation to achieve nonlinear feature enhancement and training stability, and finally generate zenith tropospheric delay information of the target grid points.

[0125] Step 3. Train the regional tropospheric delay grid rapid generation model based on the training dataset, and use the trained regional tropospheric delay grid rapid generation model to realize the rapid generation of zenith tropospheric delay information of target grid points.

[0126] During model training, the zenith tropospheric delay of GNSS stations in the training dataset, as well as the geospatial features of GNSS stations and target grid points, are used as inputs to the model, with the zenith tropospheric delay of the target grid points serving as the label.

[0127] Among the geospatial features, latitude, longitude, elevation, slope, and aspect are constant features, while the normalized vegetation index is updated every 16 days, so they can all be prepared in advance; the zenith tropospheric delay of the GNSS station can be obtained in real time by step 1. Therefore, after preparing the above input data, the model can quickly generate the zenith tropospheric delay information of the target grid point.

[0128] The training and optimization process of the terrain-adaptive regional tropospheric delayed grid rapid generation model is as follows:

[0129] I. Dataset Partitioning:

[0130] The entire dataset is divided into a training set, a validation set, and a test set. The training set is used to learn the model parameters, the validation set is used to tune hyperparameters and monitor the model's generalization ability, and the test set is used to evaluate the model's performance.

[0131] II. Setting model hyperparameters:

[0132] Set the model training learning rate to 0.001 and the number of iterations to 1000.

[0133] III. Define the loss function With the optimizer:

[0134] In the above model, the optimizer uses AdamW, and the loss function integrates the mean squared error and the KL divergence constraint, applying the following formula:

[0135] ;

[0136] in For the number of grid points, For grid point labels, For the true value, For predicted values, For the real mesh in the first Normalized probability of each grid point For predicting the grid in the 1st The probability of each grid point; This is a scaling factor that controls the contribution of KL divergence to the loss.

[0137] IV. Iterate through the entire training set:

[0138] Each iteration includes inputting the training dataset into the model to calculate the predicted value, calculating the loss based on the predicted value and the true value, backpropagating to calculate the gradient of the loss function with respect to each parameter, updating the model weights based on the gradient, clearing the gradient to zero and accumulating the loss value, repeating the above process until the validation set loss no longer decreases within a certain number of consecutive epochs, at which point training is stopped early.

[0139] Once the model is trained, the zenith tropospheric delay of the GNSS station and the geospatial features of the GNSS station and the target grid point are input into the trained model, and the model generates the zenith tropospheric delay information of the target grid point.

[0140] Specifically, prepare geospatial feature information such as latitude, longitude, elevation, slope, aspect, and normalized vegetation index of GNSS stations and target grid points to quickly obtain the zenith tropospheric delay of GNSS stations; after preparing the above input data, input it into the pre-trained model to quickly generate the zenith tropospheric delay information of the target grid points.

[0141] Example 2

[0142] This embodiment 2 describes a rapid generation system for regional tropospheric delayed grids, which is based on the same inventive concept as the rapid generation method for regional tropospheric delayed grids in embodiment 1 above.

[0143] In this embodiment, the regional tropospheric delayed grid rapid generation system includes a computer device; wherein the computer device includes a memory and a processor; a computer program is stored in the memory; when the processor executes the computer program, it is used to implement the steps of the regional tropospheric delayed grid rapid generation method as described in Embodiment 1 above.

[0144] This invention can quickly acquire high-precision tropospheric delay grids for target areas and more accurately capture small-scale variations in tropospheric delay in complex terrain regions, which is of great significance for enhancing real-time precision positioning performance under complex terrain conditions.

[0145] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for rapid generation of regional tropospheric delayed grids, characterized in that, Includes the following steps: Step 1. Obtain zenith tropospheric delay and geospatial feature information of GNSS stations and target grid points within the target area to construct a training dataset for model training in Step 2 below; Step 2. Construct a rapid generation model for regional tropospheric delayed grids that is adaptive to terrain and GNSS station network, which includes a GNSS station feature extraction module, a target grid point feature extraction module, and a GNSS station-to-grid point mapping module; The GNSS station feature extraction module is used to realize a high-dimensional representation of the original GNSS station input data, including station coordinates, station topography, and station tropospheric delay data, to obtain node features. The target grid point feature extraction module is used to perform geospatial feature embedding operations to obtain grid point features; The GNSS station-to-grid point mapping module achieves the mapping from GNSS stations to grid points through cross attention. The grid point features are used as query Q, and information is learned from the node feature key K / value V to generate the zenith tropospheric delay information of the target grid point. Step 3. Train the regional tropospheric delay grid rapid generation model based on the training dataset, and use the trained regional tropospheric delay grid rapid generation model to realize the rapid generation of zenith tropospheric delay information of target grid points; During model training, the zenith tropospheric delay of GNSS stations in the training dataset, as well as the geospatial features of GNSS stations and target grid points, are used as inputs to the model, with the zenith tropospheric delay of the target grid points serving as the label.

2. The method for rapid generation of regional tropospheric delayed grids according to claim 1, characterized in that, In step 1, the geospatial feature information includes the latitude and longitude of the GNSS station, the terrain and the latitude and longitude of the target grid point, and the terrain attributes include elevation, slope, aspect, surface roughness index and normalized vegetation index (NDVI).

3. The method for rapid generation of regional tropospheric delayed grids according to claim 1, characterized in that, In step 2, the GNSS station feature extraction module adopts a dual-branch feature extraction structure; The input to the first feature extraction branch is the coordinates of the GNSS station and the terrain attributes; The input to the first feature extraction branch is first processed by graph batching, and then the station coordinates and terrain attributes after graph batching are mapped into a high-dimensional geospatial feature vector through a neural network via geospatial feature embedding. The input to the second feature extraction branch is the station (node) tropospheric delay and the sparse spatial graph topology (edge ​​index); the edge index is constructed using the k-nearest neighbor method based on the station coordinates (latitude and longitude information). The information input to the second feature extraction branch first passes through a graph attention network, which is based on a sparse spatial graph topology constructed from the latitude and longitude of the station and adaptively aggregates node features within the neighborhood. After aggregation, a sparse node linear mapping layer is applied to the sparse node features output by the graph attention network; Subsequently, the features output after linear mapping of sparse nodes are processed by graph batching to obtain tropospheric delayed feature vectors; The node features are obtained by adding the high-dimensional geospatial feature vectors obtained above to the tropospheric delay feature vectors.

4. The method for rapid generation of regional tropospheric delayed grids according to claim 3, characterized in that, In step 2, the geospatial feature embedding process is as follows: The input for geospatial feature embedding is the station coordinates and terrain attributes after batch processing of the map; the station coordinates are the station's latitude and longitude, and the station's terrain attributes include elevation, slope, aspect, surface roughness, and normalized difference vegetation index (NDVI). First, the station coordinates, i.e., the station's latitude and longitude information, are processed through a single-layer fully connected network to extract the station's latitude and longitude features. Then, the extracted station latitude and longitude features are encoded with location codes to obtain the location feature vector. Simultaneously, the terrain attribute information of the measuring station is processed by a multilayer perceptron network to obtain a terrain feature vector; By fusing the station location feature vector and the terrain feature vector based on the gating mechanism, a high-dimensional geospatial feature vector is obtained.

5. The method for rapid generation of regional tropospheric delayed grids according to claim 3, characterized in that, The edge index is constructed based on the station coordinates, i.e., latitude and longitude information, using the k-nearest neighbor method, specifically as follows: For each station (node), calculate the geographical distance between the node and the other nodes (stations), and select the k stations closest to the current node as neighboring nodes. Add edges to each neighboring node to form a connection relationship. Since each node is connected to only k neighbors, the resulting graph topology is a sparse spatial graph topology.

6. The method for rapid generation of regional tropospheric delayed grids according to claim 3, characterized in that, In step 2, the specific processing procedure of the graph attention network is as follows: I. Apply a linear mapping to the tropospheric delay at the nodes, as shown in the following formula: ； in Represents each node, Represents the original features of the node. Indicates weight, Represents the features after projection; II. Calculate the unnormalized attention score using the following formula: ； in Representative node Attention score for neighbor j; Representative node Concatenation with the feature vector of neighbor j, Represents a node The set of neighbors is determined by the k-nearest neighbor method. This is a learnable parameter vector used to calculate the attention score. It is a non-linear activation function; III. Normalize the attention weights for neighbors, as shown in the following formula: ； in For normalized attention weights, node all The sum of the indexed scores of the neighbors; IV. Weighted aggregation of neighbor features, as shown in the following formula: ； in Representative node Updated features Represents the characteristics of neighboring nodes.

7. The method for rapid generation of regional tropospheric delayed grids according to claim 1, characterized in that, In step 2, the process of handling cross-attention is as follows: I. Using grid point features as query input, a linear transformation is performed to generate Q, which is required for attention calculation. Using node features as key / value input, a linear transformation is performed to generate key K and value V, which are required for attention calculation. Each attention head has an independent Q, K, and V linear mapping to capture feature correlations in different subspaces; II. First, calculate the basic attention score, which is the dot product of Q and K for each head; Next, the structural bias is calculated in the same way as the basic attention score, but the input is not Q and K, but the original node feature vector and grid point feature vector. The node mask generated by graph batching is used again to directly overwrite the values ​​of the invalid nodes in the structural bias matrix with negative infinity, so as to ensure that these positions do not participate in attention weighting in subsequent softmax calculations. Finally, the structural bias is added to the basic attention score to obtain the final attention score matrix for each head; III. Perform softmax along K dimensions on the attention score matrix of each head to obtain the attention weights; IV. Each head uses the attention weight to perform a weighted summation on V to obtain its own head output. The outputs of all attention heads are concatenated and mapped back to the hidden dimension through the output linear layer to form the final multi-head cross-attention output. V. The output of the multi-head attention is processed through residual connections, layer normalization, and feedforward network nonlinear transformation to achieve nonlinear feature enhancement and training stability, and finally generate zenith tropospheric delay information of the target grid points.

8. The method for rapid generation of regional tropospheric delayed grids according to claim 1, characterized in that, In step 3, the following loss function is defined. : ； in For the number of grid points, For grid point labels, For the true value, For predicted values, For the real mesh in the first Normalized probability of each grid point For predicting the grid in the 1st The probability of each grid point This is the scaling factor.

9. The method for rapid generation of regional tropospheric delayed grids according to claim 1, characterized in that, In step 3, after the model is trained, the zenith tropospheric delay of the GNSS station and the geospatial feature information of the GNSS station and the target grid point are input into the trained model, and the model generates the zenith tropospheric delay information of the target grid point.

10. A system for rapidly generating regional tropospheric delayed grids, comprising a computer device; wherein the computer device includes a memory and a processor; and a computer program is stored in the memory; characterized in that, When the processor executes the computer program, it implements the steps of the method for rapid generation of regional tropospheric delayed grids as described in any one of claims 1 to 9.

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