Precise extraction method of ZHD in middle and high latitude areas based on GRNN neural network

Abstract

The application discloses a ZHD precise extraction method in a middle and high latitude area based on a GRNN neural network, and the method comprises the following steps: acquiring satellite positioning signals captured by a to-be-detected GNSS receiver in real time, and inversely calculating zenith total delay ZTD of a detection point; simultaneously acquiring longitude, latitude and elevation of the detection point, and acquiring time information comprising year, annual day and intra-day time, and the time information jointly constitutes a space-time feature vector; inputting the ZTD and the space-time feature vector as input variables into a pre-trained generalized regression neural network GRNN model; and outputting zenith dry delay ZHD estimation of the detection point corresponding to the present time through nonlinear mapping operation of a neuron layer in the model. The application utilizes the powerful nonlinear mapping capability of the GRNN model, and even in the case that there is no measured air pressure data in the middle and high latitude area, the ZHD extraction with millimeter level precision can be realized, and the accuracy of atmospheric water vapor inversion is further improved.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning and atmospheric environment monitoring technology, specifically to a method for precise extraction of ZHD in mid-to-high latitude regions based on GRNN neural network. Background Technology

[0002] Precipitable water vapor (PWV) refers to the total amount of water vapor in the entire atmosphere from the ground to the zenith. It is an important indicator for describing the total water vapor reserves in a region and has a significant correlation with the actual precipitation in the region.

[0003] High-precision tropospheric total zenith delay (ZTD) can be estimated using widely distributed GNSS (Global Navigation Satellite System) receivers. Removing the atmospheric zenith hydrostatic delay (ZHD) from this estimate yields the zenith wet delay (ZWD), which is related to the instantaneously varying water vapor content in the atmosphere. Multiplying the zenith wet delay by a conversion factor that is a function of the atmospheric weighted average temperature (Tm) gives the final atmospheric precipitable water volume (PWV). Therefore, the accuracy of obtaining the zenith hydrostatic delay (ZHD) is a crucial indicator determining the accuracy of the PWV.

[0004] Currently, the traditional methods for obtaining ZHD and their main problems include:

[0005] 1. Among the traditional Saastamoinen, Hopfield, and Black models, the Saastamoinen model is the most widely used. Although this model can achieve millimeter-level accuracy in calculating ZHD using surface air pressure, it is extremely dependent on the measured air pressure values ​​at the GNSS station elevation. In most practical GNSS applications, the stations are not equipped with high-precision air pressure sensors, which greatly limits the acquisition of high-precision ZHD and subsequent water vapor inversion.

[0006] 2. To reduce reliance on measured meteorological parameters, existing technologies often employ meteorological models such as GPT3, built using reanalysis data based on spherical harmonic functions. The GPT3 model can predict ZHD by inputting parameters such as latitude, longitude, elevation, and date. However, research has found that the accuracy of traditional GPT3 models is significantly affected by latitude, especially in mid-to-high latitude regions, where its prediction accuracy is poor and its stability is insufficient, making it difficult to meet the needs of high-precision meteorological monitoring. Furthermore, spherical harmonic functions are insufficient to accurately describe the nonlinear evolution of atmospheric parameters under complex terrain and specific climatic backgrounds. Summary of the Invention

[0007] This invention addresses the aforementioned technical problems of traditional ZHD methods by providing a precise ZHD extraction method for mid-to-high latitude regions based on a GRNN neural network, thereby improving ZHD prediction accuracy.

[0008] To achieve the above technical objectives, the present application adopts the following technical solution.

[0009] A precise ZHD extraction method for mid-to-high latitude regions based on GRNN neural networks includes:

[0010] The satellite positioning signal captured by the GNSS receiver under test is acquired in real time, and the total zenith delay (ZTD) of the station is obtained by inversion based on the positioning signal.

[0011] The longitude, latitude, and elevation of the current location of the GNSS receiver, along with the corresponding time information, are used to construct a spatiotemporal feature vector. The time information includes the year, annual day, and intraday time.

[0012] The obtained total zenith delay (ZTD) of the station and the spatiotemporal feature vector are input as input variables into a pre-trained generalized regression neural network (GRNN) model. Through the nonlinear mapping operation of each neuron layer inside the GRNN model, the estimated value of the current zenith delay (ZHD) of the station is output.

[0013] Furthermore, the method also includes atmospheric water vapor inversion, specifically including:

[0014] Subtract the estimated zenith dry delay (ZHD) from the inverted total zenith delay (ZTD) of the station to obtain the zenith wet delay (ZWD), which characterizes the real-time changes in atmospheric water vapor content.

[0015] Calculate the atmospheric weighted average temperature T m The conversion coefficient is used as the variable. The conversion coefficient is multiplied by the zenith wet delay ZWD, thereby converting the zenith wet delay ZWD into the atmospheric precipitable water volume (PWV) above the station.

[0016] Furthermore, the GRNN model training process includes:

[0017] Determining atmospheric refractive index and atmospheric dry refractive index from training data includes: the atmospheric refractive index and atmospheric dry refractive index being calculated using meteorological parameters, or being extracted directly from refractive index expansion products;

[0018] Based on the atmospheric refractive index and the atmospheric dry refractive index respectively, the ZTD observation value and ZHD reference true value corresponding to each measuring point are calculated by tropospheric layered integration processing.

[0019] The GRNN model is trained by taking the longitude, latitude, elevation, year, annual day, intraday time, and ZTD observation values ​​of each measuring point as input and the ZHD reference true value as the target output.

[0020] Furthermore, the training data consists of meteorological observation records, including air pressure data provided by radiosonde stations. ,temperature and wet ;

[0021] The ZTD observations are calculated as follows:

[0022] Using the air pressure at the station ,temperature and wet Calculate the atmospheric refractive index at each altitude level. ;

[0023] Obtain ground height To the height of the tropopause The height of each adjacent layer , and the corresponding refractive index , By integrating layer by layer, the delay within the corresponding flow layer can be obtained.

[0024] Utilizing the air pressure at the top of the troposphere Station latitude and tropopause height Calculate the residual delay above the tropopause. ;

[0025] The delay within the troposphere and the residual delay The values ​​are added together to obtain the total zenith delay (ZTD) observation value of the station.

[0026] Furthermore, the training data consists of meteorological observation records, including air pressure data provided by radiosonde stations. ,temperature and wet The calculation method for the ZHD reference truth value is as follows:

[0027] Using the air pressure at the station ,temperature and wet Calculate the atmospheric dry refractive index at each altitude level. ;

[0028] ground height To the height of the tropopause Atmospheric dry refractive index By performing layer-by-layer integration, the corresponding ZHD reference true value is obtained.

[0029] Furthermore, the GRNN model employs ten-fold cross-validation to optimize hyperparameters during training, selecting the optimal diffusion value for the model. It is 0.09.

[0030] Furthermore, the GRNN model includes interconnected input layers, pattern layers, summation layers, and output layers, wherein the pattern layer uses a Gaussian kernel function to calculate the similarity between input features and training data.

[0031] Furthermore, the training data is the refractive index extension product of the occultation detection system. The atmospheric refractive index of each altitude layer is extracted based on the refractive index extension product, and the atmospheric dry refractive index is separated by combining the temperature and pressure information in the extension product, thereby determining the ZTD observation value and ZHD reference true value corresponding to each measuring point.

[0032] Furthermore, the process of obtaining the station's total zenith delay (ZTD) based on satellite positioning signal inversion involves using ZTD as a parameter to be determined and projecting the satellite's slant path delay onto the zenith direction through a tropospheric mapping function to obtain the station's total zenith delay (ZTD).

[0033] It should be understood that the summary section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description.

[0034] Compared with existing technologies, the beneficial technical effects of the ZHD precision extraction method based on GRNN neural network in mid-to-high latitude regions provided by this invention include: This method eliminates the need for expensive barometric sensors at GNSS stations; it achieves high-precision ZHD extraction through a neural network model trained on multi-source meteorological data, while also enhancing the convenience of ZHD acquisition. Addressing the issue of poor accuracy of traditional meteorological models in mid-to-high latitude regions, the GRNN (Generalized Regression Neural Network) used in this invention possesses extremely strong nonlinear mapping capabilities, enabling it to better capture the nonlinear relationships between local meteorological elements. It considers not only location (latitude, longitude, elevation) and time (yearly days, time), but also introduces ZTD as an input variable. ZTD contains real-time tropospheric delay information; the neural network can extract the physical features related to dry delay (ZHD) from the ZTD, thus achieving more accurate results than simply relying on spatiotemporal coordinate prediction. Attached Figure Description

[0035] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of this application in any way. Furthermore, the shapes and scales of the components in the drawings are merely illustrative to aid in understanding this application and do not specifically limit the shapes and scales of the components. Those skilled in the art, guided by the teachings of this application, can select various possible shapes and scales to implement this application according to specific circumstances. In the drawings:

[0036] Figure 1 This is a schematic diagram of the ZHD precision extraction method for mid-to-high latitude regions based on GRNN neural network, provided as an example.

[0037] Figure 2 This is a schematic diagram illustrating the principle of obtaining the zenithal delay (ZHD) estimate using the GRNN model in the embodiment.

[0038] Figure 3 This is a schematic diagram of the root mean square error of the GRNN model prediction of the zenith dry delay ZHD under different diffusion factors in the example.

[0039] Figure 4 This diagram illustrates the root mean square error (RMSE) of PWV in the northern, central, and southern parts of a certain region, based on the GRNN and GPT3 models. Detailed Implementation

[0040] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0041] Traditional empirical models for calculating ZHD mainly include the Saastamoinen model, the Hopfield model, and the Black model, among which the Saastamoinen model is the most practical.

[0042] The Saastamoinen model can directly calculate ZHD using surface air pressure with an accuracy down to the millimeter level. The calculation formula is as follows:

[0043] ;

[0044] In the formula, This is the air pressure at the GNSS station (unit: hPa). It is the latitude of the GNSS station. It is the elevation (in meters) at the GNSS station.

[0045] Accurate ZHD calculations require measured air pressure values ​​at the elevation of GNSS stations. However, in most current GNSS applications, GNSS stations are not equipped with sensors for measuring air pressure. This significantly limits the acquisition of high-precision ZHD at GNSS stations, further restricting high-precision atmospheric water vapor inversion from ground-based GNSS systems.

[0046] The existing GPT3 meteorological model, built using reanalysis data based on spherical harmonics, avoids the dependence of traditional empirical models on actual observations of GNSS station pressure parameters. Its expression is as follows:

[0047] ;

[0048] In the formula, The various meteorological parameters (such as temperature and air pressure) corresponding to the grid are functions of time t; Indicates the average amplitude; and Indicates the annual periodic amplitude; and The amplitude is a six-month cycle. The term "year-end" refers to the current day within that year.

[0049] The GPT3 model does not require measured meteorological parameters; it only needs the corresponding date, latitude, longitude, elevation, and ZTD to predict the zenith dry delay (ZHD), making it an effective means of obtaining meteorological parameters (temperature, air pressure, etc.). However, the accuracy of traditional GPT3 models is significantly affected by latitude, exhibiting problems such as poor accuracy and instability in mid-to-high latitude regions.

[0050] The present invention proposes a precise ZHD extraction method for mid-to-high latitude regions based on GRNN neural network, which solves the problems of ZHD not being able to be obtained due to the lack of air pressure observations near GNSS stations and the low accuracy of ZTD acquisition by GPT3 model in mid-to-high latitude regions, and finally realizes precise ZHD extraction without the need for actual air pressure measurements at GNSS stations.

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0052] like Figure 1 As shown, the ZHD precision extraction method for mid-to-high latitude regions based on GRNN neural network includes: Step 1: Real-time acquisition of satellite positioning signals captured by the GNSS receiver under test, and inversion of the station's total zenith delay (ZTD) based on the positioning signals;

[0053] Step 2: Obtain the longitude, latitude, and elevation of the GNSS receiver's current location, as well as the corresponding time information to form a spatiotemporal feature vector. The time information includes the year, annual day, and intraday time.

[0054] Step 3: Input the obtained total zenith delay (ZTD) and spatiotemporal feature vectors of the station as input variables into the pre-trained generalized regression neural network (GRNN) model;

[0055] Step 4: Through nonlinear mapping operations of each neuron layer within the GRNN model, the estimated zenithal hourly delay (ZHD) value corresponding to the current station is obtained.

[0056] In this embodiment, the inversion process in step 1 involves using ZTD as a parameter to be determined and projecting the satellite slant path delay to the zenith direction through the tropospheric mapping function to obtain the station's total zenith delay ZTD.

[0057] In some embodiments, the ZHD precision extraction method for mid-to-high latitude regions based on GRNN neural networks also includes atmospheric water vapor inversion, specifically including: subtracting the estimated ZHD from the obtained station zenith total delay (ZTD) to separate the zenith wet delay (ZWD) characterizing the real-time changes in atmospheric water vapor content; and calculating the atmospheric weighted average temperature T. m The conversion coefficient is used as the variable. The conversion coefficient is multiplied by the zenith wet delay ZWD, thereby converting the zenith wet delay ZWD into the atmospheric precipitable water volume (PWV) above the station.

[0058] Generalized Regression Nural Network (GRNN) is a radial basis function network model based on mathematical statistics. It is a forward propagation neural network with strong nonlinear mapping ability and fast learning speed. It can also handle unstable data, making it an effective tool for function regression, fitting, and prediction.

[0059] In this embodiment, the method further includes training the GRNN model.

[0060] In this embodiment, the GRNN model is trained using radiosonde data and occultation data to establish a ZHD acquisition method based on the GRNN model, thereby solving the problem of high-precision PWV extraction when there are no barometric pressure observations at GNSS observation stations.

[0061] During model training, the input variables mainly include: latitude (Lat), longitude (Lon), elevation (Elevation), year (Year), day of year (DOY), hour of day (HOD) of the occultation and radiosonde sites, and the ZTD calculated based on the radiosonde and occultation datasets. Among the above variables, location (longitude, latitude, altitude) and time (year, day of year, hour of day) can be directly obtained from the radiosonde and occultation data, but ZTD cannot be directly obtained.

[0062] As an example, the GRNN model training process includes: determining the atmospheric refractive index and atmospheric dry refractive index from the training data, including: the atmospheric refractive index and atmospheric dry refractive index are calculated using meteorological parameters or extracted directly from refractive index extension products; based on the atmospheric refractive index and atmospheric dry refractive index, the ZTD observation value and ZHD reference true value corresponding to each measuring point are calculated respectively through tropospheric layered integration processing; using the longitude, latitude, elevation, year, annual day, intraday time and ZTD observation value of each measuring point as input, and the ZHD reference true value as the target output, the GRNN model is trained by parameter fitting.

[0063] In some embodiments, the training data are meteorological observation records, including air pressure data from radiosonde stations. ,temperature and wet .

[0064] The total zenith delay (ZTD) can be obtained by integrating the refractive index. Atmospheric refractive index is not directly provided in sounding station data; it must first be obtained through pressure analysis. (hPa) and specific humidity Calculate water vapor pressure (g / kg) (hPa), combined with temperature (K) Calculate the atmospheric refractive index .

[0065] As an example, the ZTD observations are calculated as follows:

[0066] Using the air pressure at the station ,temperature and wet Calculate the atmospheric refractive index at each altitude level. ; (1) (2)

[0067] Where: constant =77.6890 (K / hPa); =71.2952 (K / hPa); =375463 (K) 2 / hPa).

[0068] The ZTD at each point can be obtained by integrating the refractive index layer by layer to the top layer and adding it together with the part calculated by the Saastamoinen model above the top layer; the ZHD can be obtained by integrating the refractive index of dry atmosphere.

[0069] In the embodiment, the ground height is obtained. (Unit: m) to the height of the tropopause (Unit: m) Height between adjacent layers , and the corresponding refractive index , By integrating layer by layer, the corresponding delay within the troposphere is obtained; the air pressure at the top of the troposphere is used. (Unit: hpa), station latitude and tropopause height Calculate the residual delay above the tropopause. ; The delay within the troposphere and the residual delay The values ​​are added together to obtain the total zenith delay (ZTD) observation value of the station, expressed as:

[0070] (3)

[0071] In this embodiment, the ZHD reference true value is calculated as follows: using the air pressure at the station... ,temperature and wet Calculate the atmospheric dry refractive index at each altitude level. :

[0072] (4)

[0073] ground height To the height of the tropopause Atmospheric dry refractive index By performing layer-by-layer integration, the corresponding ZHD reference truth value is obtained, expressed as:

[0074] (5)

[0075] H represents the height (unit: m).

[0076] In some embodiments, the training data are refractive index spread products from occultation detection systems. For example, the COSMIC-2 occultation data product provides Level 2 wetPf2, which includes atmospheric refractive index spread information. By directly integrating the COSMIC-2 wetPf2 refractive index data using Equation 3, the zenith total delay (ZTD) observation based on occultation observations can be obtained.

[0077] In the embodiment, the atmospheric dry refractive index of each altitude layer can be determined based on the air pressure, temperature and refractive index distribution information provided by the refractive index expansion product, and then the ZHD reference true value corresponding to each measurement point can be obtained by integration.

[0078] like Figure 2As shown, in some embodiments, the GRNN model includes interconnected input layers, pattern layers (hidden layers), summation layers, and output layers, wherein the pattern layers use a Gaussian kernel function to calculate the similarity between input features and training data.

[0079] The input layer is responsible for receiving data, and each input feature corresponds to a node. The number of nodes in the input layer is consistent with the dimensions of the input data, which is usually represented as a vector. This vector is then directly transmitted to the pattern layer without further processing.

[0080] The pattern layer is responsible for calculating the similarity between the input data and the training data, typically using a Gaussian kernel function as the metric. For the input data... and the training data The pattern layer calculates the response value for each training data point. The formula is:

[0081] (6)

[0082] In the formula, This represents the Euclidean distance between the input data and the training data. is the diffusion value, which is a hyperparameter of the GRNN model.

[0083] The summation layer performs a weighted summation of the outputs of the pattern layer. It has two main parts: first, it calculates the weighted sum, that is, the weighted summation of the pattern layer output and the corresponding target value. The connection weights between its neurons are the values ​​of the first layer and the second layer. Output samples The Middle The first element; second, calculate the sum of the outputs of all pattern layers, with the connection weight of each neuron being 1. The specific formulas are as follows:

[0084] (7) (8)

[0085] In the formula, It is the amount of training data. It is the first The target output value for each training data set. For weighted summation output, Output the cumulative sum. Pattern layer The response value of each training data point.

[0086] The output layer normalizes the output of the summation layer to obtain the final network prediction. The number of neurons in this layer is equal to the dimension of the training data output. The output corresponding valuation The Middle One element:

[0087] (9)

[0088] In the GRNN model, This represents the total number of neurons in the output layer.

[0089] In this embodiment, the training process of the GRNN model also includes selecting the optimal diffusion value for the GRNN model. This involves considering the diffusion value of the pattern layer in the GRNN model. It is usually taken between 0.01 and 0.1, depending on the specific value. Ultimately, this determines the performance of GRNN in ZHD calculation. In this embodiment, ten-fold cross-validation is used to select the optimal diffusion value for the GRNN model, demonstrating high model accuracy evaluation capability. Ten-fold cross-validation divides the dataset into 10 subsets, each serving as the validation set in 10 training iterations, while the other subsets serve as the training set. This allows for a more comprehensive evaluation of the model's stability and generalization ability, reducing bias in single training results. ZHD-GRNN models built using different diffusion values ​​are used for prediction, and the prediction results are compared with the ZHD calculated by the radiosonde station. The root mean square error (RMSE) is used as the parameter accuracy evaluation criterion to select the optimal diffusion value, expressed as:

[0090] (10)

[0091] For predicted values, This is the reference true value calculated using radiosonde observations.

[0092] Depend on Figure 3 It can be seen that, overall, the root mean square error (RMSE) decreases significantly with the increase of the diffusion factor. When the diffusion value is 0.09, the RMSE is 32.27; when the diffusion value is 0.10, the RMSE is 32.21; the difference in RMSE is not significant. In this example, the optimal diffusion factor is selected as 0.09.

[0093] In this embodiment, 20 GNSS stations were selected based on the standard that there are radiosonde stations within 10 kilometers of the CMONOC GNSS station. The names of the corresponding radiosonde stations are shown in Table 1 below. Using the ZHD and PWV measurements from the radiosonde stations as the true values, and utilizing data from CMONOC and the radiosonde stations for the entire year of 2022, the root mean square errors (RMSEs) of ZHD and PWV based on GRNN and GPT3 were calculated respectively. The RMSE was used as the evaluation criterion to assess the performance of GRNN and GPT3 in ZHD prediction and calculation.

[0094] Table 1. Selected CMONOC stations and radiosonde stations

[0095]

[0096] In the examples, as shown in Table 2, the root mean square errors of the ZHD predicted by the GRNN model and calculated by the GPT3 model are 15.23 mm and 28.64 mm, respectively. This reflects that the ZHD predicted by the GRNN is closer to the true ZHD value of the radiosonde station among all samples. The maximum and minimum ZHD values ​​obtained by the GPT3 model are 83.77 mm and 5.62 mm, respectively, which are significantly larger than the GRNN values ​​of 45.16 mm and 6.10 mm. This reflects that the GRNN model can learn the atmospheric characteristics of specific regions and time periods based on training data, and can better capture the nonlinear relationships of meteorological elements in local areas.

[0097] Table 2. RMSE of GRNN prediction results and GPT3 results

[0098]

[0099] In this embodiment, the zenith total delay (ZTD) is calculated using GNSS data from the CMONOC China Land State Network, and the ZHD predicted by GRNN is subtracted to obtain the zenith wet delay (ZWD). Based on this, the ZWD is converted into atmospheric precipitable water volume (PWV) using a conversion factor. ZTD is calculated using GNSS data from three stations (KMIN, LHAS, YNMZ) in southern China, six stations (AHAQ, QHYS, SCGZ, SDQD, SNYA, XZCD) in central China, and eleven stations (GSDH, GSMQ, HLAR, JLYJ, NMEJ, NMEL, NMWT, NXYC, XJAL, XJKC, XJRQ) in northern China. The PWV is then calculated using the ZHD predicted by the GRNN method proposed in this invention.

[0100] like Figure 4 As shown, compared with the traditional harmonic function GPT3, which also does not require station pressure, the average RMSE of GNSS PWV based on GRNN and GPT3 are 5.17 mm and 10.76 mm, respectively. Among the 20 selected stations, 15 stations had PWV RMSE values ​​better than 7 mm based on GRNN, while only 3 stations had values ​​better than 7 mm based on the GPT3 model, representing a 51.9% improvement in accuracy. Due to factors such as water vapor and complex terrain, the PWV estimation based on GRNN ZHD showed relatively lower deviation values ​​in the northern region compared to the southern and central regions, but the overall deviation value was significantly better than the PWV estimation results based on GPT3 ZHD.

[0101] This invention calculates training data for the total zenith delay (ZTD) and zenith dry delay (ZHD) using radiosonde and occultation data. Subsequently, a generalized regression neural network (GRNN) prediction model is constructed, using the station's spatiotemporal coordinates and ZTD as input features and ZHD as the output target. The optimal diffusion value is determined using ten-fold cross-validation. Finally, real-time GNSS station features are input into the model to achieve high-precision extraction of ZHD and inversion of atmospheric precipitable water volume (PWV). This invention solves the problems of ZHD acquisition failure due to the lack of barometric pressure sensors at GNSS stations, and the low accuracy and large fluctuations of the traditional GPT3 model in mid-to-high latitude regions.

[0102] In practical industrial applications, ZHD estimates can be used to correct GNSS positioning errors, improve industrial measurement accuracy, and adapt to scenarios such as mine surface subsidence monitoring and large-scale building construction layout. This is achieved entirely through automated measurement equipment and systems, avoiding the need for manual calculations.

[0103] Specific usage methods may include:

[0104] 1. The ZHD estimate is automatically transmitted to the GNSS automated measurement system in real time, without the need for manual input or judgment.

[0105] 2. In the GNSS automated measurement system, a fixed data processing flow is preset (existing industrial measurement error correction logic can be used only). The ZHD estimate is used as the core correction parameter for tropospheric delay error, replacing the estimate of the traditional empirical model. The system automatically completes the correction calculation of the positioning data and outputs high-precision three-dimensional coordinate data.

[0106] The above provides a detailed description of the ZHD precision extraction method for mid-to-high latitude regions based on GRNN neural network provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The above description of the embodiments is only for the purpose of helping to understand the concept of this application and should not be construed as a limitation on the scope of protection of this application.

Claims

1. A method for precise ZHD extraction in mid-to-high latitude regions based on GRNN neural network, characterized in that, include: The satellite positioning signal captured by the GNSS receiver under test is acquired in real time, and the total zenith delay (ZTD) of the station is obtained by inversion based on the positioning signal. The longitude, latitude, and elevation of the current location of the GNSS receiver, along with the corresponding time information, are used to construct a spatiotemporal feature vector. The time information includes the year, annual day, and intraday time. The obtained total zenith delay (ZTD) of the station and the spatiotemporal feature vector are input as input variables into a pre-trained generalized regression neural network (GRNN) model. Through the nonlinear mapping operation of each neuron layer inside the GRNN model, the estimated value of the current zenith delay (ZHD) of the station is output.

2. The method for precise ZHD extraction in mid-to-high latitude regions according to claim 1, characterized in that, The method also includes atmospheric water vapor inversion, specifically including: Subtract the estimated zenith dry delay (ZHD) from the inverted total zenith delay (ZTD) of the station to obtain the zenith wet delay (ZWD), which characterizes the real-time changes in atmospheric water vapor content. Calculate the atmospheric weighted average temperature T m The conversion coefficient is used as the variable. The conversion coefficient is multiplied by the zenith wet delay ZWD, thereby converting the zenith wet delay ZWD into the atmospheric precipitable water volume (PWV) above the station.

3. The method for precise ZHD extraction in mid-to-high latitude regions according to claim 1, characterized in that, The GRNN model training process includes: Atmospheric refractive index and atmospheric dry refractive index are determined from training data. The atmospheric refractive index and atmospheric dry refractive index are calculated using meteorological parameters or extracted directly from refractive index expansion products. Based on the atmospheric refractive index and the atmospheric dry refractive index respectively, the ZTD observation value and ZHD reference true value corresponding to each measuring point are calculated by tropospheric layered integration processing. The GRNN model is trained by taking the longitude, latitude, elevation, year, annual day, intraday time, and ZTD observation values ​​of each measuring point as input and the ZHD reference true value as the target output.

4. The method for precise ZHD extraction in mid-to-high latitude regions according to claim 3, characterized in that, The training data consists of meteorological observation records, including air pressure data provided by radiosonde stations. ,temperature and wet ; The ZTD observations are calculated as follows: Using the air pressure at the station ,temperature and wet Calculate the atmospheric refractive index at each altitude level. ; Obtain ground height To the height of the tropopause The height of each adjacent layer , and the corresponding refractive index , ; By integrating layer by layer, the delay within the corresponding flow layer can be obtained; Utilizing the air pressure at the top of the troposphere Station latitude and tropopause height Calculate the residual delay above the tropopause. ; The delay within the troposphere and the residual delay The values ​​are added together to obtain the total zenith delay (ZTD) observation value of the station.

5. The method for precise ZHD extraction in mid-to-high latitude regions according to claim 3, characterized in that, The training data consists of meteorological observation records, including air pressure data provided by radiosonde stations. ,temperature and wet ; The ZHD reference truth value is calculated as follows: Using the air pressure at the station ,temperature and wet Calculate the atmospheric dry refractive index at each altitude level. ; ground height To the height of the tropopause Atmospheric dry refractive index By performing layer-by-layer integration, the corresponding ZHD reference true value is obtained.

6. The method for precise ZHD extraction in mid-to-high latitude regions according to claim 3, characterized in that, The GRNN model employs ten-fold cross-validation to optimize hyperparameters during training, selecting the optimal diffusion value for the model. It is 0.

09.

7. The method for precise extraction of ZHD in mid-to-high latitude regions according to claim 3, characterized in that, The GRNN model includes interconnected input, pattern, summation, and output layers, where the pattern layer uses a Gaussian kernel function to calculate the similarity between input features and training data.

8. The method for precise extraction of ZHD in mid-to-high latitude regions according to claim 3, characterized in that, The training data is the refractive index extension product of the occultation detection system. The atmospheric refractive index of each altitude layer is extracted based on the refractive index extension product, and the atmospheric dry refractive index is separated by combining the temperature and pressure information in the extension product, thereby determining the ZTD observation value and ZHD reference true value corresponding to each measuring point.

9. The method for precise extraction of ZHD in mid-to-high latitude regions according to claim 1, characterized in that, The process of obtaining the total zenith delay (ZTD) of a station based on satellite positioning signal inversion involves using ZTD as a parameter to be determined and projecting the satellite slant path delay to the zenith direction through a tropospheric mapping function to obtain the total zenith delay (ZTD) of the station.

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