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

Abstract

The present invention discloses a ZTD prediction method based on graph machine learning and multi-parameter separation. First, historical meteorological data of several target observation points is extracted, and the historical meteorological data is preprocessed; the preprocessed meteorological data is used to calculate the ZHD and ZWD at corresponding epoch moments. First, the Saastamoinen model is used to calculate the atmospheric delay with unified height, the PWV inversion model and the empirical exponential function are used to calculate the ZWD value with unified height, and finally the inverse distance interpolation method is used to construct a network graph of ZWD and ZHD; a pre-trained MM-FGCN graph neural network is constructed; the meteorological data of the observation point to be predicted is extracted to obtain the reference true value of ZTD at the point to be predicted; the constructed network graph of ZWD and ZHD is used as the input, and the ZWD and ZHD prediction values are respectively predicted, and then the ZWD and ZHD prediction values are added together to obtain the combined ZTD value. Thus, the accuracy, real-time performance and regional coverage of ZTD prediction are significantly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation atmospheric delay modeling and spatial data analysis, and specifically refers 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 represents 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 also can be used to invert the water vapor content in the atmosphere and provide reference information for meteorological prediction. Therefore, proposing and establishing a high-precision Zenith Total Delay (ZTD) prediction method based on spatial correlation and parameter separation prediction 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. This is one of the urgent problems to be solved in current ZTD prediction.

[0003] Currently, there are mainly two categories of zenith total delay (ZTD) prediction methods. The first category of methods is traditional statistical methods based on time series, which mainly rely on historical data of ZTD for time correlation analysis. These methods use the time trend of ZTD for prediction. Although they can obtain relatively stable prediction results in the short term in the time dimension, due to ignoring the spatial variation characteristics of ZTD, it is difficult to achieve accurate spatial prediction over a large area, has strong regionality, and has low prediction accuracy in the case of rapid water vapor changes, unable to meet the requirements of meteorological forecasts for real-time and regional predictions. The second category of methods is the ZTD prediction method based on numerical weather prediction models. These methods predict the water vapor content and atmospheric delay in the atmosphere through atmospheric physical models and can perform ZTD prediction over a large regional area with high time and spatial resolutions. However, these methods rely heavily on atmospheric models and initial conditions, and have high computational complexity, and are easily restricted by model errors and computing resources. Especially under complex terrain and severe weather conditions, the prediction accuracy is affected. In recent years, with the development of artificial intelligence, more and more research has used machine learning algorithms to predict ZTD. These methods capture the spatio-temporal characteristics of ZTD by training models and improve the prediction accuracy to a certain extent. However, existing methods often only focus on the time correlation of ZTD and ignore its spatial correlation, resulting in a reduction in prediction accuracy within the regional scope. In addition, existing machine learning models usually directly perform overall prediction on ZTD, failing to distinguish the part with large fluctuations 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 the prediction of specific points and are difficult to accurately predict the delay at any point within the entire region. Therefore, researching an algorithm that takes into account the spatial correlation of ZTD, distinguishes the different variation characteristics of ZWD and ZHD, and can efficiently predict any point within the region can not only effectively solve the deficiencies of existing methods in regional prediction accuracy and efficiency, but also meet the requirements of ZTD prediction in terms of time and spatial resolutions, improve the accuracy, real-time performance, and stability of prediction, 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 deficiencies of the prior art, the present invention proposes a ZTD prediction method based on graph machine learning and multi-parameter separation, which is a high-precision zenith total delay regional prediction method based on spatial correlation input, separate training of ZWD and ZHD, and combination of inverse distance interpolation method and graph neural network. This method can effectively overcome the problems of low prediction accuracy and low efficiency caused by ignoring the spatial correlation of ZTD, the characteristic differences between ZWD and ZHD, and inaccurate interpolation within the region, thus significantly improving the accuracy, real-time performance and regional coverage of ZTD prediction.

[0005] To solve the above technical problems, the technical solution of the present invention is as follows:

[0006] A ZTD prediction method based on graph machine learning and multi-parameter separation, comprising the following steps:

[0007] The first step: Establish a zenith total delay reference value database.

[0008] Download the original meteorological data of several target sites using the global data provided by ERA5 (ECMWF Reanalysis 5th Generation) official, mainly including original meteorological data such as surface air pressure, precipitable water vapor (PWV), surface air temperature, etc., and calculate the ZHD and ZWD at the corresponding epoch moments. Store the above information separately by site and by ZWD and ZHD. First, for the error problem caused by the composition of ZTD, the Saastamoinen model and the PWV inversion model are used to extract the composition parameters of ZTD and separate the ZWD and ZHD parameters. For the data missing problem, a method based on interpolation algorithm is used to fill in the missing data to reduce the impact of data incompleteness on subsequent processing. For the missing data within a relatively small time range, the averaging method is used to restore the signal trend; while for the missing data within a relatively large time range, linear interpolation is used for reconstruction to fill in the missing data using the information of adjacent observation points.

[0009] The second step: A regional ZWD prediction method based on spatial correlation input and graph machine learning interpolation.

[0010] Download the original meteorological data of several target sites using the global data provided by the official ERA5, mainly including original meteorological data such as surface pressure, precipitable water vapor (PWV), and surface air temperature. Store the above information separately by regional sites, and use the PWV inversion model to separate the constituent parameters of ZTD, retaining the ZWD parameter. Aiming at the large nonlinearity and rapid change characteristics of ZWD, use the MM-FGCN graph neural network for time series modeling and prediction to capture the temporal variation characteristics in ZWD, improve the calculation efficiency and prediction accuracy. Secondly, use the trained prediction model to predict each observation site respectively to obtain the ZWD prediction value of each site. Since the selected sites are few and the site distances are close, the inverse distance interpolation method has a high accuracy for interpolating and predicting the area between nodes, thus ensuring that high-precision ZWD prediction values can be obtained at any position in the entire area. Finally, after obtaining the ZWD data of the known sites and the regional interpolated ZWD, represent all the observation sites and the interpolated data as a graph structure, where the nodes represent the numerical values of the observation sites and the edges represent the spatial distance and similarity between adjacent sites. Use the MM-FGCN graph neural network to train this graph to capture the spatial correlation and the complex relationships between nodes. Use the MM-FGCN graph neural network to predict the ZWD values of each node to obtain the ZWD prediction values of the observation points and interpolation points in the area. Thus, a dot map of the ZWD prediction distribution in space is obtained.

[0011] Step 3: Regional ZHD prediction method based on spatial correlation input and graph machine learning interpolation.

[0012] Download the original meteorological data of several target stations using the global data provided by ERA5 officially, mainly including original meteorological data such as surface air pressure and surface air temperature. Store the above information separately by regional stations, use the Saastamoinen model to extract the constituent parameters of ZTD, and separate the ZHD parameters. For the relatively stable ZHD, use a shallow neural network model for modeling and prediction to improve the calculation efficiency and prediction accuracy. Secondly, use the trained prediction model to predict each observation station respectively to obtain the ZHD prediction value of each station. Since the selected stations are few and the distance between stations is close, the inverse distance interpolation method has a high accuracy for interpolating and predicting the area between nodes, so as to ensure that high-precision ZHD prediction values can be obtained at any position in the whole area. Finally, after obtaining the ZHD data of the known stations and the regional interpolated ZHD, represent all the observation stations and the interpolated data as a graph structure, where the nodes represent the observation stations and the edges represent the spatial distance and similarity between adjacent stations. Use the MM-FGCN graph neural network to train this graph to capture the spatial correlation and the complex relationship between nodes. Use the MM-FGCN graph neural network to predict the ZHD value of each node to obtain the ZHD prediction values of the observation points and interpolation points in the area. Thus, a dot map of the ZHD distribution in space is obtained.

[0013] Step 4: ZTD prediction based on the separation and training of ZWD and ZHD.

[0014] Combine the measurement results of the second and third steps for analysis and processing. Add the ZWD and ZHD data of each regional point to obtain the combined ZTD value, and form a ZTD regional map as the final ZTD data regional prediction map to improve the accuracy, stability and prediction range of the measurement results.

[0015] After being processed by the above regional ZTD prediction algorithm, it can effectively solve the problems such as small ZTD prediction range and low accuracy caused by the existing methods only considering the time correlation of ZTD, ignoring the spatial correlation; combining and predicting ZTD, ignoring the differences in ZTD constituent parameters; only being able to predict points and unable to perform graph prediction, etc., and effectively improve the real-time performance, accuracy and stability of ZTD prediction, providing guarantee for PWV data inversion and meteorological prediction.

[0016] In the above technical solution, data input within an adjacent spatial range is adopted, and high-order graph convolution operations are combined to eliminate the influence of locally irrelevant spatial noise, making full use of spatial correlation to improve the accuracy of ZTD prediction. At the same time, according to the different variation characteristics of ZWD and ZHD, a deep learning model is used to perform multi-layer training on ZWD and few-layer training on ZHD to improve the calculation efficiency and prediction accuracy. The inverse distance interpolation method is used to construct network points, and high-precision prediction is carried out for any point within the entire region through the interpolation strategy, ensuring the arbitrariness of spatial selection. Based on the node results of the interpolation map, the MM-FGCN graph neural network is used for node feature aggregation and prediction to improve the accuracy and stability of ZTD prediction within the region. Finally, the present invention can effectively solve problems such as the existing methods ignoring spatial correlation, being unable to separate the characteristics of ZWD and ZHD, and being unable to perform arbitrary region prediction, significantly improving the overall accuracy and real-time performance of ZTD prediction and meeting the requirements in fields such as meteorological forecasting, precise positioning, and climate monitoring.

[0017] The present invention has the following characteristics and beneficial effects:

[0018] Adopting the above technical solution, high-precision prediction of zenith total delay (ZTD) within a region is carried out using existing ERA5 data. Compared with the existing method that only uses time series for ZTD prediction, it can not only solve the problems of limited prediction accuracy and difficulty in capturing spatial correlation within the region, but also achieve high-spatial-resolution delay prediction within a large range, thus meeting the requirements of regional meteorological monitoring and precise positioning. By separately modeling ZWD and ZHD, it can not only improve the accuracy of the model in capturing the rapid changes of atmospheric wet delay, but also enhance the calculation efficiency of the model, ensuring stability and high efficiency. At the same time, using the graph neural network (MM-FGCN) combined with the inverse distance interpolation method to predict ZTD of each node within the region can effectively solve the problem that the existing method cannot achieve prediction of any point within the region, ensuring 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, improving the reliability of the data and the robustness of the model prediction. For the problem of data loss at different stations, a method combining linear interpolation and 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 constructed based on adjacent spatial data and spatial feature learning is carried out through MM-FGCN, enabling the model to better capture spatial correlation, improving the overall accuracy, real-time performance, and spatial coverage of ZTD prediction, and providing strong technical support for meteorological forecasting, precise positioning, and climate monitoring. Description of the Drawings

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0020] Figure 1 It is the calculation flow chart of ZWD in the embodiment of the present invention.

[0021] Figure 2 It is the calculation flow chart of ZHD in the embodiment of the present invention.

[0022] Figure 3 It is the calculation flow chart of the ZTD prediction method based on multi-parameter separation in the embodiment of the present invention.

[0023] Figure 4 It is the ZHD prediction result diagram of the TCHK site in the embodiment of the present invention.

[0024] Figure 5 It is the ZWD prediction result diagram of the TCHK site.

[0025] Figure 6 It is the ZWD prediction result diagram of the TCHK site. Specific embodiments

[0026] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0027] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings. It is 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 thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. can explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0028] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installation", "connection", and "coupling" 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 an indirect connection through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0029] The present invention provides a ZTD prediction method based on graph machine learning and multi-parameter separation, as Figures 1-3 shown, including the following steps:

[0030] Step 1: Extract the historical meteorological data of several target observation points and preprocess the historical meteorological data. The historical meteorological data includes surface air pressure, precipitable water, surface air temperature, and the PWV value at that location.

[0031] In this embodiment, the original meteorological data of the target observation points HKKS, HKSS, HKST, and HKQT on the ERA5 website, that is, the original meteorological data at the longitude and latitude of 114.1842, 22.2204; 114.1609, 22.2551; 114.1103, 22.2342; 114.1247, 22.1727, are extracted, mainly including surface air pressure, precipitable water (PWV), surface air temperature and other original meteorological data, and the ZHD and ZWD at the corresponding epoch moments are calculated. The surface air pressure, precipitable water (PWV), surface air temperature and other data can be directly downloaded from the ERA5 website, and the ZHD and ZWD information of the corresponding area can be calculated through the surface air pressure, precipitable water (PWV), surface air temperature, and PWV conversion coefficient. This process belongs to the common knowledge in the positioning field, and the calculation process will not be listed in detail here. For the convenience of subsequent description, the ZHD and ZWD calculated here are used as and in the subsequent steps, where i represents the station number.

[0032] Further, judge the range size of the missing data: within the time period , if the specific value of the calculated ZWD (or ZHD) data cannot be found, it is determined that the data in this time period is missing. When , it is determined that the data missing exists in a small range, otherwise it is defaulted that the data missing belongs to a large range.

[0033] Process the missing data according to the range of the missing data. For the missing data within a small range, use the averaging method (average the sum of the values before and after the missing value) to restore the signal trend; while for the missing data within a large range, use linear interpolation for reconstruction, so as to improve the reliability and stability of the original data by compensating for the impact of abnormally missing data.

[0034] The linear interpolation method is a method of estimating unknown points through the linear change of known data points. Between two given known points and , assuming that the numerical change is linear, interpolation can be performed through the following formula:

[0035]

[0036] When performing interpolation processing on ZWD data, and are the values of ZWD at two adjacent known points and , is the value of ZWD at the unknown point to be interpolated.

[0037] When performing interpolation processing on ZHD data, and are the values of ZHD at two adjacent known points and , is the value of ZHD at the unknown point to be interpolated.

[0038] Step 2: Calculate the ZHD and ZWD at the corresponding epoch moments using the preprocessed meteorological data;

[0039] Step 3: Use the inverse distance interpolation method to construct a network graph structure. This process is mainly divided into three steps. The first step is to determine the positions of the interpolation points of the inverse distance interpolation method. The second step is to unify the data heights of ZWD and ZHD through empirical formulas. The third step is to determine the representative meanings of the edge points of the network graph.

[0040] First, determine the positions of the interpolation points for the inverse distance interpolation method. The traditional method is to select interpolation points with equal intervals in terms of position distance, and the overall configuration tends to be the vertices of a standard square. However, since in fact the positions of GNSS stations do not necessarily present a good graphical shape, a rhombus with strong adaptability and conforming to a quadrilateral is selected here for the selection of interpolation points. This can not only better select points in irregular areas but also take into account the prediction of the graph neural network. In this embodiment, in order to better compare the predicted data of the interpolation points and take into account the selection rules of regional points, the TCHK station (latitude and longitude: 114.1304; 22.2127) is used as the interpolation point for experiments.

[0041] Secondly, objectively, the heights of stations HKKS, HKSS, HKST, HKQT, and TCHK are 44.71m, 38.7m, 258.7m, 5.17m, and 576.83m respectively, which are different. As a result, the obtained ZWD and ZHD data are not actually data on the same horizontal plane. When performing the interpolation algorithm and constructing the graph structure, the data heights should be unified to the same plane. Therefore, we select the Saastamoinen model and the empirical exponential height conversion model to adjust the data heights. The specific process is as follows:

[0042] The Saastamoinen model is used to calculate the atmospheric delay to adjust the data heights of ZWD and ZHD. The adjustment formula for ZHD is expressed as follows:

[0043]

[0044] Among them, is the air pressure at the corresponding height , with the unit of , is the latitude of the observation point, is the intermediate variable of the air pressure varying with height , is the plane air pressure, is the air pressure scale height. For , the formula for the air pressure varying with height is commonly seen in atmospheric science, and usually the logarithmic decay formula is used to describe the variation of air pressure with height . The standard formula is as follows:

[0045]

[0046] Among them, is the sea-level air pressure value, which is 1013.25 hPa, is the air pressure scale height, taking 8400 meters.

[0047] ​For ZWD, since the water vapor pressure varies greatly with height, ZWD can be corrected by the following empirical exponential height conversion model:

[0048]

[0049] where is the ZWD value at the reference height, is the water vapor pressure at height , is the water vapor pressure at the reference height. And the water vapor pressure at height can be estimated by the empirical formula in the standard atmosphere model. Usually, the water vapor pressure gradually decreases with the increase of height. The following empirical formula is used to calculate the water vapor pressure at different heights:

[0050]

[0051] is the water vapor pressure at the reference height , which is the data of the ground height, is the target height, is the elevation of the water vapor pressure, taking 2000 meters.

[0052] The specific adjustment process can be expressed as follows: set the unified height of all stations to the height of the station with the highest altitude. For stations with different heights, substitute the unified height into the formula for height replacement for replacement, mainly updating the water vapor pressure and air pressure at different heights, so as to calculate the ZWD and ZHD values at the same height. The subsequent steps use , , where i represents the station number.

[0053] Finally, based on the ZWD and ZHD values at the same height obtained in the previous step, the inverse distance interpolation method formula is used to interpolate the target points, and a scatter plot of regional ZWD and ZHD is obtained.

[0054] The inverse distance interpolation method is based on the weighted principle of distance and interpolates through the distance between the known points and the target points. It can be understood that the points closer to the target point have a greater influence on the target point. Its calculation formula is as follows:

[0055]

[0056] where represents the ZHD or ZWD value of the point to be interpolated, is the ZHD or ZWD value at the known point, is the distance between the point to be interpolated and the known point, and is a weighted index, represents the number of stations used, i represents the station number.

[0057] By adjusting the weight index , the influence of distance on the interpolation result can be more accurately reflected, thereby improving the interpolation accuracy. Through actual tests at the Hong Kong station, a relatively large value can obtain a higher-precision interpolation result. Therefore, in this embodiment, a relatively large distance weight value is selected, that is , so as to approximate the realistic spatial correlation of ZTD and improve the reliability and stability of the target point data.

[0058] Through the above process, a highly unified regional scatter plot of ZWD and ZHD can be obtained. However, the relationship representation method between the edges and points needs to be clarified to form a complete graph structure. In view of the use of the inverse distance interpolation method in this embodiment when generating points, the definition of the node edges then follows the distance weight part in the inverse distance interpolation method, representing the spatial distance and similarity between adjacent stations, while the definition of the points uses the variables and , representing the ZTD component represented by this station, that is, the numerical value of ZHD or ZWD. After the above steps, in terms of time, a regional graph structure of the ZTD component based on the original data of the surrounding stations can be constructed, improving the spatial correlation of the graph data.

[0059] Step 4: Construct an MM-FGCN graph neural network and apply the obtained mesh graphs of ZWD and ZHD to separately train the MM-FGCN graph neural network.

[0060] Specifically, the MM-FGCN graph neural network includes a GCN network, a pooling layer, a fully connected layer, and a multi-modal fusion layer.

[0061] This process can be divided into four steps. The first step is to determine the adaptive sliding window. The second step is model design, generating the time series features of each node and fusing them with the 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 perform training model evaluation and improvement of the weighted constraint strategy.

[0062] First, the node features, the edges and weights between nodes need to be determined. Each node represents the ZWD data value of a spatio-temporal position (i.e., an observation station). Since the ZWD data value has a multi-year time series, the feature of each node can be represented as a time series vector , where represents the 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.

[0063] 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:

[0064] Assume that the spatial features of the graph are , then the attention weights of each feature can be defined in the following form:

[0065]

[0066] where represents the attention weight of the -th feature , representing the time series feature and the spatial feature respectively), is a learnable vector used to map the feature to an attention score, is the activation function ReLU, and are linear transformation matrices used to convert the feature to the same dimension.

[0067] Then, all features are weighted and summed according to the attention weights to obtain the fused feature representation :

[0068]

[0069] is the final fused feature representation and is also the input for subsequent graph convolution operations.

[0070] Then, through multiple GCN layers, the node features and neighbor node features can be gradually aggregated to generate a global node representation. The formula is as follows:

[0071]

[0072] where represents the output feature (node representation) after graph convolution, is the weight matrix, H is just H i collectively referred to as learned during the model training process. The stacking of multiple GCNs can capture the high-order neighbor information of the nodes for predicting ZWD, but too many layers may lead to the problem of over-smoothing. Therefore, a graph neural network model with fewer layers is used to predict ZHD data. ZHD is the zenith hydrostatic delay, which is mainly calculated based on static characteristics such as surface air pressure, latitude, and altitude. Therefore, the change of ZHD is significantly more stable compared with ZWD. Therefore, in order to simplify the calculation and improve the prediction accuracy, a GCN model with fewer layers 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 relatively many layers and 3 layers are relatively few layers, so the empirical value is adopted).

[0073] Specifically, in this embodiment, the training steps are as follows:

[0074] 1. Data preparation: Prepare graph-structured data, including node features and the adjacency matrix of the graph.

[0075] 2. Forward propagation: The input data is processed through each layer of the network to obtain the final prediction result.

[0076] 3. Loss calculation: Calculate the loss based on the model output and the actual labels (such as cross-entropy loss or mean squared error).

[0077] 4. Backward propagation: Minimize the loss function, gradient descent.

[0078] 5. Number of training epochs: Update the model parameters through multiple training epochs until the training stop criterion is reached.

[0079] So the main stopping method is the stabilization of the loss function.

[0080] Finally, use the trained model to predict the ZWD value of each node in the graph for the next year. Input the historical ZWD time series of each node into the model to predict its value for the next 2 years. As Figure 5 shows the final prediction accuracy of the interpolation site TCHK, which has a good accuracy performance in the prediction data of the past decade. The MAE error is stable at about 5 mm, and it basically successfully predicts the ZWD data of the target site in 2018 and 2019.

[0081] Specifically, a graph neural network model with few-layer training is used to predict ZHD data. Use a graph neural network for prediction. ZHD is the zenith hydrostatic delay, which is mainly calculated based on static characteristics such as surface air pressure, latitude, and altitude. Therefore, the change of ZHD is significantly more stable compared with ZWD. Therefore, in order to simplify the calculation and improve the prediction accuracy, a relatively simple GCN model in the graph neural network is used to predict ZHD.

[0082] 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 the stations. After step 4, define the connection relationship between each station to construct the topological structure of the graph based on ZHD data, and extract the corresponding node feature matrix and the standardized adjacency matrix , where iRepresents the station 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 nodes and convert them into hidden representations. The second layer of graph convolution is used to further aggregate the information of neighboring nodes and output the final feature representation of the nodes. The final output layer is a fully connected layer, which maps the features output by the graph convolution layer to the target variable (ZHD value). The propagation formula for each layer is as follows:

[0083]

[0084] Since the above identifiers have been introduced above, they will not be repeated here.

[0085] 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, first, the feature representation of each node is calculated through the node feature matrix and the normalized adjacency matrix Then, these features are used to predict ZHD. The parameters of the model are updated using the training set data, and at the same time, the performance of the model (whether the validation error decreases) is monitored on the validation set. The early stopping strategy is adopted, that is, when the error on the validation set no longer decreases, the training is stopped in advance to prevent the model from overfitting. As Figure 4 shows the final prediction accuracy of the ZHD of the interpolation site TCHK, which has a good accuracy performance in the predicted data of the past decade. The MAE error is stable at about 0.8 mm, and compared with the meter-level data unit of ZHD, the error is almost negligible, and the ZHD data of the target site in 2018 and 2019 is basically perfectly predicted.

[0086] 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 point to be predicted;

[0087] Step 6: Apply the two pre-trained MM-FGCN graph neural networks obtained by separate training, use the mesh graphs of ZWD and ZHD constructed by the inverse distance interpolation method as inputs, predict the ZWD and ZHD predicted values respectively, then add the ZWD and ZHD predicted values, and calculate the combined ZTD value to form a ZTD area graph as the final ZTD data area prediction graph.

[0088] Furthermore, in this embodiment, the predicted ZTD data is evaluated.

[0089] Specifically, after the model training is completed, the model needs to be comprehensively tested on the test set to evaluate the generalization ability of the model on unseen data. The data in the test set is basically not involved in the training and validation of the model, so as to ensure the objectivity and fairness of model evaluation. During testing, the model will use unseen data for prediction, and then compare the predicted values with the true values to calculate various evaluation metrics. To measure the performance of the models in steps 4 and 5, this paper uses the mean squared error (MSE) and the coefficient of determination ( ) as the model evaluation metrics, and the specific formulas are as follows:

[0090]

[0091] where is the length of the sample data, is the true value of the sample, is the predicted value of the sample.

[0092]

[0093] where represents the sample mean.

[0094] During the model testing process, by calculating the above metrics one by one and outputting the values of each metric, the overall performance of the model on the test set can be demonstrated, so as to understand the graph prediction effect of the model on the sample data.

[0095] Calculate the ZTD data and calculate the relevant model evaluation metrics. ZTD refers to the zenith total delay, which is an important part of the atmospheric delay of the global navigation satellite system (GNSS) and can be further decomposed into two parts: ZHD (zenith hydrostatic delay) and ZWD (zenith wet delay). Therefore, the specific ZTD value can be obtained by simply adding ZHD and ZWD, and the solution formula is as follows:

[0096] After summing up the above formula, the finally predicted ZTD value can be obtained, and step 6 is repeated to obtain the corresponding evaluation metrics. As Figure 6 shows the final prediction accuracy of the ZTD at the interpolation site TCHK, which has a good accuracy performance in the predicted data of the past decade. The MAE error is stable at about 4.8 mm, and it has an excellent accuracy performance among the existing prediction methods and also has the spatial continuity of prediction.

[0097] The above has described the embodiments of the present invention in detail in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principles and spirit of the present invention, various changes, modifications, substitutions, and variations to these embodiments including components still fall within the protection scope 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, and also including preprocessing the historical meteorological data. The preprocessing method for extracting the historical meteorological data is: for missing data in a smaller range, the average method is used to restore the signal trend; and for missing data in a larger range, linear interpolation is used for reconstruction; 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; For the ZWD and ZHD values ​​at the same height, the inverse distance interpolation method is used to interpolate the target points to obtain the regional ZWD and ZHD scatter plots, and then the nodes and edges in the ZWD and ZHD scatter plots are defined respectively. The definition of the edge follows the distance weight part of the inverse distance interpolation method to represent the spatial distance and similarity between adjacent observation points, while the definition of the point uses the ZWD or ZHD value of the station; 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 assumed that the closer the point is, the greater the influence on the target point is. The calculation formula is as follows: Among them, t represents the ZHD or ZWD value of the interpolation point, t i is the ZHD or ZWD value at a known point, d(x,y)(x i ,y i ) is the distance between the point to be interpolated and the known point, α and p are weighted exponents, and N represents the number of stations used; 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 method for determining the range of missing data is as follows: within a preset time period [t0, t0+Δt], if the calculated ZWD and ZHD data cannot find specific values, it is determined that the data in this period is missing; when Δt≤5, it is determined that the data missing is within a small range; otherwise, it is determined that the data missing is within a large range.

3. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 1, characterized in that: Linear interpolation is used to calculate the ZHD value at the unknown point to be interpolated.

4. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 1, 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.

5. The 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.

6. A 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.

7. A ZTD prediction method based on graph machine learning and multi-parameter separation according to claim 6, 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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