GNSS regional ionospheric delay information acquisition method, device and electronic equipment

Abstract

The application relates to the technical field of satellite navigation and positioning, and provides a GNSS regional ionospheric delay information acquisition method, device and electronic equipment, which comprises the following steps: obtaining an ionospheric delay error initial value of a target grid point based on a pre-constructed polynomial fitting model; obtaining an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, wherein the residual compensation grid model is obtained by Kriging interpolation on the posterior residual of the polynomial fitting model; determining an ionospheric delay error correction value of the target grid point based on the sum of the ionospheric delay error initial value and the compensation value of the target grid point, and performing inverse distance interpolation on the ionospheric delay error correction value of the target grid point to obtain an ionospheric delay error correction value of a station to be measured. The GNSS regional ionospheric delay information acquisition method, device and electronic equipment provided by the application can improve the precision of the ionospheric delay error correction value.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation positioning data processing, and in particular to a method, device and electronic equipment for acquiring GNSS regional ionospheric delay information. Background Art

[0002] The region 50-1000 km above Earth is called the ionosphere. Solar ultraviolet rays and X-rays ionize neutral molecules in the atmosphere, producing positrons and positive ions. When Global Navigation Satellite System (GNSS) signals pass through it, they are refracted, reflected, or absorbed, increasing their propagation time and affecting the ranging accuracy between the satellite and the receiver. This effect is called ionospheric delay error. The ionosphere is a vital component of the Sun-Earth space environment and impacts human production and life. Because ionospheric delay is subject to high electronic fluctuations and is easily affected by factors such as solar and geomagnetic activity, the accuracy of the ionospheric delay error is often difficult to guarantee.

[0003] GNSS plays a vital role in modern positioning, navigation, and timing (PNT) services. However, GNSS signal propagation is significantly affected by ionospheric delay, particularly in high-precision applications, where ionospheric error becomes a major source of error. Ionospheric total electron content (TEC) is a key parameter describing the variability of the ionosphere, and its value is proportional to the amount of ionospheric delay experienced by electromagnetic wave signals. Therefore, researching and constructing high-precision ionospheric TEC models can help mitigate ionospheric delay, accelerate the convergence of precise point positioning (PPP), and enhance monitoring capabilities of the near-Earth space environment.

[0004] However, a major limitation of traditional PPP is its long convergence time, typically taking up to 30 minutes, which severely limits its use in real-time applications. To address this issue, researchers have further developed satellite phase deviation correction products based on traditional PPP, enabling rapid ambiguity fixation in real-time PPP, thus forming PPP-AR technology. However, due to the influence of atmospheric delay parameters, the convergence time still requires approximately 10 minutes, which is insufficient for practical applications. To address this, researchers, drawing on the principles of RTK (Real-Time Kinematic), have further proposed PPP regional enhancement technology (PPP-RTK). This technology, based on high-precision atmospheric delay corrections, mitigates the effects of errors such as atmospheric delay on the user end, thereby achieving rapid ambiguity fixation and high-precision positioning within tens of seconds.

[0005] Therefore, how to obtain accurate atmospheric delay information has become the key to the current PPP-RTK technology, especially the ionospheric delay correction information. Summary of the Invention

[0006] The present invention provides a method, device and electronic equipment for obtaining GNSS regional ionospheric delay information, which are used to solve the defect of poor accuracy of ionospheric delay correction information in the prior art.

[0007] The present invention provides a method for obtaining GNSS regional ionospheric delay information, comprising:

[0008] Obtaining an initial value of the ionospheric delay error of a target grid point based on a pre-constructed polynomial fitting model, where the distance between the target grid point and the station to be measured is within a preset range, the polynomial fitting model being constructed based on oblique path ionospheric delay data extracted from observation data of a GNSS reference station;

[0009] Obtaining an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, wherein the residual compensation grid model is obtained by performing Kriging interpolation on the posterior residuals of the polynomial fitting model;

[0010] Based on the sum of the initial value of the ionospheric delay error of the target grid point and the compensation value, the ionospheric delay error correction value of the target grid point is determined, and the ionospheric delay error correction value of the target grid point is subjected to inverse range interpolation to obtain the ionospheric delay error correction value of the station to be measured.

[0011] According to the method for obtaining GNSS regional ionospheric delay information provided by the present invention, the step of determining the polynomial fitting model includes:

[0012] Obtaining observation data and precise coordinates of the reference station, wherein the observation data includes raw GNSS pseudorange observation data and phase observation values;

[0013] Obtain precision products, including precise satellite orbits, precise satellite clock errors, precise decimal deviations (UPDs), and external dependency files required for precise point positioning (PPP) solutions.

[0014] Extracting the slant path ionospheric delay information of the reference station based on the observation data and precise coordinates of the reference station and the precision product;

[0015] Based on the oblique path ionospheric delay information of the reference station, the polynomial fitting model is constructed, and the model coefficients of the polynomial fitting model are determined.

[0016] According to the GNSS regional ionospheric delay information acquisition method provided by the present invention, based on the observation data and precise coordinates of the reference station and the precision product, the slant path ionospheric delay information of the reference station is extracted, including:

[0017] performing data preprocessing on the observation data of the reference station to obtain preprocessed observation data;

[0018] Calculating satellite positions based on the precise product, and calculating coordinates of satellite penetration points based on the satellite positions and the precise coordinates of the reference station, wherein the coordinates of the satellite penetration points are used to construct an ionospheric model;

[0019] Based on the non-differential non-combined precise point positioning ambiguity fixation technology and the pre-processed observation data, the ionosphere model is solved to obtain the oblique path ionosphere delay information of the reference station.

[0020] According to the GNSS regional ionospheric delay information acquisition method provided by the present invention, the step of determining the residual compensation grid model includes:

[0021] Obtain the posterior residuals of the polynomial fitting model of the reference station corresponding to the satellite;

[0022] Based on the spatial relationship between the grid points and the posterior residual, the ionospheric delay error compensation value of each grid point is obtained by the Kriging interpolation method;

[0023] The residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point.

[0024] According to the GNSS regional ionospheric delay information acquisition method provided by the present invention, the residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point, including:

[0025] Determining the accuracy of the compensation value of each reference station by cross-checking based on the difference between the true residual value of each reference station and the ionospheric delay error compensation value of each grid point;

[0026] Based on the compensation value accuracy of each reference station, determining the compensation value accuracy of each grid point by inverse distance interpolation;

[0027] The residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point and the accuracy of the compensation value.

[0028] According to the GNSS regional ionospheric delay information acquisition method provided by the present invention, the ionospheric delay error compensation value of the target grid point is acquired based on a pre-built residual compensation grid model, including:

[0029] The ionospheric delay error compensation value and the compensation value precision of the target grid point are obtained based on a pre-constructed residual compensation grid model.

[0030] The application further provides a GNSS regional ionospheric delay information acquisition device, comprising:

[0031] An initial value acquisition unit is configured to acquire an ionospheric delay error initial value of a target grid point based on a pre-constructed polynomial fitting model, the distance between the target grid point and a station to be measured being within a preset range, the polynomial fitting model being constructed based on slant path ionospheric delay data extracted from observation data of a GNSS reference station.

[0032] A compensation value acquisition unit is configured to acquire an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, the residual compensation grid model being obtained by Kriging interpolation on a posterior residual of the polynomial fitting model.

[0033] A correction value acquisition unit is configured to determine an ionospheric delay error correction value of the target grid point based on the sum of the ionospheric delay error initial value of the target grid point and the compensation value, and perform inverse distance interpolation on the ionospheric delay error correction value of the target grid point to obtain an ionospheric delay error correction value of the station to be measured.

[0034] The application further provides an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the GNSS regional ionospheric delay information acquisition method as described above when executing the computer program.

[0035] The application further provides a non-transitory computer readable storage medium having a computer program stored thereon, the computer program being executable by a processor to implement the GNSS regional ionospheric delay information acquisition method as described above.

[0036] The application further provides a computer program product comprising a computer program, the computer program being executable by a processor to implement the GNSS regional ionospheric delay information acquisition method as described above.

[0037] The GNSS regional ionospheric delay information acquisition method, device and electronic device provided by the application can improve the precision of the ionospheric delay error correction value by performing Kriging interpolation on the posterior residual of the polynomial fitting model to construct a residual compensation grid model, thereby obtaining the ionospheric delay error compensation value of the target grid point, and then performing inverse distance interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

[0038] In addition, the polynomial fitting model provides an overall trend estimate, the residual compensation model makes up for local errors, and the inverse range interpolation achieves precise correction of specific locations, making the entire scheme adaptable to ionospheric changes in different regions and environments, thereby improving the adaptability and reliability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 This is one of the flow charts of the method for obtaining GNSS regional ionospheric delay information provided by the present invention.

[0041] Figure 2 Schematic diagram of the puncture point provided by the present invention.

[0042] Figure 3 This is the second flow chart of the method for obtaining GNSS regional ionospheric delay information provided by the present invention.

[0043] Figure 4 It is a structural diagram of the GNSS regional ionospheric delay information acquisition device provided by the present invention.

[0044] Figure 5 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0045] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0046] Currently, there are two main methods for ionospheric correction. One is to directly use broadcast ionospheric models, such as the Klobuchar model used by the GPS (Global Positioning System) and BDS-2 (BeiDou Navigation Satellite System Phase 2), the BDGIM model used by BDS-3, the NeQuick model used by the Galileo (European Global Navigation Satellite System), and the global GIM model provided by the IGS (International GNSS Service). However, this method has limited accuracy in correcting ionospheric delays, and cannot meet the real-time positioning needs of high-precision GNSS users, nor can it reflect the real-time changes in the ionosphere.

[0047] Another approach is to extract ionospheric delay from GNSS observation data and model it. Both regional and global models are available. Regional ionospheric models are more suitable for PPP-RTK high-precision positioning. Mathematical models for regional ionospheric modeling include polynomial fitting, generalized trigonometric series, and spherical harmonics. Interpolation models include inverse distance weighted interpolation, linear interpolation, and kriging. While high-precision ionospheric delay correction information is crucial for PPP-RTK users, its accuracy can vary depending on factors such as reference station density, solar activity, and geomagnetic activity.

[0048] In response to the above problems, an embodiment of the present invention proposes a method for obtaining GNSS regional ionospheric delay information. In this method, first, based on a pre-constructed polynomial fitting model, an initial value of the ionospheric delay error of the target grid point is obtained, and the distance between the target grid point and the station to be measured is within a preset range. The polynomial fitting model is constructed based on the oblique path ionospheric delay data extracted from the observation data of the GNSS reference station; then, based on a pre-constructed residual compensation grid model, an ionospheric delay error compensation value of the target grid point is obtained, and the residual compensation grid model is obtained by kriging interpolation of the posterior residual of the polynomial fitting model; finally, based on the sum of the initial value of the ionospheric delay error and the compensation value of the target grid point, the ionospheric delay error correction value of the target grid point is determined, and the ionospheric delay error correction value of the target grid point is inversely interpolated to obtain the ionospheric delay error correction value of the station to be measured.

[0049] The method provided by the embodiment of the application can improve the accuracy of ionospheric delay error correction values by performing Kriging interpolation on the posterior residual error of the polynomial fitting model to construct a residual compensation grid model, thereby obtaining ionospheric delay error compensation values of target grid points, and then performing inverse distance interpolation on the ionospheric delay error correction values of the target grid points to obtain the ionospheric delay error correction values of the station to be measured.

[0050] The embodiment of the application can be applied to a scenario in which high-precision GNSS regional ionospheric delay information needs to be obtained. The execution subject of the method can be an electronic device such as a terminal device, a computer, a server, a server cluster or a specially designed GNSS regional ionospheric delay information acquisition device. The GNSS regional ionospheric delay information acquisition device can be implemented by software, hardware or a combination of both.

[0051] Figure 1 is one of the flowcharts of the GNSS regional ionospheric delay information acquisition method provided by the application, as shown in Figure 1 The method comprises the following steps:

[0052] In step 110, based on a pre-constructed polynomial fitting model, an ionospheric delay error initial value of a target grid point is obtained, the distance between the target grid point and the station to be measured is within a preset range, and the polynomial fitting model is constructed based on the extracted slant path ionospheric delay data of the observation data of the GNSS reference station.

[0053] Specifically, the station to be measured refers to a fixed or mobile station in GNSS applications that receives signals from GNSS satellites and performs various measurements and calculations through these signals. It can be static (such as geodetic control points) or dynamic (such as vehicles, ships, drones, etc.). The station to be measured is equipped with a GNSS receiver and can receive signals from multiple GNSS satellites, including signals from GPS, Beidou (BDS), Galileo (Galileo), GLONASS (GLONASS) and other systems.

[0054] In order to obtain the ionospheric delay error correction value of the station to be measured, a grid model can be established. The grid model can reduce the amount of data broadcast, and users only need to perform inverse distance interpolation on the ionospheric delay error correction value of the target grid point to obtain the high-precision ionospheric delay error correction value of the station to be measured.

[0055] In the ionospheric delay error correction grid model, the research area is divided into many small grids, and the intersection of each grid is a grid point. The target grid point is a specific one or more of these grid points, for example, the target grid point can be four. In the ionospheric delay error correction, considering that the change of the ionosphere has a certain spatial correlation, only when the distance between the target grid point and the station to be measured is within the preset range, the initial value of the ionospheric delay error based on the target grid point is more likely to be accurate for the ionospheric delay error correction of the station to be measured. There is a certain spatial relationship (distance within the preset range) between the target grid point and the station to be measured, for example, the four grid points closest to the station to be measured are taken as the target grid point.

[0056] Due to the existence of the ionosphere, the GNSS signal will have a propagation delay when passing through the ionosphere, which will cause positioning errors. The initial value of the ionospheric delay error is a preliminary estimate of such delay error, which is obtained based on a pre-constructed polynomial fitting model.

[0057] The polynomial fitting model is used to describe the relationship between the ionospheric delay error and certain variables (such as the coordinates of the grid point, etc.). The polynomial fitting model is constructed based on the ionospheric delay data extracted from the observation data of the GNSS reference station. Through analysis and fitting of a large amount of observation data, a polynomial function is found, which can accurately represent the variation law of the ionospheric delay error to a certain extent.

[0058] The GNSS reference station is a station fixed at a known accurate position, which continuously receives GNSS satellite signals and observes and records these signals. These observation data contain various information in the satellite signal propagation process, and are the basic data source for constructing ionospheric delay error correction methods such as polynomial fitting model.

[0059] For the construction of the polynomial fitting model, according to the characteristics and prior knowledge of the ionospheric delay error, a suitable polynomial function form can be selected, for example, a binary polynomial function (if considering the longitude and latitude of the grid point). The relevant information (such as carrier phase observation value, pseudorange observation value, etc.) in the GNSS reference station observation data is substituted into the selected polynomial function, and the coefficients of the polynomial function are solved by mathematical optimization methods such as least squares method, so as to construct the polynomial fitting model. This model can preliminarily calculate or estimate the ionospheric delay error.

[0060] After obtaining the polynomial fitting model, the coordinates of the target grid point can be substituted into the already constructed polynomial fitting model in the specific implementation, and the initial value of the ionospheric delay error of the target grid point is calculated.

[0061] Step 120: obtaining the ionospheric delay error compensation value of the target grid point based on a pre-built residual compensation grid model, wherein the residual compensation grid model is obtained by performing Kriging interpolation on the posterior residuals of the polynomial fitting model.

[0062] Specifically, considering that the polynomial fitting model may contain certain errors, these errors generate a posteriori residuals. Using the constructed polynomial fitting model, a fitted value of the ionospheric delay error is calculated for each observation point (the spatial point corresponding to the GNSS reference station data used when constructing the model). The fitted value is then subtracted from the actual observation value (the ionospheric delay error correlation value obtained from GNSS observations) to obtain the a posteriori residual.

[0063] Kriging interpolation is a geostatistical method. It is based on known spatial data points (in the construction of a residual compensation grid model, these data points are the spatial points corresponding to the posterior residuals of the polynomial fit model). It assumes that there is some spatial correlation between these data points (for example, describing this correlation through a variogram). Then, by constructing a system of kriging equations to solve for weight coefficients, the values ​​of the known points are used to estimate the values ​​of the unknown points. This method can provide more reasonable estimates while taking into account the spatial correlation of the data and can assess the uncertainty of the estimation results. In this way, grid points throughout the study area are interpolated to construct a residual compensation grid model.

[0064] Then, within the constructed residual compensation grid model, the ionospheric delay error compensation value corresponding to the target grid point is directly searched. This value is calculated using kriging interpolation based on the posterior residuals of the previously constructed polynomial fitting model. This ionospheric delay error compensation value can be used to compensate for the ionospheric delay error at the target grid point, thereby improving the accuracy of GNSS positioning and other related applications.

[0065] Step 130: Determine the ionospheric delay error correction value of the target grid point based on the sum of the initial ionospheric delay error value and the compensation value of the target grid point, and perform inverse range interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

[0066] Specifically, after obtaining the initial value and compensation value of the ionospheric delay error of the target grid point, the ionospheric delay error correction value of the target grid point can be obtained by adding the two.

[0067] Considering that the target grid points are the closest to the station under test, these target grid points can better represent the spatial conditions around the station under test, and their ionospheric delay error correction values ​​have already been calculated, we can perform inverse range interpolation on the ionospheric delay error correction values ​​of the target grid points to obtain the ionospheric delay error correction value of the station under test.

[0068] The method provided by the present invention utilizes a polynomial fitting model constructed based on GNSS reference station observation data to provide a preliminary and relatively accurate estimate of the ionospheric delay error at the target grid point, obtaining an initial value. The polynomial fitting model can capture the overall variation trend of the ionospheric delay error within a certain spatial range, providing a foundation for subsequent precise correction.

[0069] A residual compensation grid model is constructed by performing kriging interpolation on the posterior residuals of the polynomial fitting model to obtain compensation values ​​for the target grid points. The kriging interpolation method takes into account the spatial correlation of the data and can effectively use the information of known data points to estimate the values ​​of unknown points. This method supplements and corrects the errors of the polynomial fitting model, allowing the resulting compensation values ​​to more accurately reflect the local characteristics of the ionospheric delay error at the target grid points, further improving the accuracy of ionospheric delay error estimation.

[0070] The ionospheric delay error correction value of the target grid point is inversely interpolated to obtain the ionospheric delay error correction value of the station under test. Based on the principle that closer distances lead to stronger correlations, inverse range interpolation assigns different weights based on the distance between the target grid point and the station under test. This ensures that target grid points closer to the station under test contribute more to the final correction value, thus achieving more accurate local correction of the ionospheric delay error of the station under test and better meeting the requirements of applications such as high-precision positioning.

[0071] The method provided by the embodiment of the present invention provides an overall trend estimation through a polynomial fitting model, the residual compensation model compensates for local errors, and the inverse range interpolation achieves precise correction of specific locations, making the entire solution adaptable to ionospheric changes in different regions and environments, thereby improving the adaptability and reliability of the model.

[0072] Based on the above embodiment, the step of determining the polynomial fitting model includes:

[0073] Step 210: Obtain observation data and precise coordinates of the reference station, where the observation data includes raw GNSS pseudorange observation data and phase observation values.

[0074] Step 220: Obtain precision products, which include precise satellite orbits, precise satellite clock errors, precise decimal deviations (UPDs), and external dependency files required for precise point positioning (PPP) solutions.

[0075] Step 230: extracting the slant path ionospheric delay information of the reference station based on the observation data and precise coordinates of the reference station and the precision product;

[0076] Step 240: construct a polynomial fitting model based on the slant path ionospheric delay information of the reference station, and determine the model coefficients of the polynomial fitting model.

[0077] Specifically, the observation data of the reference station is first obtained, which includes the original GNSS pseudorange observation data and phase observations .

[0078] The original observation equations are:

[0079] (1)

[0080] Where: 、 、 Represents the station, satellite and frequency respectively; is the carrier phase observation value (in meters); is the pseudorange observation value (in meters); is the geometric distance between the phase center of the receiver antenna and the phase center of the satellite antenna; is the three-dimensional position parameter; is the three-dimensional position parameter The coefficient of For the station Receiver clock error; For satellite Satellite clock error; 、 Respectively represent measuring stations and satellite In frequency Phase hardware delay; 、 Respectively represent measuring stations and satellite In frequency Pseudorange hardware delay; is the whole-week ambiguity; Frequency The wavelength corresponding to the phase observation value; is the conversion coefficient between the ionospheric delay at different frequencies and the ionospheric delay at the first frequency; For the station to satellite The zenith ionospheric delay at the first frequency corresponding to the ionospheric puncture point on the slant path; For satellite Corresponding measuring station The tropospheric delay projection function of For the station the corresponding zenith tropospheric wet delay; is the observation noise of the phase; is the observation noise of the pseudorange. The remaining error terms such as the Earth's rotation, relativistic effects, and antenna PCO and PCV errors have been corrected by the prior model and are therefore not represented in the model.

[0081] The precise coordinates of a GNSS reference station can be obtained through long-term PPP solutions.

[0082] Precise satellite orbits and clock errors can be downloaded from the IGS or analysis center. UPD products can also be downloaded from the analysis center. Alternatively, sparsely distributed GNSS reference stations can be selected for UPD estimation. This algorithm is now relatively mature and will not be described in detail here.

[0083] In some embodiments, step 230 specifically includes:

[0084] Step 231, performing data preprocessing on the observation data of the reference station to obtain preprocessed observation data;

[0085] Step 232: Calculate the satellite position based on the precise orbit product, and calculate the coordinates of the satellite penetration point based on the satellite position and the precise coordinates of the reference station. The coordinates of the satellite penetration point are used to construct the ionospheric model.

[0086] Step 233, based on the non-differenced non-combined precise point positioning ambiguity fixation technology and pre-processed observation data, the ionospheric model is solved to obtain the oblique path ionospheric delay information of the reference station.

[0087] Specifically, data preprocessing of the reference station's observation data mainly involves removing observation values ​​containing gross errors in the observation data. For example, the conventional TurboEdit cycle slip detection method can be used to perform cycle slip detection processing on phase observation values ​​to obtain preprocessed observation data.

[0088] In step 232, the satellite positions are first calculated using the precise orbit product, and then the puncture points are calculated in combination with the precise coordinates of the GNSS reference station. Figure 2 This is a schematic diagram of the puncture point provided by the present invention. is the radius of the Earth; is the zenith distance in the direction of the satellite propagation path at the puncture point; is the zenith distance in the direction of satellite propagation path at the reference station; is the height of the thin layer, generally between 350 and 450 km; For the puncture point.

[0089] Calculation of the geomagnetic coordinates of the puncture point. The calculation steps of the geomagnetic coordinate system of the puncture point are as follows:

[0090] (2)

[0091] (3)

[0092] (4)

[0093] (5)

[0094] Where, and The geographical latitude and longitude of the puncture point can be obtained by calculating the precise coordinates of the measuring station and satellite. and is the geographic latitude and longitude of the geomagnetic North Pole, and are the geomagnetic latitude and longitude at the puncture point.

[0095] Once the coordinates of the satellite penetration point are obtained, an ionospheric model can be established. Based on this, the ionospheric model is solved using the undifferenced, non-combined precise point positioning ambiguity fixation technique and pre-processed observation data to obtain the slant path ionospheric delay information of the reference station.

[0096] The following is a calculation method for extracting slant path ionospheric information using PPP-AR. Based on the original observation equation without difference or combination, it should be noted that since the satellite clock corrections in the precise satellite clock correction file are obtained by IF combination calculation, the corrections given by the satellite clock correction product absorb the IF combination value of the satellite pseudorange hardware delay. Therefore, the precise satellite clock correction product and the actual satellite clock correction have the following relationship:

[0097] (6)

[0098] Where, represents the satellite clock error estimated by the ionosphere-free combination, represents the true satellite clock error, The ionospheric-free combined value of the pseudorange hardware delay at the satellite end, Indicates satellite In frequency The pseudorange hardware delay, Indicates satellite In frequency At the same time, since the parameters involve parameters related to the IF combination, the coefficients of the IF combination are given here:

[0099] (7)

[0100]

[0101] (8)

[0102] In order to be consistent with the ionosphere-free combination observation equation, the receiver clock bias parameter after reorganization will absorb the IF combination value of the receiver end pseudorange hardware delay, and the expression is as follows:

[0103] (9)

[0104]

[0105] (10)

[0106]

[0107] (11)

[0108]

[0109] (12)

[0110] Then step 240 is performed, and based on the slant ionospheric delay information of the reference station, a polynomial fitting model is constructed, and the model coefficients of the polynomial fitting model are determined. ​​​​​​​​​​​​​​​​​​​​

[0111] The polynomial model is generally used for regional ionospheric modeling, and its function expression is shown as follows:

[0112] (13)

[0113] Where, At the puncture point The slant path ionospheric delay value at (unit: TECU); and are the geographical latitudes of the puncture point and the center of the area, and are the geographical longitudes of the puncture point and the center of the area respectively; and are the maximum order of the polynomial model (the number of coefficients is m n); are the coefficients of the polynomial model to be estimated; is the ionospheric observation time (UTC); is the solar hour angle corresponding to the central time; Representation System The hardware delay of the receiver is absorbed in the satellite ionospheric delay. That is to say, for all satellites in the same GNSS system, the pseudorange hardware delay of the same receiver is the same.

[0114] The method provided by the present invention utilizes a polynomial fitting model constructed based on GNSS reference station observation data to provide a preliminary and relatively accurate estimate of the ionospheric delay error at the target grid point, obtaining an initial value. The polynomial fitting model can capture the overall variation trend of the ionospheric delay error within a certain spatial range, providing a foundation for subsequent precise correction.

[0115] Based on any of the above embodiments, the step of determining the residual compensation grid model includes:

[0116] Step 310, obtaining the posterior residual of the polynomial fitting model of the reference station corresponding to the satellite;

[0117] Step 320: Based on the spatial relationship between the grid points and the posterior residuals, the ionospheric delay error compensation value of each grid point is obtained by the Kriging interpolation method;

[0118] Step 330: construct a residual compensation grid model based on the ionospheric delay error compensation value of each grid point.

[0119] Specifically, in order to obtain the residual of the polynomial fitting model corresponding to the reference station satellite, the posterior residual can be calculated by the following formula:

[0120] (14)

[0121] Where, Indicates the measuring station Corresponding satellite The post-test residuals, Indicates the station extracted by PPP-AR Corresponding satellite The true value of the slant path delay through the ionosphere, Indicates the measuring station Corresponding satellite The polynomial fitting of the slant path ionospheric delay model value.

[0122] Based on the spatial relationships and posterior residuals between grid points, the ionospheric delay error compensation value for each grid point is then obtained through kriging interpolation. The posterior residuals of each reference station are used as interpolation data points, each of which includes spatial coordinates (latitude and longitude) and the corresponding posterior residual. Based on the spatial distribution of reference stations and the spatial characteristics of ionospheric delay, an appropriate spatial correlation model (such as spherical model, exponential model, Gaussian model, etc.) is selected for kriging interpolation.

[0123] Common kriging methods include simple kriging and ordinary kriging. Simple kriging assumes that the mathematical expectation of the random variable X is known for the entire region, but is more applicable when the mathematical expectation is unknown. First, a variogram is constructed and the semivariogram of the posterior residuals between reference stations is calculated to describe spatial correlation. For each grid point, the kriging equations are established using the variogram and the known reference station locations and residuals, and the weight coefficients are solved. The obtained weights are used to calculate the ionospheric delay error compensation value for the grid point.

[0124] After obtaining the ionospheric delay error compensation value of each grid point, the ionospheric delay error compensation values ​​of all grid points are stored and organized according to their corresponding grid point coordinates to form a residual compensation grid model.

[0125] The method provided in the embodiment of the present invention performs kriging interpolation based on the spatial relationship between each grid point and the posterior residuals, and can fully consider the spatial correlation of the data. The kriging interpolation method estimates the ionospheric delay error compensation value of the unknown grid point by analyzing the posterior residuals of the known grid points using the spatial weight coefficient. This method can reasonably allocate weights based on the actual distance and spatial correlation between the grid points, so that the interpolation result is more consistent with the actual spatial distribution of the ionospheric delay error, thereby effectively compensating for the shortcomings of the polynomial fitting model in local areas and improving the accuracy of the ionospheric delay error estimation.

[0126] In the process of constructing the residual compensation grid model, the spatial relationship between each grid point is fully considered. Ionospheric delay error has certain correlation and continuity in space, and the error between adjacent grid points often has certain similarity. By introducing spatial relationship information, the Kriging interpolation method can better utilize this spatial correlation, making the model more accurately reflect the changes of ionospheric delay error at different geographical locations and spatial scales, and enhancing the spatial adaptability of the model.

[0127] In addition, the Kriging interpolation method can perform adaptive interpolation calculation according to the local data characteristics of the grid points, so as to better capture the local detail characteristics of the ionospheric delay error. Compared with the traditional simple interpolation method, Kriging interpolation can more finely depict the changes of ionospheric delay error in the local area, and can provide more accurate compensation values for ionospheric delay error distribution with complex spatial structure, further improving the precision and reliability of the model.

[0128] The residual compensation grid model constructed through the above steps can provide accurate ionospheric delay error compensation values for each grid point. The compensation values can be directly applied in the correction process of ionospheric delay error, effectively reducing the influence of ionosphere on GNSS signal propagation, and improving the precision of GNSS positioning, navigation and timing applications.

[0129] Based on any of the above embodiments, step 330 specifically includes:

[0130] Step 331, based on the difference between the true residual value of each reference station and the ionospheric delay error compensation value of each grid point, the compensation value accuracy of each reference station is determined by cross-validation;

[0131] Step 332, based on the compensation value accuracy of each reference station, the compensation value accuracy of each grid point is determined by inverse distance interpolation;

[0132] Step 333, based on the ionospheric delay error compensation value and the compensation value accuracy of each grid point, a residual compensation grid model is constructed.

[0133] Specifically, the accuracy of ionospheric delay correction information is often affected by factors such as reference station density, solar activity, geomagnetic activity, etc., and will change. If there is no accurate matching precision index, these correction information cannot be effectively utilized, and even will have negative impact.

[0134] The cross-validation process primarily involves performing a residual error kriging interpolation model for each reference station (excluding the current reference station being interpolated). The true accuracy of the kriging interpolation is then determined using the reference station's true residual values. The kriging interpolation accuracy for each reference station is then determined, which in turn is the accuracy of the compensation value for each reference station. Commonly used accuracy assessment metrics include mean squared error (MSE), mean absolute error (MAE), and root mean square error (RMSE).

[0135] Determine the geographic coordinates (e.g., longitude, latitude, etc.) of each reference station within the study area, as well as the coordinates of each grid point. This coordinate information will be used to calculate the distance between the reference station and the grid point. Given the known accuracy of the compensation value for each reference station, the accuracy of the compensation value for each grid point is determined through inverse distance interpolation.

[0136] The ionospheric delay error compensation value of each grid point and the corresponding compensation value accuracy are integrated to form a data set including grid point coordinates, compensation values ​​and compensation value accuracy. A residual compensation grid model is constructed based on this data set.

[0137] The method provided by the embodiments of the present invention determines the compensation accuracy of each reference station through cross-verification and uses inverse range interpolation to obtain the compensation accuracy of each grid point. This method can more accurately reflect the reliability of ionospheric delay error compensation in different regions. This refined accuracy assessment can avoid the accumulation of errors caused by inaccurate compensation values.

[0138] When constructing the residual compensation grid model, not only is the ionospheric delay error compensation value at each grid point considered, but information on the accuracy of the compensation value is also incorporated. This ensures high accuracy of the ionospheric delay correction value while providing accuracy indicators consistent with the model's accuracy, especially during periods of active ionospheric fluctuations. The model adaptively adjusts the compensation strategy based on the accuracy of different regions, improving both accuracy and reliability.

[0139] Based on any of the above embodiments, step 120 specifically includes: obtaining the ionospheric delay error compensation value and the compensation value accuracy of the target grid point based on a pre-built residual compensation grid model.

[0140] Specifically, as described in the above embodiments, the residual compensation grid model can simultaneously obtain the ionospheric delay error compensation value and compensation value accuracy of the target grid point. The obtained ionospheric delay error compensation value and compensation value accuracy of the target grid point are integrated to form a complete result record, which may include, for example, the spatial location information of the target grid point, the ionospheric delay error compensation value, and the compensation value accuracy.

[0141] Based on any of the above embodiments, Figure 3This is the second flow chart of the method for obtaining GNSS regional ionospheric delay information provided by the present invention, such as Figure 3 As shown, a method for obtaining GNSS regional ionospheric delay information is provided, which includes: based on the observation data of the GNSS reference station network, extracting the ionospheric delay information of the reference station through the PPP-AR algorithm and calculating the corresponding satellite puncture point coordinates; then using the ionospheric delay information to construct a polynomial fitting model while retaining the residual error information of the model. When residual compensation is required, the residual error information is used to perform kriging interpolation to obtain the ionospheric compensation value for each grid point of the grid model, and the accuracy index of the ionospheric compensation value is obtained through cross-checking; finally, the ionospheric initial value of each grid point of the grid model is calculated through the polynomial fitting model, and the initial value is added to the compensation value to obtain the ionospheric delay error correction value for each grid point of the final grid model. When residual compensation is not required, the model coefficients and accuracy index of the polynomial fitting model are directly output.

[0142] When using this model, users can obtain the ionospheric delay error correction value by performing a simple inverse range interpolation of the four grid points closest to them.

[0143] Based on the polynomial surface fitting model, the embodiment of the present invention further performs Kriging interpolation processing on the residual ionospheric delay error and uses a cross-check method to obtain the uncertainty of the model, that is, the accuracy index of the ionospheric delay model. This improves the accuracy of the ionospheric model while also obtaining a more accurate accuracy index. In order to ensure the accuracy of ionospheric delay extraction, a non-differential non-combined PPP-AR method is used to extract ionospheric delay information of the GNSS reference station network. At the same time, in order to avoid the accuracy loss caused by the projection function, STEC is used for ionospheric modeling. As for the influence of hardware delay on the receiver side, it is estimated together with the ionospheric model coefficients during the ionospheric modeling process and a center of gravity constraint is applied. When used on the user side, the inter-satellite difference form is adopted. While effectively improving the accuracy of the regional ionospheric model, this embodiment can ensure that an accuracy index that meets the actual accuracy can still be given during the period of ionospheric activity.

[0144] Compared with the prior art, the embodiments of the present invention have the following features and beneficial effects:

[0145] (1) Thanks to the Kriging interpolation to compensate for the residual ionospheric error, the accuracy of the ionospheric model value obtained by this method is significantly higher than that of the traditional method.

[0146] (2) It can ensure high accuracy of ionospheric delay correction values ​​while providing accuracy indicators that are consistent with model accuracy, especially during periods of active ionospheric changes.

[0147] (3) Since a single satellite is used for modeling, the impact of inconsistent hardware delay deviations between GNSS systems can be avoided, making it more convenient for users to use.

[0148] (4) This method not only provides a residual compensation grid model, but also retains the model coefficients of the polynomial fitting model, ensuring compatibility with traditional methods. Users can select the corresponding model according to their needs. It also supports the direct use of the original oblique path ionosphere information for Kriging interpolation modeling.

[0149] (5) By establishing a grid model, the amount of data broadcast is reduced. Users only need to obtain the correction values ​​of the four grid points closest to them and perform simple inverse distance interpolation to obtain high-precision correction values ​​and accuracy indicators.

[0150] The following describes the GNSS regional ionospheric delay information acquisition device provided by the present invention. The GNSS regional ionospheric delay information acquisition device described below and the GNSS regional ionospheric delay information acquisition method described above can refer to each other.

[0151] Figure 4 : is a structural diagram of the GNSS regional ionospheric delay information acquisition device provided by the present invention, such as Figure 4 As shown, the device includes:

[0152] An initial value acquisition unit 410 is configured to acquire an initial value of the ionospheric delay error of a target grid point based on a pre-constructed polynomial fitting model, where the distance between the target grid point and the station to be measured is within a preset range, and the polynomial fitting model is constructed based on slant path ionospheric delay data extracted from observation data of a GNSS reference station;

[0153] a compensation value acquiring unit 420 configured to acquire an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, wherein the residual compensation grid model is obtained by performing Kriging interpolation on the posterior residual of the polynomial fitting model;

[0154] The correction value acquisition unit 430 is used to determine the ionospheric delay error correction value of the target grid point based on the sum of the initial ionospheric delay error value of the target grid point and the compensation value, and perform inverse range interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

[0155] Based on the above embodiment, the device further includes a polynomial fitting model construction unit, which is used to:

[0156] Obtaining observation data and precise coordinates of the reference station, wherein the observation data includes raw GNSS pseudorange observation data and phase observation values;

[0157] Obtain precision products, including precise satellite orbits, precise satellite clock errors, precise decimal deviations (UPDs), and external dependency files required for precise point positioning (PPP) solutions.

[0158] Extracting the slant path ionospheric delay information of the reference station based on the observation data and precise coordinates of the reference station and the precision product;

[0159] Based on the oblique path ionospheric delay information of the reference station, the polynomial fitting model is constructed, and the model coefficients of the polynomial fitting model are determined.

[0160] Based on the above embodiment, the polynomial fitting model construction unit is specifically used to:

[0161] performing data preprocessing on the observation data of the reference station to obtain preprocessed observation data;

[0162] Calculating satellite positions based on the precise product, and calculating coordinates of satellite penetration points based on the satellite positions and the precise coordinates of the reference station, wherein the coordinates of the satellite penetration points are used to construct an ionospheric model;

[0163] Based on the non-differential non-combined precise point positioning ambiguity fixation technology and the pre-processed observation data, the ionosphere model is solved to obtain the oblique path ionosphere delay information of the reference station.

[0164] Based on the above embodiment, the device further includes a residual compensation grid model determination unit, which is configured to:

[0165] Obtain the posterior residuals of the polynomial fitting model corresponding to the reference station;

[0166] Based on the spatial relationship between the grid points and the posterior residual, the ionospheric delay error compensation value of each grid point is obtained by the Kriging interpolation method;

[0167] The residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point.

[0168] Based on the above embodiment, the residual compensation grid model determination unit is specifically configured to:

[0169] Determining the accuracy of the compensation value of each reference station by cross-checking based on the difference between the true residual value of each reference station and the ionospheric delay error compensation value of each grid point;

[0170] Based on the compensation value accuracy of each reference station, determining the compensation value accuracy of each grid point by inverse distance interpolation;

[0171] The residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point and the accuracy of the compensation value.

[0172] Based on the above embodiment, the compensation value obtaining unit is specifically configured to:

[0173] Based on a pre-built residual compensation grid model, the ionospheric delay error compensation value and the compensation value accuracy of the target grid point are obtained.

[0174] Figure 5 An example of a physical structure diagram of an electronic device is shown below. Figure 5 As shown, the electronic device may include: a processor (processor) 510, a communication interface (Communications Interface) 520, a memory (memory) 530 and a communication bus 540, wherein the processor 510, the communication interface 520, and the memory 530 communicate with each other through the communication bus 540. The processor 510 can call the logic instructions in the memory 530 to execute the GNSS regional ionospheric delay information acquisition method, which includes: obtaining an initial value of the ionospheric delay error of the target grid point based on a pre-constructed polynomial fitting model, where the distance between the target grid point and the station to be measured is within a preset range, and the polynomial fitting model is obtained based on observation data of the GNSS reference station; obtaining an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, and the residual compensation grid model is obtained by performing kriging interpolation on the posterior residual of the polynomial fitting model; determining an ionospheric delay error correction value of the target grid point based on the sum of the initial value of the ionospheric delay error of the target grid point and the compensation value, and performing inverse range interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

[0175] Furthermore, the logic instructions in the aforementioned memory 530 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0176] On the other hand, the present invention also provides a computer program product, which includes a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the GNSS regional ionospheric delay information acquisition method provided by the above methods, the method including: obtaining an initial value of the ionospheric delay error of a target grid point based on a pre-constructed polynomial fitting model, wherein the distance between the target grid point and the station to be measured is within a preset range, and the polynomial fitting model is obtained based on observation data of the GNSS reference station; obtaining an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, and the residual compensation grid model is obtained by kriging interpolation of the posterior residual of the polynomial fitting model; determining an ionospheric delay error correction value of the target grid point based on the sum of the initial value of the ionospheric delay error of the target grid point and the compensation value, and performing inverse range interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

[0177] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the GNSS regional ionospheric delay information acquisition method provided by the above-mentioned methods, the method comprising: obtaining an initial value of the ionospheric delay error of a target grid point based on a pre-constructed polynomial fitting model, wherein the distance between the target grid point and the station to be measured is within a preset range, and the polynomial fitting model is obtained based on observation data of the GNSS reference station; obtaining an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, and the residual compensation grid model is obtained by performing kriging interpolation on the posterior residual of the polynomial fitting model; determining an ionospheric delay error correction value of the target grid point based on the sum of the initial value of the ionospheric delay error of the target grid point and the compensation value, and performing inverse distance interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

[0178] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0179] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for obtaining GNSS regional ionospheric delay information, characterized in that: include: Obtaining an initial value of the ionospheric delay error of a target grid point based on a pre-constructed polynomial fitting model, where the distance between the target grid point and the station to be measured is within a preset range, the polynomial fitting model being constructed based on oblique path ionospheric delay data extracted from observation data of a GNSS reference station; Obtaining an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, wherein the residual compensation grid model is obtained by performing Kriging interpolation on the posterior residuals of the polynomial fitting model; Based on the sum of the initial value of the ionospheric delay error of the target grid point and the compensation value, the ionospheric delay error correction value of the target grid point is determined, and the ionospheric delay error correction value of the target grid point is subjected to inverse range interpolation to obtain the ionospheric delay error correction value of the station to be measured.

2. The method for obtaining GNSS regional ionospheric delay information according to claim 1, wherein: The step of determining the polynomial fitting model includes: Obtaining observation data and precise coordinates of the reference station, wherein the observation data includes raw GNSS pseudorange observation data and phase observation values; Obtain precision products, including precise satellite orbits, precise satellite clock errors, precise decimal deviations (UPDs), and external dependency files required for precise point positioning (PPP) solutions. Extracting the slant path ionospheric delay information of the reference station based on the observation data and precise coordinates of the reference station and the precision product; Based on the oblique path ionospheric delay information of the reference station, the polynomial fitting model is constructed, and the model coefficients of the polynomial fitting model are determined.

3. The method for obtaining GNSS regional ionospheric delay information according to claim 2, wherein: Extracting the slant path ionospheric delay information of the reference station based on the observation data and precise coordinates of the reference station and the precision product includes: performing data preprocessing on the observation data of the reference station to obtain preprocessed observation data; Calculating satellite positions based on the precise product, and calculating coordinates of satellite penetration points based on the satellite positions and the precise coordinates of the reference station, wherein the coordinates of the satellite penetration points are used to construct an ionospheric model; Based on the non-differential non-combined precise point positioning ambiguity fixation technology and the pre-processed observation data, the ionosphere model is solved to obtain the oblique path ionosphere delay information of the reference station.

4. The method for obtaining GNSS regional ionospheric delay information according to claim 1, wherein: The step of determining the residual compensation grid model includes: Obtain the posterior residuals of the polynomial fitting model of the reference station corresponding to the satellite; Based on the spatial relationship between the grid points and the posterior residual, the ionospheric delay error compensation value of each grid point is obtained by the Kriging interpolation method; The residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point.

5. The method for obtaining GNSS regional ionospheric delay information according to claim 4, characterized in that: The constructing of the residual compensation grid model based on the ionospheric delay error compensation value of each grid point includes: Determining the accuracy of the compensation value of each reference station by cross-checking based on the difference between the true residual value of each reference station and the ionospheric delay error compensation value of each grid point; Based on the compensation value accuracy of each reference station, determining the compensation value accuracy of each grid point by inverse distance interpolation; The residual compensation grid model is constructed based on the ionospheric delay error compensation value of each grid point and the accuracy of the compensation value.

6. The method for obtaining GNSS regional ionospheric delay information according to claim 1, wherein: The obtaining of the ionospheric delay error compensation value of the target grid point based on the pre-built residual compensation grid model includes: Based on a pre-built residual compensation grid model, the ionospheric delay error compensation value and the compensation value accuracy of the target grid point are obtained.

7. A GNSS regional ionospheric delay information acquisition device, characterized in that: include: an initial value acquisition unit, configured to acquire an initial value of the ionospheric delay error of a target grid point based on a pre-constructed polynomial fitting model, wherein the distance between the target grid point and the station to be measured is within a preset range, and wherein the polynomial fitting model is constructed based on oblique path ionospheric delay data extracted from observation data of a GNSS reference station; a compensation value acquiring unit, configured to acquire an ionospheric delay error compensation value of the target grid point based on a pre-constructed residual compensation grid model, wherein the residual compensation grid model is obtained by performing Kriging interpolation on the posterior residual of the polynomial fitting model; a correction value acquisition unit, configured to determine the ionospheric delay error correction value of the target grid point based on the sum of the initial ionospheric delay error value of the target grid point and the compensation value, and perform inverse range interpolation on the ionospheric delay error correction value of the target grid point to obtain the ionospheric delay error correction value of the station to be measured.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the method for obtaining GNSS regional ionospheric delay information according to any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for obtaining GNSS regional ionospheric delay information according to any one of claims 1 to 6 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for obtaining GNSS regional ionospheric delay information according to any one of claims 1 to 6 is implemented.

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