ZTD prediction method based on graph machine learning and multi-parameter separation

Abstract

The invention discloses a ZTD prediction method based on graph machine learning and multi-parameter separation, and the method comprises the steps: firstly extracting historical meteorological data of a plurality of target observation points, and carrying out the preprocessing of the historical meteorological data; calculating ZHD and ZWD of corresponding epoch moments by using the preprocessed meteorological data; firstly, a Saastamoinen model is utilized to calculate highly uniform atmospheric delay, a PWV inversion model and an empirical exponential function are utilized to calculate a ZWD value with uniform height, and finally, an inverse distance interpolation method is utilized to construct a mesh diagram of ZWD and ZHD. A pre-trained MM-FGCN graph neural network is constructed; extracting meteorological data of a to-be-predicted observation point to obtain a ZTD reference true value of the to-be-predicted point; and taking the constructed ZWD and ZHD mesh diagrams as input, respectively predicting to obtain ZWD and ZHD predicted values, adding the ZWD and ZHD predicted values, and calculating and combining to obtain a ZTD value. Therefore, the accuracy, the real-time performance and the area coverage range of the ZTD prediction are obviously improved.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation atmospheric delay modeling and spatial data analysis, and in particular to a ZTD prediction method based on graph machine learning and multi-parameter separation. Background Art

[0002] Zenith Total Delay (ZTD) is a very important parameter in the meteorology of the Global Navigation Satellite System (GNSS). It indicates the signal propagation delay caused by the refraction effect of the atmosphere when the satellite signal passes through the atmosphere from the satellite to the receiver, and directly affects the accuracy of the GNSS system. At the same time, ZTD not only directly affects the accuracy of the GNSS system, but can also be used to invert the water vapor content in the atmosphere and provide reference information for meteorological forecasts. Therefore, a high-precision zenith total delay (ZTD) prediction method based on spatial correlation and parameter separation prediction is proposed and established, which can not only improve the real-time inversion accuracy of atmospheric water vapor content, but also provide reliable data support for meteorological forecasting, climate monitoring and GNSS precise positioning. It is one of the current problems to be solved in ZTD prediction.

[0003] At present, there are two main types of zenith total delay (ZTD) prediction methods. The first type of method is a traditional statistical method based on time series, which mainly relies on the historical data of ZTD for time correlation analysis. This type of method uses the time trend of ZTD for prediction. Although it can obtain relatively stable prediction results in the short term in the time dimension, it ignores the spatial variation characteristics of ZTD and is difficult to achieve accurate spatial prediction in a large range. It has strong regionality and low prediction accuracy when water vapor changes rapidly, which cannot meet the needs of meteorological forecasting for real-time and regional prediction. The second type of method is a ZTD prediction method based on numerical weather forecast models. This type of method predicts the water vapor content and atmospheric delay in the atmosphere through atmospheric physical models, and can predict ZTD in a large area with high temporal and spatial resolution. However, this type of method relies heavily on atmospheric models and initial conditions, and has high computational complexity. It is easily limited by model errors and computing resources, especially under complex terrain and severe weather conditions, and the prediction accuracy is affected. In recent years, with the development of artificial intelligence, more and more studies have used machine learning algorithms to predict ZTD. This type of method captures the spatiotemporal characteristics of ZTD by training models and improves the prediction accuracy to a certain extent. However, existing methods often only focus on the temporal correlation of ZTD and ignore its spatial correlation, resulting in reduced prediction accuracy within the regional scope. In addition, existing machine learning models usually directly predict ZTD as a whole, failing to distinguish between the relatively fluctuating part of ZWD (Zenith Wet Delay) and the relatively stable part of ZHD (Zenith Hydrostatic Delay), which also affects the final prediction accuracy and computational efficiency. At the same time, most existing ZTD prediction methods are limited to predictions at specific points, making it difficult to accurately predict the delay at any point in the entire region. Therefore, studying algorithms that take into account the spatial correlation of ZTD, distinguish the different change characteristics of ZWD and ZHD, and can efficiently predict any point in the region can not only effectively solve the shortcomings of existing methods in regional prediction accuracy and efficiency, but also meet the requirements of ZTD prediction in terms of temporal and spatial resolution, improve the accuracy, real-time and stability of predictions, and provide strong technical support for applications such as meteorological forecasting, precise positioning and climate monitoring. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a ZTD prediction method based on graph machine learning and multi-parameter separation, a high-precision zenith total delay regional prediction method based on spatial correlation input, ZWD and ZHD separation training, and a combination of inverse distance interpolation and graph neural network. This method can effectively overcome the problems of low prediction accuracy and low efficiency caused by ignoring ZTD spatial correlation, differences in ZWD and ZHD characteristics, and inaccurate interpolation within the region, thereby significantly improving the accuracy, real-time performance and regional coverage of ZTD prediction.

[0005] In order to solve the above technical problems, the technical solution of the present invention is: A ZTD prediction method based on graph machine learning and multi-parameter separation includes the following steps: Step 1: Establish a database of reference values ​​for the zenith total delay.

[0006] The original meteorological data of several target stations were downloaded using the global data officially provided by ERA5 (ECMWF Reanalysis 5th Generation), mainly including surface pressure, precipitable water vapor (PWV), surface temperature and other original meteorological data, and the ZHD and ZWD at the corresponding epoch were calculated. The above information was stored separately as ZWD and ZHD according to the sub-stations. First, in order to solve the error problem caused by the ZTD composition, the Saastamoinen model and the PWV inversion model were used to extract the composition parameters of ZTD and separate the ZWD and ZHD parameters. In order to solve the problem of missing data, the method based on the interpolation algorithm was used to fill the missing data to reduce the impact of incomplete data on subsequent processing. For missing data within a smaller time range, the average method was used to restore the signal trend; for missing data within a larger time range, the linear interpolation method was used for reconstruction to fill the missing data with the information of neighboring observation points.

[0007] Step 2: Regional ZWD prediction method based on spatial correlation input and graph machine learning interpolation.

[0008] The original meteorological data of several target stations were downloaded using the global data officially provided by ERA5, mainly including surface pressure, precipitable water volume (PWV), surface temperature and other original meteorological data. The above information was stored separately by regional stations, and the PWV inversion model was used to separate the constituent parameters of ZTD, retaining the ZWD parameters. In view of the large nonlinear and rapid change characteristics of ZWD, the MM-FGCN graph neural network was used for time series modeling and prediction to capture the temporal change characteristics in ZWD and improve the computational efficiency and prediction accuracy. Secondly, the trained prediction model was used to predict each observation station separately to obtain the ZWD prediction value of each station. Since the number of selected stations is small and the distance between stations is close, the inverse distance interpolation method has a high accuracy in interpolating the area between nodes, thereby ensuring that a high-precision ZWD prediction value can be obtained at any location in the entire region. Finally, after obtaining the ZWD data of the known station and the regional interpolation ZWD, all observation stations and interpolated data are represented as a graph structure, where the nodes represent the values ​​of the observation stations and the edges represent the spatial distance and similarity between adjacent stations. The MM-FGCN graph neural network is used to train the graph to capture the spatial correlation and complex relationships between nodes. The MM-FGCN graph neural network is used to predict the ZWD value of each node to obtain the ZWD prediction value of the observation point and interpolation point in the region. Thus, a spatial ZWD prediction distribution dot map is obtained.

[0009] Step 3: Regional ZHD prediction method based on spatial correlation input and graph machine learning interpolation.

[0010] The original meteorological data of several target stations were downloaded using the global data officially provided by ERA5, mainly including surface pressure, surface temperature and other original meteorological data. The above information was stored separately by regional stations, and the Saastamoinen model was used to extract the constituent parameters of ZTD and separate the ZHD parameters. For relatively stable ZHD, a shallow neural network model was used for modeling and prediction, thereby improving the computational efficiency and prediction accuracy. Secondly, the trained prediction model was used to predict each observation station separately to obtain the ZHD prediction value of each station. Since the number of selected stations was small and the stations were close to each other, the inverse distance interpolation method had a high accuracy in interpolating the area between nodes, thereby ensuring that a high-precision ZHD prediction value could be obtained at any location in the entire region. Finally, after obtaining the ZHD data of the known stations and the regional interpolation ZHD, all observation stations and interpolated data were represented as a graph structure, in which nodes represented observation stations and edges represented the spatial distance and similarity between adjacent stations. The MM-FGCN graph neural network was used to train the graph to capture the spatial correlation and the complex relationship between nodes. The MM-FGCN graph neural network is used to predict the ZHD value of each node, and the ZHD prediction values ​​of the observation points and interpolation points in the region are obtained, thereby obtaining a spatial ZHD distribution dot map.

[0011] Step 4: ZTD prediction based on ZWD and ZHD separate training.

[0012] Combined with the measurement results of the second and third steps, the ZWD and ZHD data of each regional point are added to obtain the combined ZTD value, forming a ZTD regional map as the final ZTD data regional prediction map, thereby improving the accuracy, stability and prediction range of the measurement results.

[0013] After being processed by the above-mentioned regional ZTD prediction algorithm, the problems of small ZTD prediction range and low accuracy caused by the existing methods, such as only considering the temporal correlation of ZTD and ignoring the spatial correlation; merging the prediction of ZTD and ignoring the differences in ZTD constituent parameters; and only being able to predict points but not graphs, can be effectively solved. This effectively improves the real-time, accuracy and stability of ZTD prediction, and provides guarantee for PWV data inversion and meteorological forecasting.

[0014] In the above technical solution, data input within the adjacent spatial range is used, combined with high-order graph convolution operations to eliminate the influence of local irrelevant spatial noise, make full use of spatial correlation, and improve the accuracy of ZTD prediction. At the same time, in view of the different change characteristics of ZWD and ZHD, a deep learning model is used to perform multi-layer training processing on ZWD, and a few-layer training is performed on ZHD to improve computational efficiency and prediction accuracy. The network points are constructed using the inverse distance interpolation method, and high-precision predictions are made for any point in the entire area through the interpolation strategy to ensure the arbitrariness of spatial selection. The MM-FGCN graph neural network is used to aggregate and predict node features based on the node results of the interpolation graph to improve the accuracy and stability of ZTD prediction in the region. Finally, the present invention can effectively solve the problems of existing methods ignoring spatial correlation, failing to separate the characteristics of ZWD and ZHD, and failing to make predictions in any area, significantly improving the overall accuracy and real-time performance of ZTD predictions, and meeting the needs of fields such as weather forecasting, precise positioning, and climate monitoring.

[0015] The present invention has the following characteristics and beneficial effects: The above technical solution is used to make high-precision predictions of the zenith total delay (ZTD) in the region using the existing ERA5 data. Compared with the existing method of ZTD prediction using only time series, it can not only solve the problem of limited prediction accuracy and difficulty in capturing spatial correlation in the region, but also achieve delay prediction with high spatial resolution in a large range, thus meeting the needs of regional meteorological monitoring and precise positioning. By separately modeling ZWD and ZHD, the accuracy of the model in capturing the rapid changes of atmospheric wet delay can be improved, and the efficiency of model calculation can be improved to ensure stability and efficiency. At the same time, the use of graph neural network (MM-FGCN) combined with inverse distance interpolation method to predict the ZTD of each node in the region can effectively solve the problem that the existing method cannot achieve prediction of any point in the region, and ensure the continuity and coverage of the prediction results in space. Through high-order graph convolution operations combined with adaptive sliding processing, the interference of local spatial noise and outliers on the model is effectively eliminated, which improves the reliability of data and the robustness of model prediction. In view of the problem of missing data at different stations, the method of combining linear interpolation with averaging is adopted to further improve the accuracy and stability of the original data of ZWD and ZHD. At the same time, a reference library is built based on adjacent spatial data and spatial feature learning is performed through MM-FGCN, so that the model can better capture spatial correlation, improve the overall accuracy, real-time and spatial coverage of ZTD prediction, and provide strong technical support for weather forecasting, precise positioning and climate monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0017] Figure 1 4 is a flow chart of calculation of ZWD in an embodiment of the present invention.

[0018] Figure 2 4 is a flow chart of calculation of ZHD in an embodiment of the present invention.

[0019] Figure 3 4 is a calculation flow chart of the ZTD prediction method based on multi-parameter separation in an embodiment of the present invention.

[0020] Figure 4 This is a diagram of the ZHD prediction results of the TCHK site in an embodiment of the present invention.

[0021] Figure 5 This is the ZWD prediction result diagram of the TCHK site.

[0022] Figure 6 This is the ZWD prediction result diagram of the TCHK site. DETAILED DESCRIPTION

[0023] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0024] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0025] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0026] The present invention provides a ZTD prediction method based on graph machine learning and multi-parameter separation, such as Figure 1-3 As shown, the following steps are included: Step 1: extract historical meteorological data of several target observation points and preprocess the historical meteorological data, wherein the historical meteorological data includes surface air pressure, precipitable water, surface air temperature, and the PWV value at the location.

[0027] In this embodiment, the original meteorological data of the target observation points HKKS, HKSS, HKST, and HKQT on the ERA5 website, that is, the longitude and latitudes of 114.1842, 22.2204; 114.1609, 22.2551; 114.1103, 22.2342; 114.1247, 22.1727, are extracted, mainly including surface pressure, precipitable water (PWV), surface air temperature and other original meteorological data, and the ZHD and ZWD of the corresponding epoch time are calculated. Data such as surface pressure, precipitable water (PWV), and surface air temperature can be downloaded directly from the ERA5 website, and the ZHD and ZWD information of the corresponding area can be calculated through the conversion coefficients of surface pressure, precipitable water (PWV), surface air temperature, and PWV. This process is common sense in the field of positioning, and the calculation process will not be listed in detail here. For the convenience of subsequent presentation, the ZHD and ZWD calculated here are used in subsequent steps. , ,in, i Indicates the site number.

[0028] Further, the scope of missing data is determined: If the calculated ZWD (or ZHD) data cannot find a specific value, it is considered that the data for this period is missing. When the missing data exists in a smaller range, it is assumed that the missing data exists in a larger range. Otherwise, it is assumed that the missing data exists in a larger range.

[0029] Missing data are processed according to the size of the missing data. For missing data in a smaller range, the averaging method (adding the values ​​before and after the missing value and averaging them) is used to restore the signal trend; for missing data in a larger range, linear interpolation is used for reconstruction, thereby improving the reliability and stability of the original data by filling the impact of abnormal missing data.

[0030] Linear interpolation is a method of estimating unknown points by linearly varying known data points. and Assuming that the value change is linear, interpolation can be performed using the following formula:

[0031] When interpolating ZWD data, and are two adjacent known points and The value of ZWD at The unknown points to be interpolated The ZWD value at .

[0032] When interpolating ZHD data, and are two adjacent known points and The value of ZHD at The unknown points to be interpolated The ZHD value at .

[0033] Step 2: Calculate the ZHD and ZWD of the corresponding epoch using the preprocessed meteorological data; Step 3: Use the inverse distance interpolation method to construct the mesh structure. This process is mainly divided into three steps. The first step is to determine the position of the interpolation point of the inverse distance interpolation method, the second step is to unify the data height of ZWD and ZHD through empirical formulas, and the third step is to determine the representative meaning of the edge points of the mesh.

[0034] First, determine the position of the interpolation point of the inverse distance interpolation method. The traditional way is to select interpolation points with equal intervals in the position distance, and the overall configuration tends to be the vertices of the standard square. However, in fact, the position of the GNSS station does not necessarily present a good graph shape, so here we select the interpolation points with strong adaptability and conforming to the quadrilateral. In this way, not only can the irregular area points be selected better, but also the prediction of the graph neural network can be taken into account. In this embodiment, in order to better compare the prediction data of the interpolation points and take into account the selection rules of the regional points, the TCHK station (latitude and longitude are 114.1304; 22.2127) is used as the interpolation point for testing.

[0035] Secondly, due to the objective differences in the heights of the stations HKKS, HKSS, HKST, HKQT, and TCHK, which are 44.71m, 38.7m, 258.7m, 5.17m, and 576.83m respectively, the ZWD and ZHD data obtained are not actually data on the same horizontal plane. When constructing the interpolation algorithm and graph structure, the data height should be unified to the same plane. Therefore, we choose to use the Saastamoinen model and the empirical index height conversion model to adjust the data height. The specific process is as follows: The Saastamoinen model is used to calculate the atmospheric delay to adjust the data height of ZWD and ZHD. The ZHD adjustment formula is as follows:

[0036] in, The corresponding height The air pressure at , is the dimension of the observation point, The air pressure changes with altitude The intermediate variable of the change, is the plane air pressure, is the barometric height. The formula for the change of air pressure with height is common in atmospheric science, and the logarithmic decreasing formula is usually used to describe the air pressure. With height The standard formula is as follows:

[0037] in, The sea level pressure is 1013.25hPa. is the barometric altitude, which is 8400 meters.

[0038] For ZWD, since the water vapor pressure varies greatly with altitude, ZWD can be corrected by the following empirical exponential altitude conversion model:

[0039] in, is the ZWD value at the base altitude, is the height The water vapor pressure at is the water vapor pressure at the base altitude. Water vapor pressure at It can be estimated by the empirical formula in the standard atmospheric model. Generally, the water vapor pressure decreases gradually with increasing altitude. Use the following empirical formula to calculate the water vapor pressure at different altitudes:

[0040] is the base height The water vapor pressure under the ground is the data of ground height, is the target height, is the altitude of water vapor pressure, taken as 2000 meters.

[0041] The specific adjustment process can be expressed as follows: the uniform height of all stations is set to the height of the highest station. For stations with different heights, the uniform height is substituted into the height replacement formula. The water vapor pressure and air pressure at different heights are mainly updated to calculate the values ​​of ZWD and ZHD at the same height. The subsequent steps are , ,in, i Indicates the site number.

[0042] Finally, based on the ZWD and ZHD values ​​at the same height obtained in the previous step, the target points were interpolated using the inverse distance interpolation formula to obtain a regional scatter plot of ZWD and ZHD.

[0043] The inverse distance interpolation method is based on the weighted principle of distance, and interpolates the distance between the known point and the target point. It is understandable that the closer the point is, the greater the influence on the target point is. The calculation formula is as follows:

[0044] in, represents the ZHD or ZWD value of the point to be interpolated. is the ZHD or ZWD value at a known point, is the distance between the point to be interpolated and the known point, and is the weighted index, Represents the number of sites used, i Indicates the site number.

[0045] By adjusting the weight index , can more accurately reflect the impact of distance on the interpolation result, thereby improving the interpolation accuracy. A higher value can obtain an interpolation result with higher precision, so in this embodiment a larger distance weight value is selected, that is, , thereby approaching the actual ZTD spatial correlation and improving the reliability and stability of the target point data.

[0046] Through the above process, a highly unified regional scatter plot of ZWD and ZHD can be obtained, but the relationship between edges and points needs to be clearly expressed to form a complete graph structure. Since the inverse distance interpolation method is used in this embodiment when generating points, the definition of node edges follows the distance weight part of the inverse distance interpolation method to represent the spatial distance and similarity between adjacent sites, while the definition of points uses the variable and , represents the ZTD component represented by the station, that is, the value of ZHD or ZWD. After the above steps, at time, a regional graph structure of the ZTD component based on the original data of the surrounding stations can be constructed to improve the spatial correlation of the graph data.

[0047] Step 4: Build an MM-FGCN graph neural network and apply the obtained ZWD and ZHD mesh graphs to perform separate training on the MM-FGCN graph neural network.

[0048] Specifically, the MM-FGCN graph neural network includes a GCN network, a pooling layer, a fully connected layer and a multimodal fusion layer.

[0049] The process can be divided into four steps. The first step is to determine the adaptive sliding window. The second step is model design, which generates time series features for each node and fuses them with graph structure features. The third step is to design a multi-layer GCN (Graph Convolutional Network) to perform graph convolution operations on the fused features. The fourth step is to evaluate the training model and improve the weighted constraint strategy.

[0050] First, we need to determine the node features and the edges and weights between nodes. Each node represents the ZWD data value of a spatiotemporal location (i.e., observation site). Since the ZWD data value has a time series of many years, the feature of each node can be represented as a time series vector ,in Indicates The weight of the edge represents the spatial distance between nodes and the relevance of ZWD data. It can be defined according to the following rules: Weighted spatial distance: The geographical distance between two nodes (locations) , which can be calculated by the inverse of the distance Power multiplication (Inverse distance method for weighting) To indicate that the closer the distance is, the greater the weight between nodes. In the future, to improve the prediction efficiency, an adaptive sliding window is used to divide the ZWD time series of each node into different subsequences. Starting from the initial year, assume that the length of each sliding window is n years, and continue to slide backward until the data of all years is covered. In this embodiment, assume that the length of the sliding window is 5 years, then the first window is , the second window is , and so on. The result of each sliding window forms a new node feature set, recorded as ,in Indicates different sliding window numbers. After the adaptive sliding windows are divided, a graph structure containing ZWD nodes and edges can be constructed, and an adjacency matrix can be generated. . Each element in the matrix Representation Node and nodes The weights between them. So far, the graph adjacency matrix of all nodes is obtained.

[0051] Secondly, since the data of each node has certain time series characteristics, the time series characteristics of each node For feature generation, since we generally have a lot of time data and a long time span when predicting, we use the long short-term memory network (LSTM) here to capture the long-term dependencies in the time series (but not predict), and generate a global node time feature representation. The specific process is to input a data with a shape of [num, sequence_length, feature_dim] (number of samples, sequence length, feature dimension), that is, the time series features of each node, and then output a hidden state vector with a shape of [num_nodes, hidden_dim] (number of nodes, hidden layer dimension). After obtaining the corresponding time series features, in order to improve the feature parameters of the graph, multimodal feature fusion is required to fuse the time series features with the graph structure features, so as to represent the graph structure features of the data without ignoring the time characteristics of the data. This article uses the attention mechanism to fuse parameters. The attention mechanism learns the importance coefficient of each feature in the fusion process and sums each feature according to the weighted importance. This method can capture the complex relationship between features, so that the model can better focus on important features and ignore unimportant parts. The main process is shown as follows: Assume that the spatial characteristics of the graph are , we can define the attention weight of each feature In the following form:

[0052] in Indicates The attention weight of each feature , representing time series characteristics and spatial characteristics respectively), is a learnable vector that maps features to attention scores, is the activation function ReLU, and is a linear transformation matrix used to transform features to the same dimension.

[0053] Then all features are weighted and summed according to the attention weights to obtain the fused feature representation :

[0054] It is the final feature representation after fusion and is also the input of subsequent graph convolution operations.

[0055] Then, through multiple GCN layers, node features and neighbor node features can be gradually aggregated to generate a global node representation. The formula is as follows:

[0056] in represents the output features after graph convolution (node ​​representation), is the weight matrix, H that is H i A general term for learning during the model training process. The superposition of multiple layers of GCN can capture the high-order neighbor information of the node to predict ZWD, but too many layers may lead to over-smoothing problems. Therefore, a graph neural network model with few layers of training is used to predict ZHD data. ZHD is the zenith static delay, which is mainly calculated based on static characteristics such as surface air pressure, latitude and altitude. Therefore, the change of ZHD is obviously more stable than that of ZWD. Therefore, in order to simplify the calculation and improve the prediction accuracy, a few-layer GCN model is used to predict ZHD. In this embodiment, the number of GCN layers for predicting ZWD is set to 7 layers (it is generally recognized that 7 layers are generally more layers, and 3 layers are less layers, so the empirical value is adopted).

[0057] Specifically, in this embodiment, the training steps are as follows: 1. Data preparation: Prepare graph structure data, including node features and the adjacency matrix of the graph.

[0058] 2. Forward propagation: The input data is processed through each layer of the network to obtain the final prediction result.

[0059] 3. Loss calculation: Calculate the loss (such as cross entropy loss or mean squared error) based on the model output and the actual label.

[0060] 4. Back propagation: minimize the loss function, gradient descent.

[0061] 5. Number of training rounds: Update the model parameters through multiple training rounds (epochs) until the training stopping criteria is reached.

[0062] So the main stopping method is to stabilize the loss function.

[0063] Finally, the trained model is used to predict the ZWD value of each node in the graph for the next year. The historical ZWD time series of each node is input into the model to predict its value in the next two years. Figure 5 The final prediction accuracy of the interpolation site TCHK is demonstrated, with good accuracy performance in the prediction data of the past decade. The MAE error is stable at around 5mm, and the ZWD data of the target sites in 2018 and 2019 are basically successfully predicted.

[0064] Specifically, a graph neural network model with few-layer training is used to predict ZHD data. Graph neural network is used for prediction. ZHD is the zenith static delay, which is mainly calculated based on static characteristics such as surface air pressure, latitude and altitude. Therefore, the change of ZHD is obviously more stable than that of ZWD. Therefore, in order to simplify the calculation and improve the prediction accuracy, the simpler GCN model in the graph neural network is used to predict ZHD.

[0065] First, in the data preparation stage, in this embodiment, historical data related to ZHD needs to be collected, including meteorological data of meteorological stations, historical ZHD values ​​of satellite measurement stations, and geographical location information of stations. The connection relationship between each station is defined after step 4, so as to construct the topological structure of the graph based on ZHD data and extract the corresponding node feature matrix. and the normalized adjacency matrix ,in i Represents the site number. The graph convolutional network (GCN) is used to learn the complex relationship between the adjacency matrix and the node feature matrix, so as to predict the graph structure of the future ZHD. In the model structure, the first layer of graph convolution is used to extract the basic features of the node and convert it into a hidden representation. The second layer of graph convolution is used to further aggregate the information of neighboring nodes and output the final feature representation of the node. The final output layer is a fully connected layer that maps the features output by the graph convolution layer to the target variable (ZHD value). The propagation formula for each layer is as follows:

[0066] Since the above signs have been introduced above, they will not be repeated here.

[0067] In the model training stage, in this embodiment, the data set is divided into a training set, a validation set, and a test set. In each training iteration, the node feature matrix and the normalized adjacency matrix Calculate the feature representation of each node, and then use these features to predict ZHD. Use the training set data to update the model parameters, and monitor the performance of the model on the validation set (to see if the validation error is reduced). Use the early stopping strategy, that is, when the error on the validation set no longer decreases, stop training in advance to prevent the model from overfitting. Figure 4 The final prediction accuracy of the ZHD of the interpolation site TCHK is demonstrated, with good accuracy performance in the prediction data of the past decade. The MAE error is stable at around 0.8mm, which is almost negligible compared with the meter-level data unit of ZHD. The ZHD data of the target sites in 2018 and 2019 are basically perfectly predicted.

[0068] Step 5, extract the meteorological data of the observation point to be predicted, and obtain the ZWD and ZHD values ​​of the observation point to be predicted according to steps 1-3, and add them to obtain the ZTD reference true value of the observation point to be predicted; Step 6. Apply the two pre-trained MM-FGCN graph neural networks obtained by separate training, take the mesh graphs of ZWD and ZHD constructed by the inverse distance interpolation method as input, predict the ZWD and ZHD prediction values ​​respectively, then add the ZWD and ZHD prediction values, and combine them to obtain the ZTD value to form a ZTD area map as the final ZTD data area prediction map.

[0069] Furthermore, in this embodiment, the predicted ZTD data is evaluated.

[0070] Specifically, after the model training is completed, the model needs to be fully tested on the test set to evaluate the model's generalization ability on unseen data. The data in the test set basically does not participate in the training and verification of the model, so as to ensure the objectivity and fairness of the model evaluation. During the test, the model will use data that has never been seen before to make predictions, and then compare the predicted values ​​with the true values ​​to calculate various evaluation indicators. In order to measure the performance of the model in steps 4 and 5, this paper uses the mean square error (MSE) and the coefficient of determination ( ) is used as the model evaluation indicator, and the specific formula is as follows:

[0071] in, is the sample data length, is the true value of the sample, is the sample prediction value.

[0072]

[0073] in Represents the sample mean.

[0074] During the model testing process, the above indicators are calculated one by one, and the value of each indicator is output to show the overall performance of the model on the test set, so as to understand the model's graph prediction effect on the sample data.

[0075] Calculate the ZTD data and calculate the relevant model evaluation indicators. ZTD refers to the total zenith delay, which is an important component of the atmospheric delay of the global navigation satellite system (GNSS) and can be further decomposed into two parts: ZHD (zenith static delay) and ZWD (zenith wet delay). Therefore, the specific ZTD value can be obtained by simply adding ZHD and ZWD. The solution formula is as follows:

[0076] By adding the above formula, we can get the final predicted ZTD value, and repeat step 6 to get the corresponding evaluation index. Figure 6 The final prediction accuracy of ZTD of the interpolation site TCHK is demonstrated, which has good accuracy performance in the prediction data of the past decade, and the MAE error is stable at around 4.8mm. It has excellent accuracy performance among the existing prediction methods and has spatial continuity of prediction.

[0077] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A ZTD prediction method based on graph machine learning and multi-parameter separation, characterized in that: The steps include: Step 1, extracting historical meteorological data of several target observation points; Step 2: Calculate the ZHD and ZWD at the corresponding epoch using meteorological data; Step 3, calculate the atmospheric delay with uniform height, then invert the ZWD value through the atmospheric precipitable water, calculate the ZWD value with uniform height, and construct the mesh diagram of ZWD and ZHD according to the ZWD value and the ZWD value with uniform height; Step 4: Build a MM-FGCN graph neural network, and use the obtained ZWD and ZHD mesh graphs to perform separate training on the MM-FGCN graph neural network; Step 5, extract the meteorological data of the observation point to be predicted, and obtain the ZWD and ZHD values ​​of the observation point to be predicted according to steps 1-3, and add them to obtain the ZTD reference true value of the observation point to be predicted; Step 6: Apply a pre-trained MM-FGCN graph neural network obtained by separation training to obtain the final ZTD data area prediction map.

2. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 1, characterized in that: The step 1 also includes preprocessing the historical meteorological data. The preprocessing method for extracting the historical meteorological data is: for missing data in a smaller range, the averaging method is used to restore the signal trend; and for missing data in a larger range, linear interpolation is used for reconstruction.

3. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 2, characterized in that: The method for determining the range of missing data is: If the calculated ZWD and ZHD data cannot find specific values, it is considered that the data for this period is missing. When the missing data is within a smaller range, it is considered that the missing data exists in a smaller range; otherwise, it is considered that the missing data belongs to a larger range.

4. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 2, characterized in that: Linear interpolation is used to calculate the ZHD value at the unknown point to be interpolated.

5. The ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 1, characterized in that: In step 3, for the ZWD and ZHD values ​​at the same height, the target point is interpolated using the inverse distance interpolation method to obtain regional ZWD and ZHD scatter plots, respectively, and then the nodes and edges in the ZWD and ZHD scatter plots are defined, respectively, wherein the definition of the edge follows the distance weight part in the inverse distance interpolation method to represent the spatial distance and similarity between adjacent observation points, and the definition of the point uses the ZWD or ZHD value of the station.

6. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 2, characterized in that: In step 3, the inverse distance interpolation is used to construct the network diagram of ZWD and ZHD, wherein the inverse distance interpolation method is based on the weighted principle of distance, and interpolation is performed through the distance between the known point and the target point. The closer the point is, the greater the influence on the target point.

7. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 1, characterized in that: In step 6, the network diagram constructed according to the ZWD and ZHD values ​​of the observation points to be predicted is used as input, and the ZWD and ZHD prediction values ​​are predicted respectively. Then, the ZWD and ZHD prediction values ​​are added together to obtain the ZTD value, forming a ZTD area diagram as the final ZTD data area prediction diagram.

8. The ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 1, characterized in that: The MM-FGCN graph neural network includes a GCN network, a pooling layer, a fully connected layer and a multimodal fusion layer.

9. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 8, characterized in that: When predicting ZWD and ZHD, in order to improve the reliability of training, the number of GCN network layers for ZWD prediction is set to 7 layers, and a 3-layer GCN network is used for ZHD prediction. At the same time, a high-round prediction of 50 rounds is used for ZWD prediction to ensure that the prediction can achieve the highest accuracy and the data will not be overfitted, while the number of training rounds for ZHD is reduced to 20 rounds to reduce training time.

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