Troposphere delay correction method and system fusing gnss and numerical weather prediction products

Abstract

The application discloses a troposphere delay correction method fusing GNSS and numerical weather prediction products, comprising the following steps: when receiving a delay calculation request of a target point at a target time, determining a grid unit where the target point is located; inputting the coordinates and elevation of the target point into a fusion model constructed in the grid unit to output predicted values of zenith dry delay and zenith wet delay; for the grid unit with a GNSS site, the construction of the fusion model comprises the following steps: obtaining first delay data of the GNSS site at the target time through time extrapolation based on a sliding autoregressive model, synchronously obtaining second delay data of a numerical weather prediction product at the same target time, and aligning the first delay data and the second delay data with the target time; adopting a double dynamic weighting strategy of distance and accuracy to fuse the time-aligned first delay data and the second delay data on zenith dry delay and zenith wet delay respectively, and outputting predicted values of the target point at the target time.

Description

Technical Field

[0001] This invention belongs to the field of global navigation satellite system technology, and in particular relates to a method for GNSS tropospheric delay modeling and tropospheric delay error correction by integrating GNSS and numerical weather prediction products. Background Technology

[0002] Tropospheric delay is a key error source affecting the accuracy of satellite navigation and positioning, and accurate correction of this error is of great significance for improving positioning accuracy. Traditional tropospheric delay correction methods mostly use a single data source to build an empirical model, which has obvious limitations: First, empirical models rely on meteorological data, and the error is large in areas where meteorological data is sparse; second, although single GNSS data has high accuracy, it is discretely distributed and has insufficient spatial coverage; third, although single numerical weather prediction models (such as GFS) can provide continuous grid data, they are affected by model accuracy and initial field errors, making it difficult to meet the requirements of high-precision positioning. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, this invention provides a tropospheric delay correction method that integrates GNSS and numerical weather prediction products. By combining the high-precision characteristics of GNSS data with the spatial continuity advantages of numerical weather prediction model data, and introducing a heterogeneous processing strategy for vertical and horizontal variations in tropospheric delay and a dynamic weighting strategy that takes into account both distance and data accuracy, a high-precision, high-spatial-resolution tropospheric delay product is finally generated.

[0004] According to one aspect of the present invention, a method for tropospheric delay correction that integrates GNSS and numerical weather prediction products is provided, comprising:

[0005] Upon receiving a request to calculate the coordinates of the target point and the delay of the target time, the grid cell in which the target is located is determined based on the coordinates of the target point;

[0006] The coordinates and elevation of the target point are input into the fusion model already constructed within the grid cell, and the predicted values ​​of zenith dry delay and zenith wet delay are output; wherein, for grid cells with GNSS stations, the construction of the fusion model includes:

[0007] Acquire the first delay data of GNSS stations at the target time obtained by time extrapolation based on the sliding autoregressive model, and simultaneously acquire the second delay data of numerical weather forecast products at the same target time. Both the first delay data and the second delay data are aligned with the target time.

[0008] A dual dynamic weighting strategy of distance and accuracy is adopted to fuse the time-aligned first and second delay data on zenith dry delay and zenith wet delay respectively, and output the predicted values ​​of zenith dry delay and zenith wet delay of the target point and the target time.

[0009] As a further technical solution, for grid cells without GNSS stations, the construction of the fusion model includes:

[0010] Obtain delayed data of numerical weather forecast products at the same target time;

[0011] The acquired delay data is time-aligned to the target time.

[0012] A dual dynamic weighting strategy of distance and accuracy is adopted to fuse time-aligned delay data on zenith dry delay and zenith wet delay, and output the predicted values ​​of zenith dry delay and zenith wet delay of the target point and the target time.

[0013] As a further technical solution, the first delay data of the GNSS station at the target time, obtained by time extrapolation based on a sliding autoregressive model, includes:

[0014] Based on historical GNSS data, a posterior parameter search strategy is used to determine the optimal order of the moving autoregressive model;

[0015] After obtaining the optimal order, the historical GNSS data is used to refit the moving autoregressive model and obtain the historical residuals;

[0016] Substitute the historical GNSS data and historical residuals into the fitted sliding autoregressive model to extrapolate and predict the zenith dry delay and zenith wet delay for a future preset time period.

[0017] Linear interpolation is performed within the extrapolated prediction data interval to obtain the zenith dry delay estimate and zenith wet delay estimate at the target time, which are used as the first delay data.

[0018] As a further technical solution, acquiring second-delay data from numerical weather prediction products at the same target time includes:

[0019] Search the numerical weather prediction product data for the two forecast times closest to the target time, and obtain the full grid data of the entire study area for these two forecast times;

[0020] For each grid point in the grid data at two forecast times, time linear interpolation is performed on its zenith dry delay and zenith wet delay values ​​to calculate the delay value of the current grid point at the target time, which is used as the second delay data.

[0021] As a further technical solution, a dual dynamic weighting strategy of distance and accuracy is adopted to fuse the time-aligned first and second delay data on zenith dry delay and zenith wet delay, respectively, including:

[0022] The vertical stratification and horizontal turbulence component of the zenith wet delay in the first and second delay data are modeled as heterogeneous separation, and the vertical component, turbulence component and error component of the zenith wet delay are calculated.

[0023] The zenith dry delay in the first and second delay data is modeled using a quadratic surface weighted fitting method, and the zenith dry delay is calculated.

[0024] A dynamic weighting strategy is adopted to fuse the vertical component, turbulence component, error component, and zenith dry delay of the zenith wet delay, and output the predicted values ​​of the zenith wet delay and zenith dry delay of the target point.

[0025] As a further technical solution, heterogeneous separation modeling of vertical stratification and horizontal turbulence components is performed, including:

[0026] The zenith wet delay is decomposed into a vertical component reflecting the attenuation of water vapor with altitude and a turbulent component reflecting horizontal non-uniform changes.

[0027] The vertical component is calculated using an exponential decay model;

[0028] The residual term after subtracting the vertical component from the zenith wet delay is regarded as a noisy turbulent component, and the turbulent component is modeled using a quadratic polynomial surface weighted fitting method.

[0029] The turbulence components are solved by weighted least squares method, and then the turbulence components and error components of the zenith wet delay are obtained.

[0030] As a further technical solution, the dynamic weighting strategy is as follows:

[0031] ,

[0032] Among them, subscript or Indexes representing data points; For the prediction point and the surface fitting target region, the first The horizontal distance between known points; For the prediction point and the surface fitting target region, the first Horizontal distance between known points; subscript Represents data type; Indicates the first Data types corresponding to the known points Standard deviation; Representative index The quantity.

[0033] As a further technical solution, the method also includes:

[0034] At fixed time intervals, using the latest GNSS and numerical weather prediction product data, data fusion and model building are performed for each grid cell, and the model parameter library is updated.

[0035] According to one aspect of the present invention, a tropospheric delay correction system integrating GNSS and numerical weather prediction products is provided, comprising:

[0036] The data acquisition module is used to determine the grid cell where the target is located based on the coordinates of the target point when it receives a request to calculate the delay of the target time.

[0037] The data processing module is used to input the coordinates and elevation of the target point into the pre-built fusion model within the grid cell, and output the predicted values ​​of zenith dry delay and zenith wet delay; wherein, for grid cells with GNSS stations, the construction of the fusion model includes:

[0038] Acquire the first delay data of GNSS stations at the target time obtained by time extrapolation based on the sliding autoregressive model, and simultaneously acquire the second delay data of numerical weather forecast products at the same target time. Both the first delay data and the second delay data are aligned with the target time.

[0039] A dual dynamic weighting strategy of distance and accuracy is adopted to fuse the time-aligned first and second delay data on zenith dry delay and zenith wet delay respectively, and output the predicted values ​​of zenith dry delay and zenith wet delay of the target point and the target time.

[0040] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the tropospheric delay correction method for fusing GNSS and numerical weather prediction products.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] This invention separates the computationally intensive "model building" from the lightweight "service response," eliminating the need to pre-generate and store high-resolution grid products covering the entire domain, thus greatly reducing storage costs; it only needs to perform fast calculations based on existing models when a user requests them, enabling efficient and flexible responses to different users' needs for high-precision latency correction at any location. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart illustrating the tropospheric delay correction method for fusing GNSS and numerical weather prediction products provided in an embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram illustrating the construction of the fusion model provided in an embodiment of the present invention.

[0046] Figure 3 This is a schematic diagram illustrating the construction of a fusion model provided in another embodiment of the present invention. Detailed Implementation

[0047] In recent years, multi-source data fusion technology has provided a new approach for high-precision tropospheric delay correction. By fusing GNSS and Numerical Weather Prediction (NWP) products, the high precision of GNSS data and the continuity of NWP data can be leveraged to generate tropospheric delay products with higher accuracy and better resolution. In areas with dense GNSS station distribution, the fusion method can significantly improve the spatial resolution of the delay field; while in areas with sparse GNSS stations, NWP data can provide effective background fields and spatial constraints, compensating for the limitations of a single data source. Therefore, developing a high-precision tropospheric delay correction method that fully utilizes the advantages of multi-source data fusion has significant application value.

[0048] The purpose of this invention is to provide a new method for correcting tropospheric delay by fusing GNSS and numerical weather prediction data. This method combines the high precision of GNSS data with the spatial continuity of numerical weather prediction model data. Furthermore, it introduces a heterogeneous processing strategy for vertical and horizontal variations in tropospheric delay and a dynamic weighting strategy that balances distance and data accuracy. The ultimate goal is to generate high-precision, high-spatial-resolution tropospheric delay products.

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0050] The method described in this invention utilizes gridded numerical weather prediction (NWP) products as one of the fusion data sources. The zenith dry delay (ZHD) and zenith wet delay (ZWD) are calculated using layered NWP grid data. Simultaneously, the zenith dry delay (ZHD) at GNSS stations is calculated using barometric pressure data provided by NWP, and then the ZHD is removed from the GNSS total zenith delay (ZTD) to obtain the zenith wet delay (ZWD). Subsequently, the ZHD and ZWD data from the GNSS stations are fused with the ZHD and ZWD grid data calculated from the NWP data to generate a high-precision, high-resolution tropospheric delay correction product.

[0051] like Figure 1 As shown in the figure, the embodiment of the present invention provides a tropospheric delay correction method for fusing GNSS and numerical weather prediction products. First, when a delay calculation request for the coordinates of a target point and the target time is received, the grid cell in which the target is located is determined based on the coordinates of the target point. Then, the coordinates and elevation of the target point are input into the fusion model that has been constructed in the grid cell, and the predicted values ​​of zenith dry delay and zenith wet delay are output.

[0052] For grid cells containing GNSS stations, the construction of the fusion model is as follows: Figure 2 As shown, it includes:

[0053] Acquire the first delay data of GNSS stations at the target time obtained by time extrapolation based on the sliding autoregressive model, and simultaneously acquire the second delay data of numerical weather forecast products at the same target time. Both the first delay data and the second delay data are aligned with the target time.

[0054] A dual dynamic weighting strategy of distance and accuracy is adopted to fuse the time-aligned first and second delay data on zenith dry delay and zenith wet delay respectively, and output the predicted values ​​of zenith dry delay and zenith wet delay of the target point and the target time.

[0055] Specifically, in view of the shortcomings of existing GNSS tropospheric delay correction methods, namely (1) it is difficult for a single data source to take into account both accuracy and spatial continuity; (2) the spatial heterogeneity of tropospheric delay components is not considered when fusing multi-source data; and (3) the fusion weighting strategy fails to take into account the dual impact of distance and accuracy at the same time, this invention proposes the following solutions.

[0056] Step 1: Construction of GNSS ZHD and ZWD Time Extrapolation Model. To achieve high-precision GNSS positioning, especially in real-time applications, it is essential to obtain tropospheric delay information that is strictly synchronized with the positioning time. However, the calculation of GNSS station data typically involves delays, making it impossible to directly provide values ​​for the current or future time. Therefore, this invention requires extrapolating the delay estimate of the target time based on historical GNSS ZHD and ZWD sequences. This invention employs a high-precision time extrapolation method based on an Autoregressive Moving Average (ARMA) model. This method effectively captures the temporal dependencies and random fluctuations in the delayed signal, thereby achieving reliable short-term predictions. The specific construction details of this model are as follows:

[0057] The core mathematical expression of the sliding autoregressive model (ARMA) is as follows:

[0058] ,

[0059] in, represents the ZWD or ZHD at the time to be determined; c represents the constant term of the model; p represents the order of the autoregressive (AR) term; i represents the summation index; Let i be the i-th autoregressive coefficient; q represents the historical observation value at time ti; q represents the order of the moving average (MA) term; j represents the summation index; Let be the coefficient of the j-th moving average; The historical prediction error for time tj; White noise was used. The extrapolation time was 2 hours, with a time interval of 5 minutes, which reduced the amount of data computation and the complexity of the fusion model while ensuring that the main changes in tropospheric delay were captured.

[0060] This invention utilizes historical GNSS data from the previous 12 hours, with a sampling interval of 5 minutes, and employs a posterior parameter search strategy to determine the optimal order (p, q) of the ARMA model. The specific steps are as follows: First, parameter search is performed. Within a set range (p from 1 to 5, q from 0 to 3), for each parameter combination (p, q), the ARMA model is fitted using historical data (from the previous 10 hours). Then, model validation is performed. The fitted ZWD and ZHD extrapolation models are used to predict ZWD and ZHD for a subsequent period (the last 2 hours), and the predicted values ​​are compared with the corresponding actual observations. Finally, the optimal order is determined by calculating the root mean square error (RMSE) of the prediction results for each parameter combination (p, q), and selecting the combination (p, q) that minimizes the RMSE as the optimal model order for the current sliding window.

[0061] After obtaining the optimal order, the ARMA model was refitted using all historical data (the first 12 hours). Then, the historical data and known historical residuals were substituted into the fitted model, ignoring currently unknown noise terms, to extrapolate and predict ZHD and ZWD for the next 2 hours. Since the target time TOI may not be perfectly aligned with the data sampling time, high-precision ZWD and ZHD estimates for the TOI time were obtained directly through linear interpolation within the predicted data interval, and these prediction results were denoted as ZHD-I and ZWD-I, respectively. Thus, the zenith dry delay estimate ZHD-I and the zenith wet delay estimate ZWD-I for all GNSS stations at the target time TOI were obtained, forming a set of high-precision, discrete, point-distributed GNSS tropospheric delay data.

[0062] Step 2: After obtaining the delay data (ZHD-I and ZWD-I) of the TOI at the GNSS station, it is necessary to simultaneously acquire the delay fields of the numerical weather prediction products at the same time for fusion. Since the NWP products are forecast fields, their output time is fixed and usually does not coincide with the target time TOI, so time registration is required.

[0063] Search the Global Forecast System (GFS) data for the two forecast times immediately before and after the target time (TOI) (denoted as ). and ,and ), to obtain full-grid data of the entire study area at these two moments (i.e., two sets corresponding to the two moments respectively). and (A field containing all grid points ZHD and ZWD). and For each grid point in the grid data at time TOI, its ZHD and ZWD values ​​are interpolated linearly over time to calculate the delay value of that grid point at time TOI. The calculation formula is as follows:

[0064] .

[0065] This operation will correspond the two input sets to... and The grid delay fields at time 1 are fused to generate a complete set of grid delay fields corresponding to the target time TOI. The interpolation results are denoted as ZHD-II and ZWD-II, respectively, as delay estimates of the GFS data source at time TOI. Thus, a set of spatially continuous grid-distributed GFS delay field data (ZHD-II and ZWD-II) synchronized with GNSS data is obtained.

[0066] Step 3: After processing in steps 1 and 2, two sets of time-aligned delay data for the target time (TOI) are obtained: one is the zenith dry and wet delay (denoted as ZHD-I and ZWD-I) obtained by extrapolating the GNSS station time, which is discrete point data; the other is the zenith dry and wet delay grid (denoted as ZHD-II and ZWD-II) obtained by time interpolation of GFS grid data, which is grid data.

[0067] ZWD-I and ZWD-II exhibit vertical stratification and horizontal turbulent fluctuation characteristics, and their variations show significant spatial heterogeneity. Direct fusion is insufficient to accurately describe their spatial variations. Furthermore, GNSS data has high accuracy but is distributed in a point-like discrete pattern, while GFS data is spatially continuous but has relatively low accuracy. Therefore, a fusion method that can simultaneously balance spatial distance and data source accuracy needs to be designed.

[0068] To address the above issues, the fusion and interpolation process in this step is divided into two parts: First, the zenith wet delay (ZWD) is modeled as a heterogeneous separation of vertical stratification and horizontal turbulence components to accurately reflect its physical characteristics; Second, a dynamic weighting strategy is adopted during the fusion process, taking into account the spatial distance between the predicted and known points as well as the accuracy differences of different data sources (GNSS and GFS).

[0069] First, the entire study area is divided into multiple regular grid cells. This invention uses a standard cell size of 1°×1°. Within each cell, two cases are handled: the presence of a GNSS station and the absence of a GNSS station within the cell.

[0070] If there is one or more GNSS stations in the current cell, then based on all the data in the cell and the buffer area (including the delay values ​​ZHD-I and ZWD-I of the GNSS station at TOI time, and the delay values ​​ZHD-II and ZWD-II of the GFS grid), a distance and accuracy dynamically weighted fitting method (as described below) is used to independently perform weighted least squares fitting, thereby generating exclusive model parameters for each point to be determined in the cell.

[0071] Then, the zenith wet delay (ZWD) is modeled using a heterogeneous separation of vertical stratification and horizontal turbulent components to accurately reflect its physical characteristics. Within each cell, based on ZWD-I and ZWD-II data, the ZWD is decomposed into two components with distinct physical meanings: a vertical component reflecting the attenuation of water vapor with altitude and a turbulent component reflecting horizontal non-uniform variations. Specifically, the ZWD at location x can be expressed as:

[0072] ,

[0073] in, This represents the vertical component related to altitude h. This represents the turbulent component related to position x. This represents the model error. The vertical component is expressed using an exponential decay model:

[0074] ,

[0075] in, It is the ZWD value at sea level. is the attenuation coefficient, and h is the altitude.

[0076] The following are the specific steps for constructing a hierarchical ZWD model using stratified meteorological data from ERA5:

[0077] Step a: Obtain vertical stratified ERA5 data. For each 1°×1° grid cell in the study area, obtain the ERA5 data corresponding to the target time (TOI) (if there is no data that corresponds exactly to the TOI, use the ERA5 data that is closest in time), including the specific humidity, air pressure and temperature grid data on each standard pressure layer.

[0078] Step b, calculate the vertical profile of ZWD within the cell: For any elevation h within the cell, the zenith wet delay ZWD(h) at that elevation can be calculated by vertical integration, as shown in the following formula:

[0079] ,

[0080] in, Where P is the vapor pressure, T is the atmospheric pressure, and P is the temperature. and The atmospheric refractive index constant, Let h be the atmospheric pressure at an altitude of h. By performing this calculation on all points within the cell, a precise reference profile of the ZWD vertical distribution, varying with altitude h, can be obtained.

[0081] Step c, Fitting the layered function: Based on the ZWD(h) vertical profile obtained in step b, the exponential decay model of the nonlinear least squares fitting formula (5) is used to solve for a set of exclusive optimal parameters for each 1°×1° grid cell. and , representing the vertical variation model of ZWD within the current cell.

[0082] Step d: Calculate the turbulence components. For any known point (whether a GNSS point or a GFS grid point), its vertical component prediction can be directly calculated using formula (5). Then, the vertical component is subtracted from ZWD-I and ZWD-II to obtain the residual term (r), which is considered as a noisy turbulence component. The turbulence components are modeled using a quadratic polynomial surface weighted fitting method:

[0083] ,

[0084] Where x and y are coordinates. These are parameters to be estimated.

[0085] A dynamic weighting strategy is adopted during the fusion process, taking into account both the spatial distance between the point to be determined and the known point, as well as the accuracy differences in tropospheric delay between GNSS and GFS. The following weighting strategy is introduced for this purpose:

[0086] ,

[0087] Where the subscript i or j represents the index of the data point; The horizontal distance between the predicted point and the i-th known point within the target area of ​​the surface fitting is given; the subscript k represents the data type (k=1 represents GNSS data, k=2 represents GFS data); Let represent the standard deviation (STD) of the data type k corresponding to the i-th known point. For data from GNSS (i.e., k=1, data are ZHD-I and ZWD-I), the standard deviation is directly taken as the mean square error of the zenith delay solution output by the GNSS data post-processing software. For data from GFS (i.e., k=2, data are ZHD-II and ZWD-II), the standard deviation is determined by comparing it with GNSS data. Within the study area, the GFS delay estimates (ZHD-II and ZWD-II) of all GNSS station locations are compared with the precise solution values ​​(as the reference true values) corresponding to the GNSS stations, and the standard deviation (STD) of the deviation is calculated. This STD is used as the prior accuracy estimate of the GFS data source. Under normal circumstances The exponent c is used to adjust the degree of attenuation of the distance effect, and is set to 2 here.

[0088] The turbulent components are solved using the weighted least squares method, and the objective function is:

[0089] ,

[0090] in This represents the weight of the i-th known point. This is the residual of the i-th known point (i.e., the part after deducting the vertical component from the wet delay). This represents the predicted turbulence component for the i-th known point. Data points that are closer and have higher accuracy have greater weights, and the surface will primarily fit the high-precision, close-range known points.

[0091] Finally, the turbulent component, vertical component, and error component of ZWD are obtained.

[0092] As for the zenith dry delay (ZHD), since its variation mainly depends on air pressure and elevation, no component decomposition is performed. Instead, it is modeled directly based on the ZHD-I and ZHD-II data within the cell using a quadratic surface weighted fitting method, with the weights calculated in the same way as above.

[0093] By using the above-mentioned dynamic weighted surface fitting method, the fused estimate of the zenith dry delay (ZHD) and zenith wet delay (ZWD) of any point (POI) within the cell can be obtained.

[0094] The above fusion method also applies to cases where there are no GNSS stations within the unit, such as... Figure 3 As shown. At this time, the only data source available for fitting is GFS grid data (ZHD-II and ZWD-II). Therefore, the fusion strategy needs to be simplified: when calculating the weights, formula (8) can be replaced with formula (10).

[0095] ,

[0096] Based on this, the direct surface fitting of ZHD and the component decomposition and fitting process of ZWD remain unchanged.

[0097] Step 4, final fusion and product generation, using the multi-source fusion model built in step 3 to solve for the ZHD and ZWD corresponding to TOI and POI (point of interest).

[0098] After the above component decomposition and calculation, the system generates and saves its own fusion model parameters (such as vertical component parameters, turbulence component fitting surface coefficients, etc.) for each 1°×1° grid cell. The final product generation of this invention adopts an efficient "service response" mode, the process of which is as follows:

[0099] 1. Model pre-calculation: The system performs data fusion and model building for each unit at fixed time intervals (e.g., every 5 minutes) using the latest GNSS and NWP data, and updates the model parameter library to ensure that the model is always based on the latest meteorological and observational conditions.

[0100] 2. Real-time on-demand calculation: When a request for delayed calculation of the coordinates of a target point (POI) and the target time (TOI) is received, the system workflow is as follows:

[0101] First, determine the cell to which it belongs: Based on the latitude and longitude coordinates of the POI, determine the 1°×1° basic grid cell to which it belongs.

[0102] Next, the unit model is invoked: the fusion model (including vertical component parameters, turbulence component fitting surface, etc.) that has been built in the unit is invoked.

[0103] Subsequently, the POI delay value is calculated: the coordinates and elevation of the POI are input into the model, and the predicted values ​​of its zenith dry delay (ZHD) and zenith wet delay (ZWD) are calculated respectively.

[0104] In the above process, when the coordinates of the target point (POI) are received, since the user provides the geodetic height, it needs to be converted into altitude first. h represents altitude, and H represents elevation. This refers to the elevation anomaly in the EGM2008 model.

[0105] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a tropospheric delay correction system that integrates GNSS and numerical weather prediction products. This system is used to execute the tropospheric delay correction method for integrating GNSS and numerical weather prediction products in the above method embodiments.

[0106] The system includes: a data acquisition module, used to determine the grid cell where the target is located based on the coordinates of the target point when a delay calculation request for the coordinates of the target point and the target time is received; and a data processing module, used to input the coordinates and elevation of the target point into a pre-built fusion model within the grid cell, and output the predicted values ​​of zenith dry delay and zenith wet delay. For grid cells containing GNSS stations, the construction of the fusion model includes: acquiring first delay data of the GNSS station at the target time obtained by time extrapolation based on a sliding autoregressive model, and simultaneously acquiring second delay data of numerical weather prediction products at the same target time, wherein both the first and second delay data are aligned with the target time; employing a dual dynamic weighting strategy of distance and accuracy, fusing the time-aligned first and second delay data on zenith dry delay and zenith wet delay respectively, and outputting the predicted values ​​of zenith dry delay and zenith wet delay for the target point at the target time.

[0107] The tropospheric delay correction system that integrates GNSS and numerical weather prediction products provided in this invention addresses the limitations of traditional tropospheric delay correction methods that often use a single data source to build empirical models. By employing the aforementioned modules, it combines the high-precision characteristics of GNSS data with the spatial continuity advantages of numerical weather prediction model data. Furthermore, it introduces a heterogeneous processing strategy for vertical and horizontal variations in tropospheric delay and a dynamic weighting strategy that balances distance and data accuracy, ultimately generating a high-precision, high-spatial-resolution tropospheric delay product.

[0108] It should be noted that the system embodiments provided by this invention, in addition to implementing the methods in the above method embodiments, are also used to implement the methods in other method embodiments provided by this invention. The difference lies only in setting corresponding functional modules, and their principles are basically the same as those of the above system embodiments provided by this invention. As long as those skilled in the art, based on the above system embodiments and referring to the specific technical solutions in other method embodiments, obtain corresponding technical means and technical solutions composed of these technical means by combining technical features, and improve the modules in the above system embodiments while ensuring the practicality of the technical solutions, they can obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments. For example:

[0109] Based on the above system embodiments, as a preferred embodiment, the tropospheric delay correction system that integrates GNSS and numerical weather prediction products provided in this embodiment of the invention also executes the following instructions:

[0110] For grid cells without GNSS stations, the construction of the fusion model includes: acquiring delay data from numerical weather prediction products at the same target time; aligning the acquired delay data to the target time; and using a dual dynamic weighting strategy of distance and accuracy to fuse the time-aligned delay data on zenith dry delay and zenith wet delay, and outputting the predicted values ​​of zenith dry delay and zenith wet delay at the target point and target time.

[0111] Based on the same inventive concept as any of the foregoing embodiments, this embodiment of the invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the tropospheric delay correction method for fusing GNSS and numerical weather prediction products.

[0112] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for tropospheric delay correction fusing GNSS and numerical weather prediction products, characterized in that, Without pre-generating and storing high-resolution grid products covering the whole domain, the method comprises: Upon receiving a delay calculation request of a target point and a target time, determining a grid cell where the target is located according to the coordinates of the target point; inputting the coordinates and the elevation of the target point into the fusion model already constructed in the grid cell to output the predicted values of the zenith dry delay and the zenith wet delay, comprising: inputting the coordinates and the elevation of the target point into the model to calculate the predicted values of the zenith dry delay and the zenith wet delay respectively; wherein, for the grid cell with GNSS sites, the construction of the fusion model comprises: obtaining first delay data of GNSS sites at the target time obtained by time extrapolation based on the sliding autoregressive model, and synchronously obtaining second delay data of numerical weather prediction products at the same target time, wherein the first delay data and the second delay data are both aligned with the target time; using a dual dynamic weighting strategy of distance and accuracy to fuse the first delay data and the second delay data after time alignment in the zenith dry delay and the zenith wet delay, and output the predicted values of the zenith dry delay and the zenith wet delay of the target point at the target time, comprising: modeling the zenith wet delay in the first delay data and the second delay data by vertical layering and horizontal turbulence component heterogenization separation to calculate the vertical component, the turbulence component and the error component of the zenith wet delay; modeling the zenith dry delay in the first delay data and the second delay data by a quadratic surface weighted fitting method to calculate the zenith dry delay; using a dynamic weighting strategy to fuse the vertical component, the turbulence component and the error component of the zenith wet delay and the zenith dry delay respectively, and output the predicted values of the zenith wet delay and the zenith dry delay of the target point.

2. The method of claim 1, wherein the GNSS and numerical weather prediction product are fused to correct for tropospheric delay. For the grid cell without GNSS sites, the construction of the fusion model comprises: obtaining delay data of numerical weather prediction products at the same target time; time aligning the obtained delay data at the target time; using a dual dynamic weighting strategy of distance and accuracy to fuse the delay data after time alignment in the zenith dry delay and the zenith wet delay, and output the predicted values of the zenith dry delay and the zenith wet delay of the target point at the target time.

3. The method of claim 1, wherein the GNSS and numerical weather prediction product are fused to correct for tropospheric delay. obtaining first delay data of GNSS sites at the target time obtained by time extrapolation based on the sliding autoregressive model, comprising: determining the optimal order of the sliding autoregressive model using a posterior parameter search strategy based on historical GNSS data; after obtaining the optimal order, re-fitting the sliding autoregressive model using the historical GNSS data and obtaining historical residuals; substituting the historical GNSS data and the historical residuals into the fitted sliding autoregressive model to extrapolate and predict the zenith dry delay and the zenith wet delay in a future preset period; performing linear interpolation in the data interval of the extrapolation and prediction to obtain zenith dry delay estimation value and zenith wet delay estimation value at the target time as the first delay data.

4. The method of claim 1, wherein the GNSS and numerical weather prediction product are fused to correct for tropospheric delay. obtaining second delay data of numerical weather prediction products at the same target time, comprising: searching for two closest forecast time points of the target time point in the numerical weather prediction product data, and obtaining the full grid data of the entire study area at the two forecast time points; respectively performing time linear interpolation on the zenith dry delay and zenith wet delay values of each grid point in the grid data of the two forecast time points, to calculate the delay values of the current grid point at the target time point as the second delay data.

5. The method of claim 1, wherein the GNSS and numerical weather prediction product are fused to correct for tropospheric delay. performing heterogeneous separation modeling of vertical stratification and horizontal turbulence components, including: decomposing the zenith wet delay into a vertical component reflecting the attenuation of water vapor with altitude and a turbulence component reflecting the horizontal non-uniform change; calculating the vertical component by using an exponential decay model; regarding the residual term obtained by subtracting the vertical component from the zenith wet delay as a turbulence component with noise, and modeling the turbulence component by using a quadratic polynomial surface weighted fitting method; solving the turbulence component by using a weighted least squares method, and further obtaining the turbulence component and error component of the zenith wet delay.

6. The method of claim 1, wherein the GNSS and numerical weather prediction product are fused to correct for tropospheric delay. the dynamic weighting strategy is: ， Among them, subscript or Indexes representing data points; For the prediction point and the surface fitting target region, the first The horizontal distance between known points; For the prediction point and the surface fitting target region, the first Horizontal distance between known points; subscript Represents data type; Indicates the first Data types corresponding to the known points Standard deviation; Representative index The quantity.

7. The method of claim 1, wherein the GNSS and numerical weather prediction product are fused to correct for tropospheric delay. the method further includes: at fixed time intervals, using the latest GNSS and numerical weather prediction product data to perform data fusion and model construction for each grid unit, and updating the model parameter library.

8. A tropospheric delay correction system fusing GNSS and numerical weather prediction products, characterized in that, without pre-generating and storing high-resolution grid products covering the entire domain, including: a data acquisition module, configured to, when receiving a delay calculation request of a target point at a target time point, determine a grid unit where the target point is located according to the coordinates of the target point; a data processing module, configured to input the coordinates and elevation of the target point into the fusion model constructed in the grid unit, and output the predicted values of the zenith dry delay and the zenith wet delay, including: inputting the coordinates and elevation of the target point into the model to calculate the predicted values of the zenith dry delay and the zenith wet delay respectively; wherein, for the grid unit with GNSS stations, the construction of the fusion model includes: obtaining first delay data of the GNSS stations at the target time point obtained by time extrapolation based on an autoregressive model, and synchronously obtaining second delay data of the numerical weather prediction product at the same target time point, the first delay data and the second delay data being aligned with the target time point; using a dual dynamic weighting strategy of distance and accuracy to fuse the first delay data and the second delay data after time alignment in the zenith dry delay and the zenith wet delay, and output the predicted values of the zenith dry delay and the zenith wet delay of the target point at the target time point, including: performing heterogeneous separation modeling of vertical stratification and horizontal turbulence components on the zenith wet delay in the first delay data and the second delay data, to calculate the vertical component, the turbulence component and the error component of the zenith wet delay; modeling the zenith dry delay in the first delay data and the second delay data by using a quadratic surface weighted fitting method, to calculate the zenith dry delay; using a dynamic weighting strategy to fuse the vertical component, the turbulence component and the error component of the zenith wet delay and the zenith dry delay respectively, and output the predicted values of the zenith wet delay and the zenith dry delay of the target point.

9. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium stores computer instructions that cause the computer to perform the method of fusing GNSS with numerical weather prediction product for troposphere delay correction according to any one of claims 1 to 7.

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