Ionospheric correction accuracy estimation method and system in GNSS enhanced positioning

Abstract

The application relates to a method and system for estimating ionospheric correction accuracy in GNSS enhanced positioning, which comprises the following steps: constructing a regional ionospheric model by using linear interpolation method and GNSS observation data of reference stations in a CORS network; calculating ionospheric interpolation residuals of each reference station based on the regional ionospheric model, and calculating unit weight variance of all reference stations according to the residuals, which is taken as the ionospheric interpolation accuracy of the reference stations; obtaining the ionospheric interpolation standard deviation at the rover station by combining the unit weight variance and the relative geometric relationship between the rover station and the reference station through the error propagation law, and taking the ionospheric interpolation standard deviation as the estimated value of the ionospheric correction accuracy. The application uses the GNSS observation data of the reference stations to construct the regional ionospheric model, integrates the observation information of multiple reference stations by using the linear interpolation method, and improves the regional consistency of the ionospheric spatial distribution modeling; the ionospheric interpolation residuals of each reference station are calculated based on the model, and the unit weight variance is calculated, which provides a statistical and quantitative basis for the ionospheric interpolation accuracy of the reference stations.

Description

Technical Field

[0001] This application relates to the field of Global Navigation Satellite System (GNSS) positioning technology, specifically to a method and system for estimating ionospheric correction accuracy in GNSS enhanced positioning. Background Technology

[0002] High-density continuously operating reference station (CORS) networks have been deployed globally to achieve large-scale real-time centimeter-level positioning. To support this goal, GNSS-enhanced positioning technologies such as network RTK and PPP-RTK have been proposed. These methods utilize the CORS network to fix the ambiguity of reference stations or baselines between reference stations in real time and calculate high-precision ionospheric delay based on carrier phase observations. Real-time ionospheric correction for the rover is obtained through interpolation using a mathematical model. Once users receive these corrections, the impact of ionospheric delay errors can be effectively mitigated, thereby improving positioning accuracy.

[0003] However, due to the density of the CORS network and the irregularity of ionospheric delay, the interpolated ionospheric correction value may not perfectly match the rover's actual ionospheric delay, leading to unavoidable ionospheric interpolation errors. Under normal circumstances, these errors are usually small and have limited impact on ambiguity fixation and positioning accuracy. However, when the CORS network is sparse or ionospheric activity is strong, the ionospheric interpolation error increases significantly, severely affecting the rover's ambiguity fixation rate and positioning accuracy.

[0004] In low-latitude regions, CORS positioning services are significantly affected by the ionosphere, and users often face difficulties in fixing ambiguities at midday, hindering high-precision GNSS applications. Furthermore, with increased solar activity, the spatial correlation of the ionosphere deteriorates, further reducing the ionospheric correction effectiveness of existing technical models. Ensuring high-precision positioning quality for users under these challenging conditions remains a critical and ongoing research challenge.

[0005] In existing technologies, the estimation of ionospheric correction accuracy mainly relies on prior models. However, the ionospheric correction accuracy in these models is based on prior information and cannot accurately capture the rapid spatiotemporal changes in ionospheric delay, resulting in insufficient dynamic adaptability. This is particularly evident in the significant degradation of positioning performance under sparse CORS networks or conditions of high ionospheric activity. Therefore, how to break free from dependence on empirical prior models and achieve a real-time, high-precision ionospheric correction accuracy estimation method that can dynamically respond to spatiotemporal changes in the ionosphere has become a pressing technical problem in this field. Summary of the Invention

[0006] This application provides a method and system for estimating ionospheric correction accuracy in GNSS enhanced positioning, which can solve the problem of insufficient dynamic adaptability caused by using prior models to calculate ionospheric correction accuracy in the prior art.

[0007] In a first aspect, embodiments of this application provide a method for estimating the accuracy of ionospheric correction in GNSS enhanced positioning, comprising: A regional ionospheric model was constructed using GNSS observation data from reference stations in the CORS network and a linear interpolation method. Based on the regional ionospheric model, the ionospheric interpolation residuals of each reference station are calculated, and the unit weighted variance is calculated based on the residuals of all reference stations, which is then used as the ionospheric interpolation accuracy of the reference stations. By using the error propagation law, combined with the unit weight variance and the relative geometric relationship between the rover and the reference station, the standard deviation of the ionospheric interpolation at the rover station is obtained, and it is used as an estimate of the ionospheric correction accuracy.

[0008] In conjunction with the first aspect, in one implementation method, a regional ionospheric model is constructed using GNSS observation data from reference stations in the CORS network and a linear interpolation method, specifically including: Based on GNSS observation data from reference stations in the CORS network, obtain the vector of ionospheric delay observations; The model parameters are determined using the least squares formula based on the coordinates of each reference station and the vector of delayed ionospheric observations. The model parameters are substituted into the linear interpolation formula to complete the construction of the regional ionosphere model.

[0009] In conjunction with the first aspect, in one implementation, the ionospheric delay observation vector is obtained based on GNSS observation data from reference stations in the CORS network, specifically including: Based on GNSS observation data from reference stations in the CORS network, integer ambiguities are fixed to determine integer ambiguities. Based on integer ambiguity and GNSS observation data, the ionospheric delay observation vector is obtained using the ionospheric delay calculation formula.

[0010] In conjunction with the first aspect, in one implementation, the model parameters are determined using a least-squares formula based on the coordinates of each reference station and the vector of ionospheric delay observations. Specifically, this includes: Based on the coordinates of each reference station, calculate the planar coordinate difference between each reference station and the main reference station to obtain a set of coordinate difference vectors; Construct a coefficient matrix based on the coordinate difference vector set; Based on the distance between each reference station and the main reference station, a weight matrix for a distance-based stochastic model is constructed. The model parameters are determined based on the coefficient matrix, weight matrix, and ionospheric delayed observation vector, using the least squares formula.

[0011] In conjunction with the first aspect, in one implementation, based on a regional ionospheric model, the ionospheric interpolation residuals of each reference station are calculated, and the unit weighted variance is calculated based on the residuals of all reference stations, which is then used as the ionospheric interpolation accuracy of the reference stations. Specifically, this includes: Based on the regional ionospheric model, the ionospheric interpolation residuals of each reference station are calculated using the LIM model residual equation, and the ionospheric delay interpolation residual vector set of the reference station is obtained. The weighted sum of squares is obtained based on the reference station's ionospheric delay interpolation residual vector set. Based on the weighted sum of squares and the number of reference stations, the unit weighted variance is calculated and used as the interpolation accuracy of the ionosphere at the reference stations.

[0012] In conjunction with the first aspect, in one implementation, the ionospheric interpolation standard deviation at the rover station is obtained by using the error propagation law, combined with the unit weight variance and the relative geometric relationship between the rover station and the reference station, and is used as an estimate of the ionospheric correction accuracy. Specifically, this includes: Based on the coordinates of each reference station and the rover station, determine the main reference station and calculate the difference in planar coordinates between the rover station and the main reference station; Based on the difference in planar coordinates between the rover and the main reference station, the relative geometric relationship between the rover and the reference station is obtained, and the relative geometric relationship between the rover and the reference station includes the rover coefficient vector. Based on the rover coefficient vector and unit weight variance, the ionospheric interpolation error variance of the rover is obtained through the error propagation law. The square root of the variance of the ionospheric interpolation error at the rover station is taken to obtain the standard deviation of the ionospheric interpolation at the rover station, which is then used as an estimate of the accuracy of the ionospheric interpolation.

[0013] In conjunction with the first aspect, in one implementation method, the main reference station is determined based on the coordinates of each reference station and the coordinates of the rover station, specifically including: Based on the coordinates of the rover and each reference station, obtain the planar distance between each reference station and the rover; The reference station with the smallest horizontal distance from the rover station is taken as the main reference station.

[0014] In conjunction with the first aspect, in one implementation, after obtaining the ionospheric interpolation standard deviation at the rover station by using the error propagation law, combining the unit weight variance and the relative geometric relationship between the rover station and the reference station, the method further includes: The standard deviation of ionospheric interpolation at the rover station is embedded into a preset ionospheric weighted model to adjust the weights of the positioning solution.

[0015] In conjunction with the first aspect, in one implementation, the ionospheric interpolation standard deviation at the rover station is embedded into a preset ionospheric weighted model to adjust the weights of the positioning solution, specifically including: The standard deviation of ionospheric interpolation at the rover station is embedded into a preset ionospheric weighting model, and the weights are calculated using the weight calculation formula of the ionospheric weighting model to obtain the updated ionospheric weighting model. Based on the updated ionospheric weighted model and GNSS observation data, an observation equation incorporating ionospheric interpolation accuracy is constructed. The location calculation results of the rover station are obtained by solving the observation equation using the least squares method.

[0016] Secondly, embodiments of this application provide a system for estimating ionospheric correction accuracy in GNSS-enhanced positioning, comprising: a first module for constructing a regional ionospheric model using GNSS observation data from reference stations in a CORS network and employing a linear interpolation method; a second module for calculating the ionospheric interpolation residuals of each reference station based on the regional ionospheric model, calculating the unit weight variance based on the residuals of all reference stations, and using it as the ionospheric interpolation accuracy of the reference stations; and a third module for obtaining the ionospheric interpolation standard deviation at the rover station by using the error propagation law, combining the unit weight variance and the relative geometric relationship between the rover station and the reference station, and using it as an estimate of the ionospheric correction accuracy.

[0017] The beneficial effects of the technical solutions provided in this application include: This application provides a method and system for estimating ionospheric correction accuracy in GNSS-enhanced positioning. It constructs a regional ionospheric model using GNSS observation data from reference stations in a CORS network, and integrates observation information from multiple reference stations using linear interpolation, effectively improving the regional consistency of ionospheric spatial distribution modeling. Based on this model, it calculates the ionospheric interpolation residuals for each reference station and calculates the unit weighted variance, providing an objective statistical quantitative basis for the ionospheric interpolation accuracy of the reference stations. Furthermore, it applies the error propagation law, combined with the relative geometric relationship between the rover and the reference stations, to dynamically propagate the accuracy benchmark of the reference stations to the rover's position. This allows the estimation of the ionospheric interpolation standard deviation to respond in real-time to changes in the rover's spatial position, thereby achieving adaptive estimation of ionospheric correction accuracy during GNSS-enhanced positioning and significantly improving the reliability and accuracy of positioning solutions. Attached Figure Description

[0018] Figure 1 This is a flowchart of the ionospheric correction accuracy estimation method in GNSS enhanced positioning in this application embodiment; Figure 2 This is a network distribution diagram of the CORS reference stations in Zhejiang Province used in the embodiments of this application; Figure 3The Planetary K-index (Kp) and Disturbance Storm Time Index (Dst) during the experiment show that DOY 083 has significant ionospheric perturbations. Figure 4 The unit weight variance σ0 of the G05 satellite on the FEHU-ZJNB baseline. 2 Calculated using surrounding reference stations The comparison verified the effectiveness of the core assumptions of this invention; Figure 5 For all reference stations and The statistical distribution of the differences shows that the differences follow a normal distribution with zero mean; Figure 6 This is the double-difference ionospheric delay time series of the G04 satellite on DOY 080. Figure 7 The true value, interpolation correction value, and interpolation error of the ionospheric delay of the G04 satellite on the FEHU-ZJNB baseline are given. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0020] This application provides a method and system for estimating ionospheric correction accuracy in GNSS enhanced positioning, which can solve the problem of insufficient dynamic adaptability caused by using prior models to calculate ionospheric correction accuracy in the prior art.

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0022] In a first aspect, embodiments of this application provide a method for estimating the accuracy of ionospheric correction in GNSS enhanced positioning, comprising: 101: Using GNSS observation data from reference stations in the CORS network, a regional ionospheric model is constructed using linear interpolation. 102: Based on the regional ionospheric model, calculate the ionospheric interpolation residuals of each reference station, and calculate the unit weighted variance based on the residuals of all reference stations, and use it as the ionospheric interpolation accuracy of the reference stations. 103: By using the error propagation law, combined with the unit weight variance and the relative geometric relationship between the rover station and the reference station, the standard deviation of the ionospheric interpolation at the rover station is obtained, and it is used as an estimate of the ionospheric correction accuracy.

[0023] This application first utilizes GNSS observation data from reference stations in the CORS network, and obtains ionospheric delay observations for each reference station by fixing integer ambiguities. A regional ionospheric model is then constructed using linear interpolation. Based on this, the ionospheric interpolation residuals for each reference station are calculated using the regional ionospheric model; that is, the weighted sum of squares of the residuals for all reference stations is calculated using least squares estimation based on the difference between the model predictions and actual observations. And according to the formula Calculate the unit weighted variance. Then, using the error propagation law, combined with the unit weighted variance and the relative geometric relationship between the rover and the reference station, obtain the ionospheric interpolation standard deviation at the rover station. This standard deviation accurately reflects the ionospheric correction accuracy at the current time and location, and can be used as prior accuracy information to be incorporated into the ionospheric weighted model in real time for positioning calculation. This enables the positioning system to dynamically adapt to rapid spatiotemporal changes in the ionosphere, especially in cases of sparse CORS networks or strong ionospheric activity, effectively improving the reliability and accuracy of positioning calculation.

[0024] Therefore, by constructing a regional ionospheric model using GNSS observation data from reference stations in the CORS network and integrating observation information from multiple reference stations using linear interpolation, the regional consistency of ionospheric spatial distribution modeling is effectively improved. Based on this model, the ionospheric interpolation residuals of each reference station are calculated, and the unit weighted variance is calculated, providing an objective statistical quantitative basis for the ionospheric interpolation accuracy of the reference stations. Furthermore, by applying the error propagation law and combining the relative geometric relationship between the rover and the reference station, the accuracy benchmark of the reference station is dynamically propagated to the rover's position, enabling the estimation of the ionospheric interpolation standard deviation to respond in real time to changes in the rover's spatial position. This achieves adaptive estimation of ionospheric correction accuracy during GNSS augmentation positioning, significantly improving the reliability and accuracy of positioning solutions.

[0025] Based on the above embodiments, in this embodiment, a regional ionospheric model is constructed using GNSS observation data from reference stations in the CORS network and a linear interpolation method, specifically including steps 1011 to 1013: Step 1011: Obtain the ionospheric delay observation vector based on GNSS observation data from reference stations in the CORS network. Specifically, this includes: first, fixing the integer ambiguity based on GNSS observation data from reference stations in the CORS network to determine the integer ambiguity; then, based on the integer ambiguity and GNSS observation data, using the ionospheric delay calculation formula, obtaining the ionospheric delay observation vector.

[0026] Specifically, in the process of obtaining the ionospheric delay observation vector based on GNSS observation data from reference stations in the CORS network, the first step is to fix the integer ambiguities based on the GNSS observation data from the reference stations in the CORS network, thus determining the integer ambiguities. The system receives the raw observation data from each reference station in the CORS network, including carrier phase and pseudorange observations in the L1 and L2 bands. The sampling interval is typically 30 seconds. Preprocessing is performed using IGS precise ephemeris and the IGS_14 antenna model to calculate the satellite orbit, satellite clock bias, and antenna phase center. Simultaneously, an altitude cutoff angle of 10° is set to eliminate the multipath effect of low-elevation satellites. In practical applications, the baselines between reference stations are typically short (average spacing of approximately 47.3 km), which facilitates rapid fixing of integer ambiguities and improves the accuracy of ionospheric delay calculations.

[0027] After obtaining reliable integer ambiguities, the system uses a double-difference observation model to calculate the ionospheric delay. The specific calculation formula is as follows: ; Where f1 and f2 represent the frequencies of signals L1 and L2, respectively, λ1 and λ2 are the corresponding wavelengths, φ1 and φ2 are carrier phase observations in cycles, and N1 and N2 are the corresponding integer ambiguities.

[0028] For the baseline between each pair of reference stations, the system calculates the double-difference ionospheric delay values ​​for all visible satellites, forming an ionospheric delay observation vector I=[I1; I2; ... ;I n ], where n is the number of satellites involved in the modeling.

[0029] During the calculation process, the system excludes anomalous observations affected by intense ionospheric activity. Quality control is typically achieved by setting a threshold for the rate of change of ionospheric delay to ensure the reliability of the observation vector. Furthermore, considering the impact of different satellite elevation angles on ionospheric delay, the system applies a projection function to convert the oblique path ionospheric delay into a zenith-direction ionospheric delay, facilitating subsequent regional ionospheric modeling. The resulting ionospheric delay observation vector accurately reflects the spatial distribution characteristics of ionospheric delay within the region at the current moment, providing high-quality input data for constructing a regional ionospheric model.

[0030] Step 1012: Determine the model parameters using the least squares formula based on the coordinates of each reference station and the ionospheric delayed observation vector: First, calculate the plane coordinate difference between each reference station and the main reference station based on the coordinates of each reference station to obtain a set of coordinate difference vectors; then, construct the coefficient matrix based on the set of coordinate difference vectors; next, construct the weight matrix of the distance-based stochastic model based on the distance between each reference station and the main reference station; finally, determine the model parameters using the least squares formula based on the coefficient matrix, the weight matrix, and the ionospheric delayed observation vector.

[0031] Specifically, the first step is to determine the primary reference station. The system automatically selects the reference station closest to the rover as the primary reference station. This selection ensures that the regional ionospheric model has the highest accuracy near the rover. In determining the primary reference station, the planar distance between each reference station and the rover needs to be obtained based on the rover's coordinates and the coordinates of each reference station.

[0032] The system receives the real-time location coordinates of the rover and the known precise coordinates of each reference station in the CORS network. These coordinates are then converted from the geographic coordinate system (latitude and longitude) to a Cartesian coordinate system to ensure the accuracy of distance calculations. During the coordinate transformation, considering the typically small area (the average distance between reference stations is approximately 47.3 km), a simple projection method is used to avoid errors caused by large-scale projection distortion. After the transformation, the Euclidean distance formula in the Cartesian coordinate system is used to calculate the planar distance between each reference station and the rover. In actual calculations, to improve efficiency, the system usually first calculates the square of the distance for comparison, avoiding unnecessary square root calculations. The square root is only performed after determining the minimum distance to obtain the actual distance value. The reference station with the smallest planar distance to the rover is selected as the master reference station. This selection is based on the strong spatial correlation of ionospheric delay, meaning that the closer two points are, the more similar their ionospheric delays are. The selection of the master reference station is crucial for the subsequent construction of the regional ionospheric model because, in the linear interpolation model, the master reference station serves as the origin, and the coordinate differences of other reference stations are calculated relative to the master reference station. In practical applications, when multiple reference stations are very close to the rover, the system further considers factors such as the observation quality of the reference stations, satellite visibility, and ionospheric activity levels, selecting the reference station with higher observation data quality and better satellite geometric distribution as the primary reference station. Furthermore, to avoid frequent switching of the primary reference station leading to model instability, the system typically sets a switching threshold to ensure the continuity and stability of the primary reference station. The selected primary reference station is not only used to construct the regional ionospheric model but also serves as the basis for subsequent calculations of the planar coordinate difference between the reference stations and the primary reference station, directly affecting the accuracy and reliability of the linear interpolation model. Throughout the positioning process, the selection of the primary reference station is dynamic, updated in real time as the rover's position changes, ensuring that the regional ionospheric model is always centered on the reference station with the highest accuracy near the rover.

[0033] Then, based on the coordinates of each reference station, the planar coordinate difference between each reference station and the main reference station is calculated. Specifically, the latitude and longitude coordinates of the reference stations are converted to a Cartesian coordinate system, and the east-west coordinate difference ΔX and the north-south coordinate difference ΔY are calculated to form a coordinate difference vector set. For n reference stations participating in the modeling, the coordinate difference vector set is represented as {(ΔX1,ΔY1),(ΔX2,ΔY2),...,(ΔX... n ,ΔYn )}, where the subscripts 1, 2, ..., n represent the surrounding reference stations.

[0034] Based on the above coordinate difference vector set, construct the coefficient matrix Br, which is an n×2 matrix, represented as: .

[0035] The coefficient matrix Br reflects the spatial distribution of the reference stations relative to the main reference station and is a core component of the linear interpolation model. In practical applications, to avoid singularity in the coefficient matrix, it is necessary to ensure that the reference stations involved in the modeling are not all located on the same straight line; typically, the reference stations are required to form a certain spatial distribution pattern.

[0036] Next, based on the distances between each reference station and the main reference station, a weight matrix for the distance-based stochastic model is constructed. The weight matrix P is expressed as: , QL i The cofactor of baseline i is calculated as follows: .

[0037] This weight matrix reflects the spatial correlation characteristics of ionospheric delay; that is, the closer a reference station is to the main reference station, the higher the correlation between its ionospheric delay and the main reference station, and the greater its weight in model construction. The diagonal elements of the weight matrix are QL. i Essentially, it is the square of the distance between the reference station and the main reference station, reflecting the impact of spatial distance on the ionospheric delay correlation.

[0038] Finally, based on the coefficient matrix, weight matrix, and ionospheric delayed observation vector, the model parameters are determined using the least squares formula. Ionospheric delayed observation vector: Includes ionospheric delayed observations from various reference stations, and model parameters. The solution is obtained using the least squares estimation formula. Here, a1 and a2 are the coefficients of the linear interpolation model, representing the rates of change of ionospheric delay in the east-west and north-south directions, respectively.

[0039] During the calculation process, it is necessary to ensure that the number of reference stations (n) participating in the modeling is greater than the number of parameters to be estimated (t) to guarantee a unique solution to the equation system. The obtained model parameters accurately reflect the spatial variation characteristics of the regional ionospheric delay, providing a foundation for subsequent construction of regional ionospheric models and estimation of ionospheric correction accuracy. In practical applications, this calculation process is typically repeated every 30 seconds to accommodate rapid spatiotemporal changes in the ionosphere and to exclude outliers caused by poor satellite geometry or intense ionospheric activity.

[0040] Step 1013: Substitute the model parameters into the linear interpolation formula to complete the construction of the regional ionosphere model.

[0041] Specifically, the model parameters a1 and a2 obtained in step 1012 are substituted into the linear interpolation formula to calculate the ionospheric delay value at any location within the region. For the rover location, the interpolated ionospheric delay value is calculated as follows: ,in Let u be the planar coordinate difference vector between the rover and the main reference station, and r represent the surrounding reference stations. The constructed regional ionospheric model can reflect the spatial variation characteristics of ionospheric delay within the region, and its expression is: , where Vr represents the interpolation residual.

[0042] This model can not only be used to predict ionospheric delay at any location within the region, but also provides a basis for subsequent calculation of ionospheric interpolation residuals and unit weighted variance.

[0043] Based on the above embodiments, in this embodiment, the ionospheric interpolation residuals of each reference station are calculated based on the regional ionospheric model, and the unit weighted variance is calculated based on the residuals of all reference stations, which is then used as the ionospheric interpolation accuracy of the reference stations. Specifically, this includes steps 1021-1023: Step 1021: Based on the regional ionospheric model, use the LIM model residual equation to calculate the ionospheric interpolation residuals of each reference station, and obtain the reference station ionospheric delay interpolation residual vector group.

[0044] Specifically, the system utilizes the constructed regional ionospheric model to predict ionospheric delay for each participating reference station. Specifically, it calculates the predicted value Îr = Br·X using a linear interpolation model, where Br is the coefficient matrix constructed in step 1012, and X is the solved model parameter vector [a1; a2]. The predicted value is compared with the actual ionospheric delay observation value Lr provided by the CORS network, and the interpolation residual Vr = Îr - Lr = Br·X - Lr is calculated. This residual reflects the prediction error of the regional ionospheric model at each reference station, and its magnitude directly reflects the local fitting quality of the model. In actual calculations, the system performs residual calculations for each reference station individually, forming an ionospheric delay interpolation residual vector V = [v1; v2; ...; v n ], where v i This represents the interpolation residual of the i-th reference station, where n is the number of reference stations involved in the modeling. To ensure the reliability of the residual calculation, the system excludes outlier residual values ​​affected by multipath effects or severe ionospheric disturbances, typically through quality control by setting a residual threshold. The resulting residual vector set accurately reflects the overall fit of the regional ionospheric model at the reference stations, providing fundamental data for subsequent calculation of the unit weight variance.

[0045] Step 1023: Obtain the weighted sum of squares based on the reference station ionospheric delay interpolation residual vector set.

[0046] Specifically, the system combines the ionospheric delay interpolation residual vector V obtained in step 1021 with the weight matrix P constructed in step 1012 to calculate the weighted sum of squares. .

[0047] The calculation process first transposes the residual vector V to obtain V0. Then calculate V sequentially. P and (V) P)V, ultimately yielding a scalar value. The calculation of the weighted sum of squares takes into account the spatial distribution characteristics of different reference stations, with the diagonal elements QL in the weight matrix P. i This reflects the distance relationship between the reference stations and the main reference station. Reference stations closer to each other have higher weights, and their residuals contribute more to the weighted sum of squares. In practical applications, the calculation of the weighted sum of squares needs to ensure numerical stability. The system checks whether the weight matrix P is a positive definite matrix to avoid calculation anomalies caused by unreasonable reference station distribution. Furthermore, the system performs a rationality check on the weighted sum of squares. When its value exceeds a preset threshold, it indicates that the regional ionospheric model may have a significant bias, requiring a reassessment of model parameters or reference station selection. As a comprehensive indicator, the weighted sum of squares effectively integrates the residual information and spatial weights of all reference stations, providing a reliable input for subsequent calculations of the unit weight variance.

[0048] Step 1023: Calculate the unit weighted variance based on the weighted sum of squares and the number of reference stations, and use it as the interpolation accuracy of the ionosphere at the reference stations.

[0049] Specifically, the system uses the following formula: ; Calculate the unit weighted variance, where V PV is the weighted sum of squares obtained in step 1022, n is the number of reference stations involved in the modeling, and t is the number of parameters to be estimated. This calculation process considers the influence of the model's degrees of freedom; the denominator (nt) represents the number of redundant observations, ensuring an unbiased estimate of the unit weight variance. In actual calculations, the system checks whether the condition n>t is met, i.e., the number of reference stations must be greater than the number of parameters to be estimated; otherwise, a unique solution cannot be obtained. The calculated unit weight variance... It has a clear physical meaning, representing the variance of ionospheric interpolation error under unit weight (weight is 1), and its square root is the unit weight mean error.

[0050] This value accurately reflects the overall accuracy level of the regional ionospheric model at the reference station. The smaller the value, the better the model fit and the higher the ionospheric interpolation accuracy. In GNSS positioning applications, unit weight variance is a key accuracy indicator, used not only to evaluate the quality of the regional ionospheric model but also to provide a basic parameter for calculating the variance of the ionospheric interpolation error at subsequent rover stations.

[0051] Based on the above embodiments, in this embodiment, the ionospheric interpolation standard deviation at the rover station is obtained by using the error propagation law, combined with the unit weight variance and the relative geometric relationship between the rover station and the reference station, and is used as an estimate of the ionospheric correction accuracy. Specifically, steps 1031 to 1034 are included: Step 1031: Determine the main reference station based on the coordinates of each reference station and the rover station, and calculate the difference in planar coordinates between the rover station and the main reference station.

[0052] Specifically, the system first receives the real-time location coordinates of the rover and the known precise coordinates of each reference station in the CORS network. These coordinates are then converted from a geographic coordinate system (latitude and longitude) to a Cartesian coordinate system to ensure the accuracy of distance calculations. Next, the system calculates the planar distance between each reference station and the rover, selecting the reference station with the smallest distance as the master reference station. This selection is based on the strong spatial correlation of ionospheric delay; that is, the closer two points are, the more similar their ionospheric delays are. After determining the master reference station, the system calculates the planar coordinate differences ΔXu and ΔYu between the rover and the master reference station, where ΔXu represents the east-west coordinate difference and ΔYu represents the north-south coordinate difference. In practical applications, to avoid frequent switching of the master reference station leading to model instability, the system typically sets a switching threshold to ensure the continuity and stability of the master reference station. The calculated planar coordinate differences ΔXu and ΔYu are used to construct the rover coefficient vector Bu = [ΔXu ΔYu]. This vector reflects the spatial positional relationship of the rover relative to the master reference station and is the basis for subsequent calculations of the rover's ionospheric delay interpolation values.

[0053] Step 1032: Based on the planar coordinate difference between the rover and the main reference station, obtain the relative geometric relationship between the rover and the reference station, which includes the rover coefficient vector.

[0054] Specifically, the system uses the planar coordinate differences ΔXu and ΔYu calculated in step 1031 to construct the rover coefficient vector Bu = [ΔXu ΔYu]. This vector has the same form as the reference station coefficient matrix Br constructed in step 1012, both reflecting the spatial geometric relationship between the reference station network and the rover. The relative geometric relationship between the rover and the reference station includes not only spatial positional relationships but also implicitly contains spatial correlation information about ionospheric delay; that is, the closer the rover is to the reference station, the higher the correlation of its ionospheric delay. In practical applications, the system checks whether the rover is located inside the reference station network (i.e., surrounded by reference stations), because when the rover is located at the edge or outside of the network, the ionospheric interpolation accuracy will be significantly reduced. For rover located inside the network, its relative geometric relationship with each reference station can be quantitatively expressed through coefficient vectors and matrices, providing a geometric basis for subsequent error propagation calculations. The accurate acquisition of this relative geometric relationship is crucial for calculating the variance of the rover's ionospheric interpolation error and directly affects the reliability of the ionospheric correction accuracy estimation.

[0055] Step 1033: Based on the rover coefficient vector and unit weight variance, obtain the rover ionospheric interpolation error variance through the error propagation law.

[0056] Specifically, the system first defines the ionospheric delay interpolation error at the rover station as: Where Bu is the rover coefficient vector obtained in step 1032, X is the model parameter vector solved in step 1012, and Lu is the actual ionospheric delay at the rover station. = Substituting into the above formula, we get: , in E is the identity matrix, where the subscript u represents the mobile station and the subscript r represents the reference station.

[0057] According to the law of error propagation, the variance of the ionospheric delay interpolation error can be calculated as follows: , Where D(LL) is the covariance matrix of the ionospheric delayed observations. Considering D(LL) = ,in It is the unit weight variance of the n baselines involved in the modeling and the 1 baseline to be interpolated. Since it is a cofactor matrix, therefore: .

[0058] In calculation First, it is necessary to clarify that the calculation formula is: ; Since the interpolation station is located inside the network, its ionospheric interpolation residual characteristics are similar to those of the surrounding reference stations. Therefore, the following key assumptions are proposed: , Therefore, we can deduce that: , in: , where n is the number of reference stations participating in the modeling, and t is the number of parameters to be estimated.

[0059] To verify the validity of the core assumption that "the variance of the ionospheric interpolation error at the rover station is approximately equal to the variance of the ionospheric interpolation residuals of the surrounding baselines," a method was designed to measure σ0² and... A comparative experiment was conducted using σ0². The ZJNB station was selected as the rover station, and Network RTK ionospheric modeling was performed using observational data from surrounding reference stations. σ0² was calculated using observational data from the surrounding reference stations. σ0² was calculated using observation data from surrounding reference stations and the ZJNB station. Experimental results show that σ0² is consistent with... The distribution of the 0² difference follows a normal distribution with zero mean, verifying the effectiveness of the core assumption of this invention. To further verify the accuracy of the proposed ionospheric interpolation method, ZJNB station is still selected as the rover station, and FEHU station is selected as the reference station for ZJNB station. The ionospheric slant range delay of the surrounding baseline is obtained by fixing the double-difference ambiguity. The ionospheric delay of G04 satellite at DOY 080 is analyzed, as well as the true value of the double-difference ionospheric delay of the FEHU-ZJNB baseline of this satellite, the interpolation correction amount, and the interpolation error. Figure 5 This shows the ionospheric delay of the G04 satellite on day 80 of 2023 (DOY 080). Figure 6 The true value of the double-difference ionospheric delay, interpolation correction, and interpolation error of the FEHU-ZJNB baseline of the satellite are shown.

[0060] Finally, the variance of the ionospheric interpolation error of the rover station was calculated as follows: This variance accurately reflects the level of uncertainty in ionospheric correction at the rover station. This can be calculated using a distance-based stochastic model. This calculation process considers the covariance relationship of (n+1) baselines (n reference station baselines and 1 rover baseline), ensuring the accuracy of error propagation. In actual calculations, when the rover is located at the edge or in the external region of the reference station network, the system automatically detects the relationship between the rover's location and the reference station network.

[0061] Step 1034: Take the square root of the variance of the ionospheric interpolation error at the rover station to obtain the standard deviation of the ionospheric interpolation at the rover station, and use it as an estimate of the ionospheric interpolation accuracy.

[0062] Specifically, the system performs a square root operation on the ionospheric interpolation error variance D(Vu,Vu) calculated in step 1033 to obtain the ionospheric interpolation standard deviation σ(Vu)=√D(Vu,Vu), which represents the accuracy level of the ionospheric delay interpolation value at the rover station.

[0063] In practical calculations, since D(Vu,Vu) is a scalar value, the square root operation directly yields the standard deviation. This standard deviation, as a real-time estimate of ionospheric correction accuracy, accurately reflects the reliability of ionospheric correction at the current time and location. Unlike the fixed prior models used in traditional methods, it can dynamically adapt to the rapid spatiotemporal changes of the ionosphere. In subsequent positioning calculations, this standard deviation is incorporated into the ionospheric weighted model as the basis for calculating the weights of the ionospheric delay virtual observations. Specifically, this is achieved by assigning a weight of 1 / σ(Vu)² to the ionospheric delay term Iru^ij in the observation equation. During periods of ionospheric activity, this real-time estimated ionospheric correction accuracy can significantly improve the ambiguity fixation rate and positioning accuracy.

[0064] Based on the above embodiments, in this embodiment, after obtaining the ionospheric interpolation standard deviation at the rover station by using the error propagation law, combining the unit weight variance and the relative geometric relationship between the rover station and the reference station, the method further includes: The standard deviation of ionospheric interpolation at the rover station is embedded into a preset ionospheric weighted model to adjust the weights of the positioning solution. Specifically, this involves: first, embedding the standard deviation of ionospheric interpolation at the rover station into the preset ionospheric weighted model, and calculating the weights using the weight calculation formula of the ionospheric weighted model to obtain an updated ionospheric weighted model; then, based on the updated ionospheric weighted model and GNSS observation data, constructing an observation equation that includes the ionospheric interpolation accuracy; and finally, solving the observation equation using the least squares method to obtain the positioning solution result of the rover station.

[0065] Specifically, the system uses the ionospheric interpolation standard deviation σ(Vu) calculated in step 1034 as the prior accuracy information of the ionospheric delay virtual observation. Based on the inverse relationship between weight and the square of accuracy, the system calculates the weight P of the ionospheric delay term. I =1 / σ(Vu)². In practical applications, for each visible satellite, the system calculates the corresponding ionospheric interpolation standard deviation and determines the weight of the satellite's ionospheric delay observations accordingly.

[0066] Since ionospheric delay is frequency-dependent, the ionospheric delay weights for the L1 and L2 frequency bands are adjusted according to the square ratio of the frequency, specifically P. I1 =1 / σ(Vu)² and P I2=(f1² / f2²)² / σ(Vu)². When constructing the ionospheric weighted model, the system integrates these weights into the weight matrix of the observation equations, forming the updated ionospheric weighted model.

[0067] This model not only considers the accuracy characteristics of traditional GNSS observations (carrier phase and pseudorange) but also incorporates real-time estimation information of ionospheric correction accuracy, enabling the weight matrix to dynamically reflect the observation quality under current ionospheric conditions. In actual calculations, the system checks whether the weight values ​​are within a reasonable range to avoid excessively large weights due to a small ionospheric interpolation standard deviation, which could affect the stability of the solution. A minimum standard deviation threshold (e.g., 0.1 TECU) is typically set to ensure the reasonableness of the weights.

[0068] Based on the updated ionospheric weighted model and GNSS observation data, observation equations incorporating ionospheric interpolation accuracy are constructed. The system estimates the ionospheric delay parameter separately for each satellite and epoch, constructing a complete set of observation equations including virtual ionospheric delay observations. For double-difference observations of satellites i and j, the observation equation expression is: ; ; ; ; ; in, and These represent the double-difference pseudorange and double-difference geometric distance between satellites i and j and receivers r and u, respectively. For double-difference ionospheric delay, f1 and f2 are the frequencies of the L1 and L2 signals, respectively. This is the interpolation correction for tropospheric delay. In this observation equation, the last equation, Iru^ij=Iru^ij, is a virtual observation equation for ionospheric delay, whose observed values... The ionospheric delay estimate is obtained through interpolation using a regional ionospheric model, and the weights of this equation are calculated based on 1 / σ(Vu)², which is obtained from the standard deviation of the ionospheric interpolation. In the actual construction process, the system constructs corresponding observation equations for each visible satellite and combines all equations according to their weights to form a complete set of observation equations.

[0069] To verify the effectiveness of the proposed real-time estimation method for ionospheric interpolation accuracy, observational data from 17 CORS stations in Zhejiang Province, China, during days 80 to 85 of 2023 (DOY 080–085) were used for experimental verification. It is worth noting that, as... Figure 4 As shown, severe ionospheric disturbances occurred on day 83. The geographical distribution of CORS stations is as follows: Figure 2As shown, the geographical distribution of CORS stations indicates an average spacing of approximately 47.3 km between reference stations. The sampling interval for observation data is 30 seconds, and the altitude cutoff angle is set to 10°. The experiment uses the IGS precise ephemeris and the IGS_14 antenna model to calculate satellite orbit, satellite clock bias, and antenna phase center, ensuring the accuracy of preprocessing. Experimental results show that, compared with existing methods, this invention significantly improves ambiguity fixation rate and positioning accuracy during periods of ionospheric activity. Especially during the midday ionospheric activity period (12:00-14:00), the ambiguity fixation rate is improved by more than 39% (from 62.3% to 86.7%), the horizontal positioning accuracy is improved by 22% (from 0.045m to 0.035m), and the vertical accuracy is improved by 8% (from 0.082m to 0.075m). Specific data are shown in Table 1. Table 1 Comparison of localization performance of different methods

[0070] The observation equations are solved using the least squares method to obtain the positioning results of the rover station. The system expresses the constructed weighted observation equations in a linearized form V=AX-L, where V is the residual vector, A is the design matrix, X is the vector of parameters to be estimated (including rover coordinates, double-difference ambiguity, and ionospheric delay, etc.), and L is the observation vector. According to the least squares principle, the parameter solution is X=(A PA) - ¹A PL, where P is the weight matrix, contains the weight information of all observations, especially the weights of the virtual observations with ionospheric delay. During the solution process, the system first fixes the double-difference integer-cycle ambiguity, then iteratively solves for the rover position and ionospheric delay parameters until the solution converges.

[0071] To improve the reliability of the solution, the system performs multiple iterations, re-evaluating the residuals and adjusting the weights of outlier observations after each iteration. The final rover positioning result not only considers traditional GNSS observation information but also incorporates real-time estimated ionospheric correction accuracy information, enabling the positioning solution to dynamically adapt to rapid spatiotemporal changes in the ionosphere.

[0072] In practical applications, the entire calculation process is repeated every 30 seconds to ensure timely reflection of rapid changes in ionospheric conditions. During each calculation, the system performs quality control to exclude abnormal observations affected by multipath effects, cycle slips, or severe ionospheric disturbances. Quality control is typically achieved by setting a threshold for the rate of change of ionospheric delay. If there are fewer than three reference stations, the system automatically switches to a backup scheme, using an empirical model for coarse estimation and issuing an alert indicating insufficient network density. During the solution process, the system monitors the changes in unit weight variance in real time. When its value suddenly increases beyond a threshold, it indicates potential ionospheric disturbances or data quality issues. In this case, the system automatically adjusts model parameters or reselects reference stations to ensure the reliability of the ionospheric correction accuracy estimate.

[0073] During the positioning process, the system dynamically adjusts the ambiguity fixing strategy based on the standard deviation of the ionospheric interpolation. For example, when the standard deviation is less than 0.3 TECU, the LAMBDA method is used for ambiguity fixing; when the standard deviation is between 0.3 and 0.5 TECU, a partial ambiguity fixing strategy is adopted; and when the standard deviation is greater than 0.5 TECU, a floating-point solution is used as the final solution, and the user is alerted that the current ionospheric activity is strong and the positioning accuracy may decrease. This adaptive strategy ensures positioning reliability under different ionospheric conditions, especially during periods of ionospheric activity, significantly improving the ambiguity fixing rate and positioning accuracy.

[0074] In practical deployment, this method has been integrated into the real-time processing system of the Zhejiang Province CORS network, providing users with centimeter-level positioning services. System operation results show that during the period of severe ionospheric disturbances (such as on day 83 of 2023, DOY 083)... Figure 3 As shown in the variations of the Planetary K-index and Dst exponent, this method still maintains a high ambiguity fixation rate and positioning accuracy, verifying its robustness under conditions of high ionospheric activity. Especially in low-latitude regions and during midday ionospheric activity, the advantages of this method are more pronounced, effectively solving the ambiguity fixation difficulties often faced by users in traditional methods at midday, and providing reliable technical support for high-precision GNSS applications.

[0075] Secondly, embodiments of this application provide a system for estimating ionospheric correction accuracy in GNSS-enhanced positioning, comprising: a first module for constructing a regional ionospheric model using GNSS observation data from reference stations in a CORS network and employing a linear interpolation method; a second module for calculating the ionospheric interpolation residuals of each reference station based on the regional ionospheric model, calculating the unit weight variance based on the residuals of all reference stations, and using it as the ionospheric interpolation accuracy of the reference stations; and a third module for obtaining the ionospheric interpolation standard deviation at the rover station by using the error propagation law, combining the unit weight variance and the relative geometric relationship between the rover station and the reference station, and using it as an estimate of the ionospheric correction accuracy.

[0076] By constructing a regional ionospheric model using GNSS observation data from reference stations in the CORS network and integrating observation information from multiple reference stations using linear interpolation, the regional consistency of ionospheric spatial distribution modeling is effectively improved. Based on this model, the ionospheric interpolation residuals of each reference station are calculated, and the unit weighted variance is calculated, providing an objective statistical quantitative basis for the ionospheric interpolation accuracy of the reference stations. Furthermore, by applying the error propagation law and combining the relative geometric relationship between the rover and the reference stations, the accuracy benchmark of the reference stations is dynamically propagated to the rover's position, enabling the estimation of the ionospheric interpolation standard deviation to respond in real time to changes in the rover's spatial position. This achieves adaptive estimation of ionospheric correction accuracy during GNSS augmentation positioning, significantly improving the reliability and accuracy of positioning solutions.

[0077] The functions of each module in the above-mentioned GNSS enhanced positioning ionospheric correction accuracy estimation system correspond to the steps in the above-mentioned GNSS enhanced positioning ionospheric correction accuracy estimation method embodiment, and their functions and implementation processes will not be described in detail here.

[0078] Thirdly, embodiments of this application provide an ionospheric correction accuracy estimation device for GNSS enhanced positioning. The ionospheric correction accuracy estimation device for GNSS enhanced positioning can be a personal computer (PC), laptop computer, server, or other device with data processing capabilities.

[0079] In this embodiment of the application, the ionospheric correction accuracy estimation device in GNSS enhanced positioning may include a processor, a memory, a communication interface, and a communication bus.

[0080] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.

[0081] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces. These interfaces are used for interconnecting internal components of the ionospheric correction accuracy estimation equipment in GNSS enhanced positioning, as well as for interconnecting the ionospheric correction accuracy estimation equipment with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.

[0082] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0083] The processor can be a general-purpose processor, which can call the GNSS-enhanced positioning ionospheric correction accuracy estimation program stored in the memory and execute the GNSS-enhanced positioning ionospheric correction accuracy estimation method provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the GNSS-enhanced positioning ionospheric correction accuracy estimation program is called can refer to the various embodiments of the GNSS-enhanced positioning ionospheric correction accuracy estimation method of this application, and will not be repeated here.

[0084] Fourthly, embodiments of this application also provide a computer-readable storage medium.

[0085] The present application stores a GNSS-enhanced positioning ionospheric correction accuracy estimation program on a computer-readable storage medium, wherein when the GNSS-enhanced positioning ionospheric correction accuracy estimation program is executed by a processor, it implements the steps of the GNSS-enhanced positioning ionospheric correction accuracy estimation method as described above.

[0086] The method implemented when the ionospheric correction accuracy estimation procedure in GNSS enhanced positioning is executed can be referred to in the various embodiments of the ionospheric correction accuracy estimation method in GNSS enhanced positioning of this application, and will not be repeated here.

[0087] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0088] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0089] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0090] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0091] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0092] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0093] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for estimating the accuracy of ionospheric correction in GNSS enhanced positioning, characterized in that, It includes: A regional ionospheric model was constructed using GNSS observation data from reference stations in the CORS network and a linear interpolation method. Based on the regional ionospheric model, the ionospheric interpolation residuals of each reference station are calculated, and the unit weighted variance is calculated based on the residuals of all reference stations, which is then used as the ionospheric interpolation accuracy of the reference stations. By using the error propagation law, combined with the unit weight variance and the relative geometric relationship between the rover and the reference station, the standard deviation of the ionospheric interpolation at the rover station is obtained, and it is used as an estimate of the ionospheric correction accuracy.

2. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 1, characterized in that, Using GNSS observation data from reference stations in the CORS network, a regional ionospheric model is constructed using linear interpolation, specifically including: Based on GNSS observation data from reference stations in the CORS network, obtain the vector of ionospheric delay observations; The model parameters are determined using the least squares formula based on the coordinates of each reference station and the vector of delayed ionospheric observations. The model parameters are substituted into the linear interpolation formula to complete the construction of the regional ionosphere model.

3. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 2, characterized in that, Based on GNSS observation data from reference stations in the CORS network, the ionospheric delay observation vector is obtained, specifically including: Based on GNSS observation data from reference stations in the CORS network, integer ambiguities are fixed to determine integer ambiguities. Based on integer ambiguity and GNSS observation data, the ionospheric delay observation vector is obtained using the ionospheric delay calculation formula.

4. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 2, characterized in that, Based on the coordinates of each reference station and the vector of delayed ionospheric observations, the model parameters are determined using the least squares formula, specifically including: Based on the coordinates of each reference station, calculate the planar coordinate difference between each reference station and the main reference station to obtain a set of coordinate difference vectors; Construct a coefficient matrix based on the coordinate difference vector set; Based on the distance between each reference station and the main reference station, a weight matrix for a distance-based stochastic model is constructed. The model parameters are determined based on the coefficient matrix, weight matrix, and ionospheric delayed observation vector, using the least squares formula.

5. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 1, characterized in that, Based on the regional ionospheric model, the ionospheric interpolation residuals for each reference station are calculated. The unit weighted variance is then calculated based on the residuals from all reference stations and used as the ionospheric interpolation accuracy for each reference station. Specifically, this includes: Based on the regional ionospheric model, the ionospheric interpolation residuals of each reference station are calculated using the LIM model residual equation, and the ionospheric delay interpolation residual vector set of the reference station is obtained. The weighted sum of squares is obtained based on the reference station's ionospheric delay interpolation residual vector set. Based on the weighted sum of squares and the number of reference stations, the unit weighted variance is calculated and used as the interpolation accuracy of the ionosphere at the reference stations.

6. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 1, characterized in that, By applying the error propagation law, combining the unit weight variance, and the relative geometric relationship between the rover and the reference station, the standard deviation of the ionospheric interpolation at the rover station is obtained and used as an estimate of the ionospheric correction accuracy. Specifically, this includes: Based on the coordinates of each reference station and the rover station, determine the main reference station and calculate the difference in planar coordinates between the rover station and the main reference station; Based on the difference in planar coordinates between the rover and the main reference station, the relative geometric relationship between the rover and the reference station is obtained, and the relative geometric relationship between the rover and the reference station includes the rover coefficient vector. Based on the rover coefficient vector and unit weight variance, the ionospheric interpolation error variance of the rover is obtained through the error propagation law. The square root of the variance of the ionospheric interpolation error at the rover station is taken to obtain the standard deviation of the ionospheric interpolation at the rover station, which is then used as an estimate of the accuracy of the ionospheric interpolation.

7. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 4 or 6, characterized in that, The main reference station is determined based on the coordinates of each reference station and the rover station, specifically including: Based on the coordinates of the rover and each reference station, obtain the planar distance between each reference station and the rover; The reference station with the smallest horizontal distance from the rover station is taken as the main reference station.

8. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 1, characterized in that, After obtaining the ionospheric interpolation standard deviation at the rover station by using the error propagation law, combining the unit weight variance and the relative geometric relationship between the rover station and the reference station, the method further includes: The standard deviation of ionospheric interpolation at the rover station is embedded into a preset ionospheric weighted model to adjust the weights of the positioning solution.

9. The method for estimating ionospheric correction accuracy in GNSS enhanced positioning as described in claim 8, characterized in that, The standard deviation of ionospheric interpolation at the rover station is embedded into a pre-defined ionospheric weighted model to adjust the weights of the positioning solution. Specifically, this includes: The standard deviation of ionospheric interpolation at the rover station is embedded into a preset ionospheric weighting model, and the weights are calculated using the weight calculation formula of the ionospheric weighting model to obtain the updated ionospheric weighting model. Based on the updated ionospheric weighted model and GNSS observation data, an observation equation incorporating ionospheric interpolation accuracy is constructed. The location calculation results of the rover station are obtained by solving the observation equation using the least squares method.

10. A system for estimating the accuracy of ionospheric correction in GNSS enhanced positioning, characterized in that, It includes: The first module is used to construct a regional ionospheric model using GNSS observation data from reference stations in the CORS network and employing linear interpolation. The second module is used to calculate the ionospheric interpolation residuals of each reference station based on the regional ionospheric model, and to calculate the unit weighted variance based on the residuals of all reference stations, and use it as the ionospheric interpolation accuracy of the reference stations. The third module is used to obtain the standard deviation of ionospheric interpolation at the rover station by using the error propagation law, combined with the unit weight variance and the relative geometric relationship between the rover station and the reference station, and to use it as an estimate of the ionospheric correction accuracy.

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