A regional relative tropospheric delay modeling method based on sliding window

Abstract

The present invention discloses a regional relative tropospheric delay modeling method based on a sliding window, which belongs to the field of satellite navigation positioning. The method comprises the following steps: calculating the ZTD difference between any point and a reference point at the same latitude in the sliding window, and taking the minimum value of the ZTD difference within 80km-100km of the reference point as a threshold; in the same sliding window, establishing a function model between the ZTD difference and the longitude according to ERA5 data, and using a BP neural network to predict the coefficients of the function model at different times of the same reference point, and then calculating the ZTD difference per hour; or in the process of window movement, using a BP neural network to predict the coefficient of the predicted point with the coefficient of a reference point, and then calculating the ZTD difference between the predicted point and the surrounding points; comparing the above ZTD difference with the threshold, if it is less than the threshold, directly performing double difference correction. The present invention can perform high-precision modeling and prediction of tropospheric delay differences.

Description

Technical Field

[0001] The invention relates to the field of satellite navigation and positioning, and in particular to a regional relative tropospheric delay modeling method based on a sliding window. Background Art

[0002] The high-precision positioning technology of the Global Navigation Satellite System (GNSS) is widely used in scientific research, engineering practice and daily life. As a high-precision positioning method, Real-Time Kinematic (RTK) technology relies on differential technology to solve the errors in GNSS positioning. However, tropospheric delay error is one of the important factors affecting the accuracy of RTK solution. Tropospheric delay error is closely related to the atmospheric state on the satellite observation path, especially in the baseline with a large distance, the error has a more significant impact on the positioning accuracy.

[0003] At present, the processing methods of tropospheric delay in RTK solution mainly include model method and differential estimation method. The model method establishes a prediction model based on the physical characteristics of the atmosphere, which is suitable for tropospheric delay correction of long-distance baselines, but the accuracy of the model is limited by the selection of parameters and changes in regional atmospheric characteristics. The differential estimation method relies on the tropospheric delay difference correction error between the reference station and the user station, which is suitable for short baselines but has limited accuracy for long-distance baselines. Especially in dynamic application scenarios (such as rapid movement or drastic meteorological changes), existing methods are difficult to achieve real-time and accurate prediction of tropospheric delay.

[0004] The Chinese invention patent with publication number CN117741709A discloses a tropospheric delay modeling method and system of ERA5 fusion GNSS. The method first constructs a tropospheric vertical correction model based on ERA5 atmospheric reanalysis data; then optimizes the ERA5 tropospheric vertical correction model by using the fusion GNSS tropospheric delay data; constructs a tropospheric delay empirical grid model by combining the optimized model with ERA5 data; and fuses GNSS data again to generate a high-precision ERA5 fusion GNSS tropospheric delay empirical grid model, and provides high-precision real-time GNSS atmospheric correction services based on the final model. This method improves the accuracy and timeliness of GNSS tropospheric delay correction, which is of great significance to high-precision navigation positioning and GNSS atmospheric service performance. However, although the change from the vertical correction model to the empirical grid model can improve the modeling accuracy, it depends on a large number of empirical parameters, and improper parameter selection may lead to a decrease in model accuracy.

[0005] The Chinese invention patent with publication number CN115932920A discloses a method for interpolating tropospheric delay, which includes obtaining the double-difference tropospheric delay of the target network baseline and the target satellite pair; calculating the single-difference tropospheric delay correction term according to the height of the main reference station, the auxiliary reference station and the mobile station, and correcting the double-difference tropospheric delay; using the horizontal and vertical coordinate differences between the reference station and the mobile station, and the corrected double-difference tropospheric delay, the target double-difference tropospheric delay is obtained; and the double-difference tropospheric delay of the mobile station is estimated by a linear interpolation method. This method corrects the systematic error in the elevation direction and improves the accuracy of the double-difference tropospheric delay estimation between the main reference station and the mobile station, thereby improving the positioning accuracy of the user. However, the tropospheric delay may change dramatically in a dynamic environment (such as rapidly changing atmospheric conditions or mobile scenarios), and based on static interpolation, it lacks the ability to respond to dynamic changes in real time. Moreover, although the linear interpolation method is simple and efficient, its ability to capture nonlinear changes is limited, which may cause the interpolation result to deviate from the actual value and reduce the accuracy. Summary of the invention

[0006] The purpose of the present invention is to propose a regional relative tropospheric delay modeling method based on a sliding window. This method uses ERA5 reanalysis data combined with a sliding window and a BP neural network method to model the tropospheric delay difference, thereby enhancing the ability to capture real-time dynamic changes, which is of great significance for improving the reliability and accuracy of RTK solutions.

[0007] The technical solution adopted by the present invention is:

[0008] A regional relative tropospheric delay modeling method based on a sliding window comprises the following steps:

[0009] (1) Select a sliding window in the study area, obtain the ERA5 data within the sliding window, and establish a function model between the ZTD difference and latitude;

[0010] (2) Establish a function model between the coefficients of the function model between the ZTD difference and latitude in step (1) and longitude. This function model is called the longitude relationship model;

[0011] (3) Further organize the longitude relationship model established in step (2) to obtain a longitude optimization relationship model that can represent the relationship between any point and a reference point at the same latitude; combine the function model between the ZTD difference and latitude established in step (1) with the longitude optimization relationship model to calculate the ZTD difference between any point in the sliding window and a reference point at the same latitude; and use the minimum value of the ZTD difference between any point and the reference point at the same latitude within 80 km to 100 km as the threshold;

[0012] (4) In the same sliding window, a function model between the ZTD difference and longitude is established based on the ERA5 data, and the coefficients of the function model at different times of the same reference point are predicted using the BP neural network, thereby calculating the ZTD difference between the same reference point and the surrounding points at different times; the obtained ZTD difference is compared with the threshold value obtained in step (3); if the ZTD difference is less than the threshold value, the RTK directly performs double difference correction in the positioning solution;

[0013] (5) During the window movement process, the BP neural network is used to predict the coefficient of the predicted point using the coefficient of a reference point, and then the ZTD difference between the predicted point and the surrounding points at different times is calculated; if the ZTD difference is less than the threshold obtained in step (3), the double difference method is directly used for correction.

[0014] The beneficial technical effects of the present invention are as follows:

[0015] The present invention introduces sliding window and BP neural network, utilizes BP neural network in combination with ERA5 reanalysis data and sliding window method to construct a tropospheric delay difference fitting model with high efficiency, strong dynamic adaptability and high calculation accuracy, performs high-precision modeling and prediction on the tropospheric delay difference, and significantly improves the positioning accuracy of RTK solution.

[0016] The present invention determines the size of the threshold by constructing a polynomial fitting model, and then determines whether the double difference method can be directly used to eliminate the influence of tropospheric delay on the positioning result by comparing the ZTD difference with the threshold. The present invention reduces the dependence on a large number of empirical parameters by optimizing the model structure, thereby reducing the modeling error caused by improper parameter selection and improving the stability and robustness of the model. The present invention combines the sliding window and the BP neural network to model relative tropospheric delay. The method has real-time response capability and can quickly adapt to the nonlinear changes of tropospheric delay in rapidly changing atmospheric conditions and mobile scenes, improve the applicability of the correction model in a dynamic environment, thereby improving the efficiency of tropospheric delay error calculation, and further improving the reliability and applicability of real-time dynamic positioning (RTK) technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the regional relative tropospheric delay modeling method based on sliding window of the present invention;

[0018] Figure 2 A comparison chart of ERA5 data at the same reference point and data predicted by the method of the present invention;

[0019] Figure 3 It is a difference diagram of ERA5 data of the same reference point and the data predicted by the method of the present invention;

[0020] Figure 4 It is a comparison chart of ERA5 data of the predicted point and the predicted data;

[0021] Figure 5 It is the difference diagram between the ERA5 data of the predicted point and the predicted data;

[0022] Figure 6 This is an example diagram of a sliding window. DETAILED DESCRIPTION

[0023] At present, the processing methods of RTK tropospheric delay mainly include model method and differential estimation method. The model method establishes a prediction model based on the physical characteristics of the atmosphere, which is suitable for long baseline delay correction, but the accuracy of the model depends on parameter selection and regional atmospheric characteristics, and is greatly affected by dynamic changes; the differential estimation rule corrects the error through the tropospheric delay difference between the reference station and the user station, which is suitable for short baselines, but has limited effect in long-distance baseline scenarios. Especially in dynamic scenarios (such as rapid movement or drastic meteorological changes), it is difficult for existing methods to accurately predict tropospheric delays in real time, and existing methods still have deficiencies in dynamic response capabilities, computational efficiency and prediction accuracy. It is impossible to quickly solve the tropospheric delay difference between the two stations. Under what circumstances can RTK directly use the double difference method to remove the influence of tropospheric delay on positioning results. In this regard, the present invention proposes a modeling method based on ERA5 reanalysis data combined with sliding windows and BP neural networks to construct a relative tropospheric delay fitting model with high efficiency, strong dynamic adaptability and high computational accuracy. The present invention uses ERA5 data to provide long-term stable tropospheric delay statistical information, and the combination of sliding window and neural network enhances the ability to capture real-time dynamic changes, further improving the reliability and accuracy of RTK solution.

[0024] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

[0025] like Figure 1 As shown, a regional relative tropospheric delay modeling method based on a sliding window includes the following steps:

[0026] Step 1: First, select a sliding window with a spatial resolution of 2° (LAT) × 2.5° (LON) in the study area, such as Figure 6 As shown in the figure, in order to ensure the accuracy of the threshold, it is necessary to download the ERA5 (0.25°×0.25°) data of the required grid points in the window for one year, calculate the annual average value of ZTD of each grid point as the experimental data; and select a grid point in the window as the reference point, calculate the ZTD difference between other grid points in the window and the reference point, and use the least squares method to fit, and get the function model between ZTD difference and latitude, as follows:

[0027] (1)

[0028] In formula (1), It is the difference between the annual mean ZTD of the surrounding grid points and the reference point, or the difference between the annual mean ZTD of the tropospheric delay; is the model coefficient, is the latitude of the surrounding grid points, The latitude of the reference point.

[0029] Step 2: In equation (1), only the function model of tropospheric delay and latitude is established, but the relationship with longitude is not considered. On this basis, the coefficient The relationship between longitude and latitude is shown in the figure below:

[0030] (2)

[0031] In the formula, is the coefficient The coefficients of the model with longitude, is the longitude of the surrounding grid points, The longitude of the base point.

[0032] Step 3: Since equations (1) and (2) can only obtain the ZTD difference around a specified reference point, it is impossible to know the ZTD difference around other reference points at the same latitude. Therefore, equations (1) and (2) are fitted to multiple grid points at the same latitude, and the function models of multiple grid points are sorted out to obtain the function model of the ZTD difference between any point and the reference point at the same latitude, as follows:

[0033] (3)

[0034] (4)

[0035] In formula (3), is the coefficient of the function model in formula (4) The coefficients of the model with longitude, is the longitude of the surrounding grid points, is the longitude of the reference point; in formula (4), is the difference between the annual mean ZTD of any point and a reference point at the same latitude, is the latitude of the surrounding grid points, The latitude of the reference point.

[0036] Combining equation (3) and equation (4), a function model between the ZTD difference and longitude and latitude is constructed. According to the function model, the ZTD difference between any reference point and the surrounding grid points on the latitude can be obtained.

[0037] Using the combined function model, grid points with a distance of 80km to 100km around the benchmark point are selected. According to the function model, the ZTD difference between the selected grid points and the benchmark point is calculated. The minimum value of the calculated ZTD difference is selected as the threshold, and used as the range basis for the subsequent tropospheric delay difference.

[0038] Step 4: The establishment of the above function model can only solve the threshold of ZTD difference and the application of annual data in data processing, and the coefficients of each benchmark point need to be refitted, and the ZTD difference of each latitude every hour cannot be calculated. In order to ensure that the ZTD difference can be obtained in real time during the sliding window, the coefficients are modeled in combination with the BP neural network method to ensure the adaptability of the function model coefficients and achieve the purpose of obtaining the hourly ZTD difference.

[0039] First, in the same window, the daily average of ERA5 data is used as experimental data to facilitate the addition of real-time data. Points within the spatial resolution of 0.25°×0.25° of ERA5 data are selected as grid points. The daily average of ZTD of each grid point is calculated. A grid point is selected as the reference point in the sliding window. The ZTD difference between other grid points and the reference point in the sliding window is calculated. The least squares method is used for fitting to obtain the function model between the ZTD difference of the reference point every hour and the longitude, as follows:

[0040] (5)

[0041] In the formula, is the daily mean difference of ZTD between the surrounding grid points and the reference point, or the daily mean difference of tropospheric delay, is the model coefficient, is the longitude of the surrounding grid points, is the longitude of the reference point. The BP neural network is used to perform time series prediction of the model coefficients to achieve the prediction of the model coefficients for the next 24 hours, and finally calculate the ZTD difference. Among them, the input layer includes the hourly time, the latitude difference between the reference point and the surrounding points, and the model coefficients for the first 48 hours. The output layer is the model coefficients for the next 24 hours of the same reference point. Subsequently, the data is normalized to improve the training stability of the neural network. The data set is divided into a training set and a test set. The training set is used for network training and the test set is used for model verification. After the training is completed, the test set data is used for neural network reasoning to obtain the predicted value of the model coefficients for the next 24 hours, and then denormalized to restore to the original data scale. Finally, the ZTD difference of each latitude every hour is calculated by the predicted model coefficients to analyze the spatiotemporal variation characteristics of ZTD. The obtained ZTD difference is compared with the threshold obtained in the third step. If the difference is less than the threshold, the double difference method can be directly corrected. If the difference is greater than the threshold, the double difference method cannot be directly corrected. Figure 2 A comparison chart of the ERA5 data at the same reference point and the data predicted using the above method; Figure 3 The difference diagram of ERA5 data at the same reference point and the data predicted by the above method is shown in Figure 2. Figure 2 and Figure 3 It can be seen that the difference accuracy of the same point predicted by the present invention is within 1 cm, which is relatively high.

[0042] Step 5: During the window movement, the model coefficients in equation (5) are , use the BP neural network to predict the coefficient of another reference point in this window with the coefficient of a known reference point in other windows. Among them, the input layer includes the time of each hour, the latitude difference between the reference point and the surrounding points, and the model coefficient of the first 48 hours, and the output layer is the model coefficient of the predicted point 24 hours later. Subsequently, the data is normalized to improve the training stability of the neural network. The data set is divided into a training set and a test set. The training set is used for network training and the test set is used for model verification. After the training is completed, the test set data is used for neural network reasoning to obtain the predicted value of the model coefficient for the next 24 hours, and then the denormalization is performed to restore it to the original data scale. Finally, the ZTD difference of each latitude per hour is calculated by the predicted model coefficient, that is, the ZTD difference between the predicted point and the surrounding points is obtained to analyze the spatiotemporal variation characteristics of ZTD. The obtained ZTD difference is compared with the threshold value obtained in step 3. If the difference is less than the threshold, RTK can directly perform double difference correction in positioning solution. If the difference is greater than the threshold, double difference correction cannot be directly performed. Figure 4 It is a comparison chart of ERA5 data of the predicted point and the predicted data; Figure 5 This is the difference diagram between the ERA5 data of the predicted point and the predicted data. Figure 4 and Figure 5It can be seen that the difference accuracy of the present invention in predicting one point by another point is within 1 cm, which is relatively high.

[0043] Specifically, the input layer of the above BP neural network includes time, latitude difference between the benchmark point and the surrounding grid points, and model coefficients for the previous 48 hours, and the output layer is the model coefficients for the next 24 hours. After the data is read and sorted, the input data and output data are normalized. The purpose of normalization is to convert the scale of the data to the same range. The input data of the training set is normalized to [0,1], and the output data of the training set is normalized to [-1,1], so as to speed up the training process and improve the performance of the model. For the test set data, the same normalization method as the training set is used to ensure that the characteristics of the test data are consistent with the training data. The data set is divided into a training set and a test set. Generally, the first 70% is divided into a data training set, and the last 30% of the data is used as a test set. In the BP neural network training process, the selection of the number of hidden layer nodes uses a traversal method, which is tried within the range of the number of nodes to find the number of hidden layer nodes that minimizes the mean square error (MSE). The training process uses the Levenberg-Marquardt algorithm (i.e., trainlm), a commonly used efficient training algorithm in BP neural networks. During the training process, the neural network continuously updates its weights and biases to minimize the prediction error of the training set. Through the back propagation algorithm, the error is calculated and propagated backwards to adjust the parameters in the network. After training, the neural network is validated using the test set to evaluate its performance on unseen data. The data is denormalized to restore to the original data scale to establish the BP neural network. The trained neural network is used to simulate the test set data. The prediction results are compared with the actual output values.

[0044] Although the input layer content of the above BP neural network is the same, the output layer represents different goals, so the neural network tasks of the two are different. The output layer of the same point only needs to predict the model coefficients of the next 24 hours of the benchmark point, which are related to the time series of the target point. The output layer of different points needs to predict the model coefficients of the next 24 hours of the points different from the benchmark point. Although the input data is similar, the goal is to predict the future values ​​of different points.

[0045] In summary, RTK can be directly corrected using double difference in two parts:

[0046] (1) Construct a polynomial fitting model to obtain the threshold of the benchmark point. The ZTD annual average of ERA5 in the window is used as the experimental data, and the least squares fitting is performed to obtain the ZTD difference function model. The relationship between the coefficients and longitude in the difference function model is established to obtain the ZTD difference function model of longitude and latitude. According to the model, the ZTD difference around the benchmark point can be calculated. According to the fitting model of a single benchmark point, multiple benchmark points are fitted, and further sorted to obtain a longitude relationship model that can represent any point and the benchmark point at the same latitude; according to the model, the ZTD difference between the surrounding points and any benchmark point at the latitude can be calculated; and the minimum value of the ZTD difference within 80km-100km from any point to the benchmark point is used as the threshold, which is used as the basis for the subsequent range of tropospheric delay difference.

[0047] (2) BP neural network prediction to obtain real-time coefficients. The daily average ZTD value of ERA5 in the window is used as experimental data, and the least squares fitting is performed to obtain the ZTD difference function model; the BP neural network is used to predict the coefficient of the same reference point or the coefficient of a known reference point is used to predict the coefficient of another reference point. The 48-hour prediction is performed for 24 hours respectively, and the coefficient of each hour and latitude of the predicted point can be obtained. Finally, the ZTD difference between the predicted point and the surrounding points is obtained. The obtained ZTD difference is compared with the required threshold. If the difference is less than the threshold, the RTK positioning solution can be directly corrected by the double difference method. If the difference is greater than the threshold, the double difference method cannot be directly corrected.

Claims

1. A regional relative tropospheric delay modeling method based on a sliding window, characterized in that The following steps are involved: (1) Select a sliding window in the study area, obtain the ERA5 data within the sliding window, and establish a function model between the ZTD difference and latitude; (2) Establish a function model between the coefficients of the function model between the ZTD difference and latitude in step (1) and longitude. This function model is called the longitude relationship model; (3) Further organize the longitude relationship model established in step (2) to obtain a longitude optimization relationship model that can represent the relationship between any point and a reference point at the same latitude; combine the function model between the ZTD difference and latitude established in step (1) with the longitude optimization relationship model to calculate the ZTD difference between any point in the sliding window and a reference point at the same latitude; The minimum value of the ZTD difference between any point within 80km-100km from the reference point is taken as the threshold; (4) In the same sliding window, a function model between the ZTD difference and longitude is established based on the ERA5 data, and the coefficients of the function model at different times of the same reference point are predicted using the BP neural network, thereby calculating the ZTD difference between the same reference point and the surrounding points at different times; the obtained ZTD difference is compared with the threshold value obtained in step (3); if the ZTD difference is less than the threshold value, the RTK directly performs double difference correction in the positioning solution; (5) During the window movement process, the BP neural network is used to predict the coefficient of the predicted point using the coefficient of a reference point, and then the ZTD difference between the predicted point and the surrounding points at different times is calculated; if the ZTD difference is less than the threshold obtained in step (3), the double difference method is directly used for correction.

2. According to the sliding window-based regional relative tropospheric delay modeling method of claim 1, it is characterized in that: In step (1): obtain the ERA5 data of the required grid point in the sliding window for one year, calculate the annual average value of ZTD of each grid point, select a grid point in the sliding window as the reference point, calculate the ZTD difference between other grid points in the sliding window and the reference point, and use the least squares method to fit, and obtain the function model between the ZTD difference between the surrounding grid points and the reference point and the latitude, as follows: （1） In formula (1), is the difference between the annual mean ZTD values ​​of the surrounding grid points and the benchmark point, is the model coefficient, is the latitude of the surrounding grid points, The latitude of the reference point.

3. The method for modeling regional relative tropospheric delay based on sliding window according to claim 1, characterized in that: In step (1): within the study area, select a sliding window with a spatial resolution of 2° latitude × 2.5° longitude, and download one year of ERA5 data for the required grid points of 0.25° × 0.25° within the sliding window.

4. The method for modeling regional relative tropospheric delay based on sliding window according to claim 2, characterized in that: In step (2): Model coefficients The function model with longitude is as follows: （2） In formula (2), is the model coefficient The coefficients of the longitude function model, is the longitude of the surrounding grid points, The longitude of the base point.

5. The method for modeling regional relative tropospheric delay based on sliding window according to claim 4, characterized in that: In step (3): multiple grid points at the same latitude are fitted with equations (1) and (2) to obtain the longitude relationship model between any point at the same latitude and the reference point, as follows: （3） （4） In formula (3), is the coefficient of the function model in formula (4) The coefficients of the model with longitude, is the longitude of the surrounding grid points, is the longitude of the reference point; in formula (4), is the difference between the annual mean ZTD of any point and a reference point at the same latitude, is the latitude of the surrounding grid points, is the latitude of the reference point; According to equations (3) and (4), the ZTD difference between any point and the reference point at the same latitude can be calculated.

6. The method for modeling regional relative tropospheric delay based on sliding window according to claim 1, characterized in that: In step (4): In the same window, the ERA5 daily mean data is used as the experimental data. Points within the 0.25°×0.25° spatial resolution of the ERA5 daily mean data are selected as grid points, and the difference is made with the benchmark point. The daily mean value of the ZTD difference of each grid point is calculated. The least squares method is used for fitting to obtain the function model between the ZTD difference of the surrounding grid points and the benchmark point and the longitude, as follows: （5） In formula (5), is the difference between the daily mean ZTD values ​​of the surrounding grid points and the benchmark point; is the model coefficient, is the longitude of the surrounding grid points, The longitude of the base point.

7. The method for modeling regional relative tropospheric delay based on sliding window according to claim 6, characterized in that: In steps (4) and (5): The input layer of the BP neural network includes time, latitude difference between the reference point and the surrounding grid points, and the model coefficients of the previous 48 hours, and the output layer is the model coefficients of the next 24 hours; Select a data set, normalize it, and then divide it into a training set and a test set. The training set is used for BP neural network training, and the test set is used for verification. After the training is completed, the test set data is used for neural network inference to obtain the predicted value of the model coefficient for the next 24 hours, and then the model coefficient is denormalized and restored to the original data scale to establish the BP neural network.

8. The method for modeling regional relative tropospheric delay based on sliding window according to claim 7, characterized in that: In step (4): use the BP neural network to calculate the model coefficients of the same reference point in the same window for the next 24 hours Predict and then calculate the ZTD difference between the same reference point and surrounding points at different times.

9. A method for modeling regional relative tropospheric delay based on sliding windows according to claim 8, characterized in that: In step (5): During the window movement, the BP neural network is used to predict the model coefficients of the prediction point in this window using the coefficients of a reference point in another window. , and then calculate the ZTD difference between the predicted point and the surrounding points at different times.

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