Deep learning-based zenith troposphere wet delay calculation method

Abstract

The invention relates to the technical field of satellite navigation and positioning, in particular to a zenith troposphere wet delay calculation method based on deep learning, and the basic steps of segmented ZWD multi-source data fusion based on an improved Transform model are as follows: establishing a ZTD model, establishing a TCA-Transform model, and fusing data. The task of establishing the ZTD model is to calculate the atmospheric refractive index according to meteorological data so as to obtain ZTDPP; the TCA-Transform model establishment comprises the following steps of: improving a Transform model by using a domain self-adaptive method; according to the data fusion, the ZWDPP and the ZWDMODIS are fused by using a TCA-Transform model. And finally, a ZWD product with high temporal-spatial resolution and high precision can be obtained. The generalization ability of an original Transform model is improved, so that the troposphere delay correction ability in a specific area is improved, and a zenith troposphere delay (ZWD) product with high resolution and high precision is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation and positioning, and specifically refers to a method for calculating zenith tropospheric wet delay based on deep learning. Background Art

[0002] Tropospheric delay is an important factor affecting high-precision satellite navigation and positioning, and its variation in the vertical direction is much greater than that in the horizontal direction. At present, in GNSS tropospheric delay atmospheric services, tropospheric delay model estimation is used for correction. Therefore, the accuracy of tropospheric delay atmospheric correction depends on the performance of the model. The tropospheric delay correction model is an empirical formula obtained by analyzing meteorological data, and there are differences due to different analytical methods. According to whether meteorological parameters are required during model calculation, it can be divided into models that require meteorological parameters and models without meteorological parameters. The main zenith tropospheric delay models that require meteorological parameters include the Hopfield model, the Saastamoinen model, etc.

[0003] Common tropospheric delay empirical models with meteorological parameters are all established as global tropospheric delay models through the analysis of global average meteorological data and the global climate. In a local area or when using regional meteorological data, the model accuracy of such models is poor, especially in regions with vast territory and complex environments like China, and the correction effect is limited. Therefore, it is necessary to construct a regional tropospheric model by means of the function method and fuse multi-source data using machine learning.

[0004] Problems that can be solved:

[0005] Firstly, constructing a regional tropospheric delay model can help us better understand the physical characteristics and spatial structure of the troposphere. By analyzing meteorological data, the distribution of meteorological elements in the current region can be understood, so as to obtain a more accurate regional tropospheric delay model.

[0006] Secondly, the Transformer model, with its self-attention mechanism and parallel processing ability, can better fit complex non-linear relationships. When there is a complex non-linear relationship between meteorological data and tropospheric delay, the Transformer model can more accurately capture this relationship and improve the fitting accuracy of the model. The Transformer model is trained through the backpropagation algorithm, and during the training process, the weights and biases are continuously adjusted to minimize the error between the predicted value and the actual value. This learning ability enables the Transformer model to learn patterns and rules from a large amount of data, improving the generalization ability and prediction accuracy of the model.

[0007] Finally, the improved TCA-Transformer model makes the feature distributions of the source domain and the target domain more consistent, further improving the generalization ability of the model. When there are significant differences between the training data and the test data, it can still perform well in regression prediction.

[0008] Introduction to the Transformer model network:

[0009] The Transformer model is a deep learning model based on the self-attention mechanism, first proposed by Vaswani et al. in 2017. It has been widely used in the field of natural language processing (NLP) and has also achieved remarkable results in other fields such as image processing and time series analysis. The core idea of the Transformer model is to capture the global dependencies in sequential data through the self-attention mechanism to improve the learning efficiency and effectiveness of the model.

[0010] The structure of the Transformer model consists of two parts: an encoder and a decoder, each composed of multiple identical layers stacked together. Each layer includes a multi-head self-attention mechanism and a feed-forward neural network. The encoder converts the input sequence into a set of context-sensitive representations, and the decoder uses these representations to generate the target sequence. During the training process, through the backpropagation algorithm, the model continuously adjusts the weights to minimize the error between the predicted value and the actual value.

[0011] The TCA-Transformer model performs well in dealing with long-range dependencies and parallel computing, making the feature distributions of the source domain and the target domain more consistent and enhancing the generalization ability. It has been successfully applied to various tasks such as image captioning and regression prediction. Although the TCA-Transformer model has some drawbacks, such as high computational resource requirements and long training time, it is still an important part of the deep learning field and is of great significance for solving complex problems.

[0012] Existing problems:

[0013] Although the TCA-Transformer model has achieved success in many fields and improved the generalization ability by combining TCA technology, it still faces some challenges when applied to tropospheric delay correction. The specific analysis is as follows:

[0014] 1. High computational resource requirements: The TCA-Transformer model requires a large amount of computational resources and memory during the training process, especially when dealing with large-scale datasets. This may make it difficult to apply in resource-constrained environments.

[0015] 2. High demand for training data: The TCA-Transformer model requires a large amount of labeled data during training to adjust network parameters and improve prediction accuracy. In some fields, it may be very difficult to obtain sufficient labeled data.

[0016] 3. Complex hyperparameter tuning: The TCA-Transformer model has many hyperparameters that need to be tuned, such as the number of attention heads, model dimensions, scaling factors, etc. Inappropriate hyperparameter selection may lead to unstable training processes or degraded model performance.

[0017] 4. Low efficiency in processing long sequence data: Although the TCA-Transformer model performs well in capturing long-range dependencies, when dealing with very long sequence data, the computational complexity is still high, affecting training and inference efficiency.

[0018] 5. Difficulty in interpretability: As a black-box model, the internal structure and relationships between parameters of the Transformer model are relatively complex, making it difficult to explain the reasons for its prediction results.

[0019] The disadvantages of the Long Short-Term Memory network (LSTM) compared to the TCA-Transformer model are as follows:

[0020] (1) Long training time: The training time of the LSTM network is relatively long, especially when dealing with long sequence data, and the training efficiency is low.

[0021] (2) High computational complexity: During the training and inference processes of the LSTM network, the computational complexity is high, which may make it difficult to apply in resource-constrained environments.

[0022] (3) Vanishing gradient problem: Although LSTM alleviates the vanishing gradient problem through gating mechanisms, when dealing with very long sequence data, it may still face the situation of vanishing or exploding gradients.

[0023] The disadvantages of the Gated Recurrent Unit (GRU) compared to the TCA-Transformer model are as follows:

[0024] (1) Poor model performance: Although GRU performs well in some tasks, there is still a certain gap compared to the performance of TCA-Transformer in dealing with long-range dependencies.

[0025] (2) Higher complexity: Similar to LSTM, when dealing with long sequence data, the computational complexity of GRU is high, which may make it difficult to apply in resource-constrained environments.

[0026] (3) Lack of flexibility: The GRU model is relatively simple in structure, but it has poor flexibility and adaptability when dealing with complex non - linear relationships.

[0027] The convolutional neural network (CNN) has the following disadvantages compared with the TCA - Transformer model:

[0028] (1) Local receptive field limitation: CNN is good at capturing local features, but when dealing with long - range dependence relationships, it is limited by the local receptive field and difficult to capture global information;

[0029] (2) Layer number limitation: Although deep CNN can enhance the feature extraction ability, increasing the number of layers will lead to a significant increase in computational complexity and training time;

[0030] (3) Not suitable for sequence data: CNN is mainly used for image processing and performs worse than the TCA - Transformer model when dealing with sequence data.

[0031] The Bayesian network has the following disadvantages compared with the TCA - Transformer model:

[0032] (1) Complex structure and large computational overhead: The Bayesian network needs to estimate a large number of parameters in the modeling process. Especially when the network structure is complex or the relationships between variables are complex, the computational overhead will become very large. In contrast, although TCA - Transformer is computationally complex, it performs better in parallel processing and training efficiency.

[0033] (2) Dependence on prior knowledge: The construction and inference processes of the Bayesian network rely on the selection of prior knowledge and require a certain understanding and assumption of the probability distribution and the relationships between variables. If the prior knowledge is selected improperly or the assumptions are inaccurate, it may lead to biases in the model.

[0034] (3) Not suitable for large - scale data: The Bayesian network may face challenges in terms of computation and storage when dealing with large - scale data. Especially when the network scale is large or the data dimension is high, the model construction and inference processes may become complex and time - consuming;

[0035] (4) Difficulty in dealing with non - linear relationships: The Bayesian network usually assumes that the relationships between variables are linear or can be described by parameterized functions, and its ability to model non - linear relationships is relatively weak. Summary of the Invention

[0036] The present invention aims to at least solve the problem of poor generalization ability of the original Transformer model in the prior art.

[0037] This solution provides a method for calculating the zenith tropospheric wet delay based on deep learning. It studies the variation rules of meteorological data at different altitudes, constructs a regional refraction index model to obtain a more accurate ZTD, and combines it with the saastomonien model to obtain ZWD. An improved Transformer model is used for multi-source data fusion to construct a regional ZWD model, which improves the generalization ability of the original Transformer model, so as to enhance the tropospheric delay correction ability in a specific area and obtain a zenith tropospheric delay (ZWD) product with high resolution and high precision.

[0038] A method for calculating the zenith tropospheric wet delay based on deep learning includes the following steps:

[0039] Step 1: Refer to the variation law of meteorological data, use the least squares method for fitting, and obtain the meteorological parameter model at different altitudes:

[0040]

[0041] In the formula, P represents the air pressure at height h, T represents the air temperature, t d represents the dew point temperature. At altitudes above 13 km, there is no dew point temperature; h represents the height, h0 represents the station height, and H T represents the tropopause height;

[0042] Step 2: According to the meteorological parameter model, obtain the segmented model of the atmospheric refraction index (1.5):

[0043]

[0044] In the formula, e represents the water vapor pressure, t d represents the dew point temperature, k1, k2, and k3 represent seasonal parameters, h0 represents the GNSS station height, and N(h) represents the atmospheric refractive index corresponding to height h; a three-segment model is adopted, which is applicable to a specific area and can improve the accuracy of tropospheric delay correction;

[0045] Step 3: Construction of the regional ZWD model:

[0046] According to the atmospheric refractive index model obtained from formula 1.5 in step 2, expand the signal path integral to obtain the GNSS ZTD, and subtract the zenith tropospheric dry delay (ZHD) calculated by the saastamoinen model to obtain ZWD:

[0047]

[0048] In the formula, ZTD PPDenote the total zenith tropospheric delay obtained by precise point positioning through a piecewise function. When the zenith tropospheric delay (ZTD) is obtained by means of precise point positioning technology, a high-precision ZTD model is conducive to controlling the convergence duration;

[0049] Combined with the refractive index model parameters calculated in step 2, obtain the tropospheric zenith delay model of the region. The Saastamoinen model is:

[0050]

[0051] ZWD PP = ZTD PP - ZHD SAAS (0.9)

[0052] In the formula, ZHD SAAS is the zenith tropospheric dry delay obtained from the Saastamoinen model, is the latitude at the station, h is the elevation at the station, and P0 is the station pressure; Using the Saastamoinen model, calculate ZWD according to the extracted MODIS humidity profile data:

[0053]

[0054] In the formula, ZWD MODIS is the ZWD obtained through MODIS, e is the water vapor pressure, T is the temperature, k'2, k3 are model constants, and R d is the dry air gas constant, and appropriate parameter values are selected according to the region;

[0055] Step 4: Optimize the transformer model using transfer component analysis (TCA) in the domain adaptation improvement method. TCA can maximize the trace of the covariance between two domains while minimizing the variance within the domain, thereby effectively reducing the distribution difference between the source domain and the target domain and enhancing the generalization ability of the model to new domain data:

[0056]

[0057] max tr(A T X'(L - I / n)X' T A)(0.12)

[0058] In the formula, X s and X t are the data matrices of the source domain and the target domain respectively, u s and u t are the means of the source domain and the target domain data respectively, X t ' and X s ' are the centered data matrices, and X' and X' TThe source domain and target domain data matrices and their transpose matrices for merging and centering processing, A and A T are the projection matrix and its transpose matrix, L is the Laplacian matrix, and I is the identity matrix; n is the sum of the source domain and target domain sample numbers;

[0059] Step 5: Use the transformer model improved by the TCA optimization objective function in Formula 1.12 to fuse the ZWD obtained by GNSS PPP in Step 3 PP with the ZWD estimated by MODIS MODIS ;

[0060] Interpolate the ZWD MODIS to the GNSS station location; learn the characteristics of ZWD on the spatial and temporal scales through the improved transformer model, and use the ZWD PP to correct the ZWD with lower accuracy MODIS to obtain a ZWD product with high spatial resolution and high accuracy.

[0061] Adopting the above structure enables this solution to have the following beneficial effects:

[0062] The current tropospheric empirical model is mainly constructed based on the global or large regions. If it is applied to a small region, there will be certain systematic errors. At the same time, the acquisition of ZWD is affected by GNSS stations, and the spatial resolution is insufficient. Therefore, it is necessary to construct a regional tropospheric model by means of the model function method and use the TCA-Transformer model for data fusion to eliminate systematic errors and obtain a ZWD product with high spatio-temporal resolution and high accuracy;

[0063] Tropospheric delay is the main way of meteorological research. However, the tropospheric delay settlement methods represented by precise point positioning and radiosondes still have the following four problems:

[0064] (1) Radiosondes can only provide the atmospheric parameter information of a certain point on the vertical profile and cannot provide continuous information in the horizontal direction; this means that it cannot cover a wide spatial range and cannot reflect the spatial variation of atmospheric delay. Therefore, it has certain limitations for large-scale atmospheric delay monitoring and research;

[0065] (2) The time and spatial resolution of radiosonde observations of tropospheric zenith delay are limited; each observation can only obtain the data of one point, and the observation interval is usually long, and continuous spatio-temporal monitoring data cannot be provided, thus limiting the accurate description and research of atmospheric delay;

[0066] (3) Traditional precise point positioning is not applicable in some small areas. Precise point positioning uses an atmospheric model to estimate tropospheric delay, usually calculating it using carrier phase data from GNSS dual-frequency receivers. However, there may be uncertainties and errors in the atmospheric model itself, and such model errors may affect the accuracy of the final tropospheric delay calculation.

[0067] (4) The ZWD obtained through precise point positioning is affected by the site and has low spatial resolution.

[0068] The establishment of a segmented tropospheric zenith delay model and the correction of tropospheric delay by the model can solve the problems existing in the above three aspects. In terms of the calculation of zenith tropospheric delay, segmenting the integration of meteorological data according to the region and altitude where the station is located is a more accurate method. Compared with traditional precise point positioning, due to its fitting method of atmospheric refractive index, the segmented tropospheric zenith delay model makes the calculation of regional tropospheric zenith delay more accurate. At the same time, combining with TCA-Transformer has better model advantages. Its advantages are mainly manifested in the following four aspects:

[0069] (1) To further improve the correction accuracy of tropospheric zenith delay, after establishing the stratified index of tropospheric refractive index, a regional tropospheric model is obtained with the help of radiosonde meteorological information, getting rid of the uneven horizontal distribution of tropospheric meteorological factors caused by the differences in latitude and surface properties in different regions and the respective physical characteristics of the air in the horizontal path on the ground, as well as the uneven horizontal layout of factors such as air pressure and temperature.

[0070] (2) By using precise point positioning technology to obtain ZTD, a high-precision tropospheric delay model is beneficial to controlling the convergence time.

[0071] (3) Traditional recurrent neural networks tend to lose information as the distance increases. The Transformer model can effectively capture long-range dependencies in data through the self-attention mechanism.

[0072] (4) The standard Transformer model may have insufficient generalization ability when facing test data with a distribution different from the training set and may overfit during training. Using the TCA-Transformer model can enhance the model's adaptability to data in new fields.

[0073] Referring to Steps 1, 2, and 3 in the second part, the advantages shown by the segmented model are as follows:

[0074] According to the geographical and meteorological conditions of the region, a meteorological model that conforms to a specific region is fitted to calculate a ZWD with higher accuracy using meteorological data.

[0075] Referring to Steps 4 and 5 of the second part, the advantages shown by the TCA-Transformer model are as follows:

[0076] Use deep learning to eliminate the systematic bias generated by the model, and correct the low-precision data with high-precision data to obtain a fused product with high precision and high spatio-temporal resolution. The training process has great flexibility, and appropriate GNSS stations can be selected during actual application. Brief Description of the Drawings

[0077] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0078] Figure 1 It is a technical flow chart of the Transformer model for fusing ZWD in this solution. Detailed Embodiments

[0079] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0080] Please refer to Figure 1 , a method for calculating zenith tropospheric wet delay based on deep learning, including the following steps:

[0081] Step 1: Refer to the variation law of meteorological data, use the least squares method for fitting, and obtain the meteorological parameter model at different heights:

[0082]

[0083] In the formula, P represents the air pressure at height h, T represents the air temperature, t d represents the dew point temperature. At altitudes above 13 km, there is no dew point temperature; h represents the height, h0 represents the station height, and H T represents the tropopause height;

[0084] Step 2: According to the meteorological parameter model, obtain the segmented model of the atmospheric refractive index (1.5):

[0085]

[0086]

[0087] In the formula, e represents the water vapor pressure, t drepresents the dew point temperature, k1, k2, and k3 represent seasonal parameters, h0 represents the GNSS station height, N(h) represents the atmospheric refractive index corresponding to height h, and a, b1, b2, b3, c, and k1, k2, k3 are all seasonal parameters with different performances in different seasons. The least squares method is used to obtain the values of the constant coefficients in the fitting of the refractive index piecewise function; a three-segment model is adopted, which is applicable to a specific area and can improve the accuracy of tropospheric delay correction;

[0088] Step 3: Construction of the regional ZWD model:

[0089] According to the atmospheric refractive index model obtained from Equation 1.5 in Step 2, expand the signal path integral to obtain the GNSS ZTD, and subtract the zenith tropospheric dry delay (ZHD) calculated by the Saastamoinen model to obtain ZWD:

[0090]

[0091] where N(h) is the atmospheric refractive index obtained in Step 2, and ZTD PP represents the total zenith tropospheric delay obtained by precise point positioning through a piecewise function. The values of a, b1, b2, b3, c, and k1, k2, k are the same as the parameter values in Equation 1.5 in Step 2. When using precise point positioning technology to obtain the zenith tropospheric delay (ZTD), a high-precision ZTD model is beneficial to controlling the convergence time;

[0092] Combined with the refractive index model parameters calculated in Step 2, obtain the tropospheric zenith delay model for the region. The Saastamoinen model is:

[0093]

[0094] ZWD PP = ZTD PP - ZHD SAAS (0.21)

[0095] where ZHD SAAS is the zenith tropospheric dry delay obtained from the Saastamoinen model, is the latitude at the station, h is the elevation at the station, and P0 is the station pressure; use the Saastamoinen model to calculate ZWD according to the extracted MODIS humidity profile data:

[0096]

[0097] where, ZWD MODIS is the ZWD obtained through MODIS, e is the water vapor pressure, T is the temperature, k'2, k3 are model constants, and R dis the dry air gas constant, and appropriate parameter values are selected according to the region;

[0098] Step 4: Optimize the transformer model using Transfer Component Analysis (TCA) in the domain adaptation improvement method. TCA can maximize the trace of the covariance between two domains while minimizing the variance within the domain, thereby effectively reducing the distribution difference between the source domain and the target domain and enhancing the generalization ability of the model to new domain data:

[0099]

[0100] maxtr(A T X'(L - I / n)X' T A)(0.24)

[0101] where X s and X t are the data matrices of the source domain and the target domain respectively, u s and u t are the means of the source domain and the target domain data respectively, X t ' and X s ' are the centered data matrices, X' and X' T are the combined and centered data matrices of the source domain and the target domain and their transposed matrices, A and A T are the projection matrix and its transposed matrix, L is the Laplacian matrix, I is the identity matrix; n is the sum of the sample numbers of the source domain and the target domain;

[0102] Step 5: Use the transformer model improved by the TCA optimization objective function of Formula 1.12 to fuse the ZWD obtained by GNSS PPP in Step 3 PP with the ZWD estimated by MODIS MODIS ;

[0103] Adopt the linear interpolation in time and the spherical cap harmonic interpolation method in space to interpolate the ZWD MODIS to the GNSS station positions;

[0104] Learn the characteristics of ZWD at the spatial scale and the time scale through the improved transformer model, and use the ZWD PP to correct the ZWD with lower accuracy MODIS to obtain a ZWD product with high spatial resolution and high accuracy.

[0105] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the zenith tropospheric wet delay based on deep learning, characterized in that, Step 1: Refer to the variation law of meteorological data, perform fitting using the least squares method, and obtain the meteorological parameter model at different heights: Wherein, P represents the air pressure at height h, T represents the air temperature, and t d represents the dew point temperature. At altitudes above 13 km, there is no dew point temperature; h represents height, h0 represents the station height, and H T represents the tropopause height; Step 2: Obtain the segmented model of the atmospheric refraction index (1.5) according to the meteorological parameter model: where e represents the water vapor pressure, and t d represents the dew point temperature, k1, k2, and k3 represent seasonal parameters, h0 represents the GNSS station height, and N(h) represents the atmospheric refractive index corresponding to height h; a three-segment model is adopted, which is applicable to a specific area and can improve the accuracy of tropospheric delay correction; Step 3: Construction of the regional ZWD model: According to the atmospheric refractive index model obtained from Formula 1.5 in Step 2, expand the signal path integral to obtain the GNSS ZTD, and subtract the zenith tropospheric dry delay (ZHD) calculated by the Saastamoinen model to obtain ZWD: where N(h) is the atmospheric refraction index obtained in step 2, and ZTD PP represents the total zenith tropospheric delay obtained by piecewise function through precise point positioning; when the zenith tropospheric delay (ZTD) is obtained by means of precise point positioning technology, a high-precision ZTD model is conducive to controlling the convergence time; Combined with the refractive index model parameters calculated in Step 2, obtain the tropospheric zenith delay model of the region. The Saastamoinen model is: ZWD PP = ZTD PP - ZHD SAAS (0.9) where ZHD SAAS is the zenith tropospheric dry delay obtained from the Saastamoinen model, is the latitude at the station, h is the elevation at the station, and P0 is the station pressure; Use the Saastamoinen model to calculate ZWD according to the extracted MODIS humidity profile data: where, ZWD MODIS is the ZWD obtained by MODIS, e is the water vapor pressure, T is the temperature, k'2 and k3 are model constants, and R d is the dry air gas constant, and appropriate parameter values are selected according to the region; Step 4: Optimize the transformer model using transfer component analysis (TCA) in the domain adaptation improvement method. TCA can maximize the trace of the covariance between two domains while minimizing the variance within the domain, thereby effectively reducing the distribution difference between the source domain and the target domain and enhancing the generalization ability of the model to new domain data: maxtr(A T X'(L-I / n)X' T A)(0.12) where X s and X t are the data matrices of the source domain and the target domain respectively, u s and u t are the means of the source domain and target domain data respectively, X t ' and X s ' are the data matrices after centering, X' and X' T are the data matrices of the source domain and target domain after merging and centering and their transposed matrices, A and A T are the projection matrix and its transposed matrix, L is the Laplacian matrix, I is the identity matrix; n is the sum of the sample numbers of the source domain and the target domain; Step 5: Use the transformer model improved by the TCA optimization objective function of Formula 1.12 to fuse the ZWD obtained by GNSSPPP in Step 3 PP with the ZWD estimated by MODIS MODIS ; Interpolate ZWD MODIS to the GNSS station locations; learn the features of ZWD at spatial and temporal scales through an improved transformer model, and use ZWD PP to correct the lower-precision ZWD MODIS to obtain a ZWD product with high spatial resolution and high precision.

2. The method for calculating the wet delay of the zenith troposphere based on deep learning according to claim 1, wherein, In Step 2, the constant coefficients a, b1, b2, b3, c and k1, k2, k3 are all seasonal parameters and have different performances in different seasons. The values of the constant coefficients are obtained using the least squares method in the fitting of the refractive index piecewise function.

3. The method for calculating the wet delay of the zenith troposphere based on deep learning according to claim 2, characterized in that, In Step 3, the values of the constant coefficients a, b1, b2, b3, c and k1, k2, k are the same as the parameter values in Formula 1.5 in Step 2.

4. A method for calculating zenith tropospheric wet delay based on deep learning according to claim 1, wherein In step 5, the ZWD is interpolated to the GNSS station positions by using the linear interpolation in time and the spherical cap harmonic interpolation in space. MODIS Interpolate to the GNSS station positions.

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