CORS ionized layer modeling method and device based on linear change characteristics

Abstract

The invention discloses a linear change characteristic-based CORS ionized layer modeling method and device, and the method comprises the steps: firstly selecting a plurality of linearly distributed GNSS observation stations, carrying out the preprocessing of observation data, calculating the STEC, and enabling the STEC to be projected into VTEC through a single-layer model; and then constructing a VTEC data set along the target direction at the same moment, normalizing the IPP distance of the ionosphere puncture point, calling an international reference ionosphere model to calculate a VTEC reference value as a fitting weight, and adopting a dynamic order determination strategy to complete polynomial fitting through a weighted least square method to obtain a regional ionosphere model. VTEC corresponding to the virtual reference station is obtained through interpolation, ionosphere delay is obtained, the ionosphere delay is further applied to virtual observation value calculation, and linear region high-precision network RTK calculation is achieved. According to the method, the physical characteristic that the ionosphere has change regularity in the longitude / latitude direction is fully utilized, the precision of the regional ionosphere model is remarkably improved while the requirement for the distance of the observation station is lowered, and the observation precision of the linear regional network RTK is further improved.

Description

Technical Field

[0001] This invention belongs to the field of space science and technology, and in particular relates to a CORS ionosphere modeling method and device based on linear variation characteristics. Background Technology

[0002] Network RTK technology, as a key support for high-precision positioning services, achieves regional error modeling and elimination through a network of multiple continuously operating reference stations (CORS). However, as its application scenarios expand from local areas to wide-area linear regions, traditional network RTK technology faces the serious challenge of insufficient ionospheric modeling accuracy in long-distance linear distribution areas.

[0003] Global Navigation Satellite System (GNSS) signals traverse the ionosphere during propagation, where they are affected by free electrons, resulting in ionospheric delay. This delay has become one of the core error sources limiting the improvement of network RTK positioning accuracy. The total electron content, a key parameter describing the ionospheric state, varies complexly, but research has found that it exhibits stronger predictability within specific linear regions (such as geographic longitude zones and geomagnetic latitude zones). This crucial physical characteristic provides an important direction for improving ionospheric modeling; however, current network RTK technologies have not yet fully explored and utilized this potential.

[0004] To achieve real-time ionospheric delay correction, current network RTK systems widely employ TEC parameters broadcast by the CORS system and obtain the information of the target point through interpolation methods such as inverse distance weighting and Kriging interpolation. Research continues to advance, from early integrated error interpolation methods to subsequent improved integrated error interpolation methods and other models.

[0005] Commonly used methods for modeling ionization delay errors include the Combined Error Interpolation (CBI) and the Modified Combined Error Interpolation (MCBI). As early as 2002, the Combined Error Interpolation method was proposed as a regional error modeling method for network RTK, capable of accurately interpolating the ionospheric delay of mobile stations. Subsequently, based on the Combined Error Interpolation method, researchers proposed improved algorithms for calculating ionospheric delay corrections, further enhancing the interpolation accuracy of the network RTK regional error model for mobile station ionospheric delay. By 2007, related research further improved the Combined Error Interpolation method, resulting in the Modified Combined Error Interpolation (MCBI). This method not only has higher accuracy than the Combined Error Interpolation method but is also more suitable for mobile station applications, marking a new stage in the research of regional ionospheric delay error models for network RTK.

[0006] For long baseline network RTK, a network difference method has been proposed, enabling high-precision, real-time, and rapid positioning in offshore areas. Furthermore, multiple experiments have compared the interpolation accuracy of the LSM, LIM, LCM, and DIM models, showing that the LSM model outperforms the other three. Other research has focused on the LIM and DIM models, experimentally verifying that the LIM model has superior interpolation accuracy compared to the DIM model.

[0007] However, these existing modeling methods have two major limitations: First, they do not optimize the selection and modeling strategies of reference stations based on the aforementioned linear variation characteristics of the ionosphere, and still mainly rely on geographically uniform or gridded reference stations, which makes the modeling accuracy greatly affected by geographical distribution, especially when modeling along latitudinal zones and other directions with significant errors; Second, in order to compensate for the accuracy loss caused by not utilizing the linear pattern, the requirements for the spacing between stations are extremely strict, and reference stations need to be densely deployed, which greatly increases the construction and operation and maintenance costs of the system, and it is difficult to guarantee accuracy in areas where reference stations are sparse.

[0008] In particular, these defects are amplified dramatically in long-distance linear regions (such as typical linear engineering scenarios like coastlines, river basins, highways, and railways). Traditional reference station layout methods cannot effectively capture the gradient change characteristics of the ionosphere along the linear direction, resulting in a significant reduction in ionospheric modeling accuracy. The ionospheric delay error generated by virtual reference stations is also large, ultimately causing a decrease in the positioning accuracy and a lengthening of convergence time for network RTK in such regions.

[0009] In summary, existing network RTK ionospheric modeling methods suffer from insufficient accuracy in long-distance zonal regions, high requirements on station spacing, and poor regional adaptability due to their failure to fully explore and utilize the linear variation characteristics of the ionosphere. There is an urgent need for a new modeling method that uses a linear model as its core and can fully utilize the linear variation laws of the ionosphere to overcome the current technological bottlenecks. Summary of the Invention

[0010] To address the problem that existing ionospheric modeling methods fail to fully utilize the physical characteristics of the ionosphere's linear variation patterns, leading to stringent requirements on station spacing and low and unstable regional modeling accuracy, this invention provides a CORS ionospheric modeling method based on linear variation characteristics. By using dynamic fixed-order polynomial fitting to accurately estimate high-order gradients, it can capture detailed changes in the ionosphere within linear regions, avoiding the accuracy loss caused by traditional low-order or fixed-order fitting, optimizing the model's ability to characterize TEC distribution, and significantly reducing dependence on station density.

[0011] According to one aspect of the present invention, a method for CORS ionosphere modeling based on linear variation characteristics is provided, comprising: Based on the observation data of multiple GNSS stations linearly distributed in the target area at the same time on satellites at the same elevation angle, the oblique total electron content of the ionosphere is calculated, and then the oblique total electron content is projected into the vertical total electron content through a single-layer model; Based on a single-layer model, the ionospheric puncture point of each station when observing the satellite is calculated, and the puncture point is associated with the corresponding vertical total electron content to construct a time-series modeling dataset. The total vertical electron content at the puncture point was calculated using the international reference ionospheric model and used as the fitting weight. The modeling dataset was used as input, and a dynamic order determination strategy was adopted to perform polynomial fitting using the weighted least squares method to obtain the linear ionospheric model.

[0012] As a further technical solution, the method also includes: Based on the obtained linear ionospheric model, the vertical total electron content at any point in the region is interpolated. Set the coordinates of the virtual reference station, calculate the total vertical electron content of the virtual reference station relative to each satellite, and construct the observation values ​​of the virtual reference station; Based on the observations of the virtual reference station, the pseudorange and phase observations of the virtual reference station are inverted to form a virtual observation file.

[0013] As a further technical solution, after obtaining the virtual observation file, the method further includes: Differential positioning is performed based on virtual observation files, and ambiguity is fixed using carrier phase to achieve RTK calculation for linear area networks.

[0014] As a further technical solution, before performing polynomial fitting, the following is also included: Calculate the relative distance of each puncture point along the distribution direction of the sites, and then normalize it.

[0015] As a further technical solution, the method also includes: Using the normalized relative distance as the independent variable and the vertical total electron content at the fitted puncture point as the dependent variable, an m-order polynomial is constructed. The polynomial coefficients are solved using the weighted least squares method, with the objective function being to minimize the weighted sum of squared residuals. Dynamic cross-validation is used to determine the optimal polynomial order.

[0016] As a further technical solution, dynamic cross-validation is used to determine the optimal polynomial order, including: Remove one puncture point from the n puncture points at a time, and reconstruct the m-th order polynomial using the modeling dataset of the remaining n-1 puncture points; The total vertical electron content at the removed puncture point is predicted using the constructed m-order polynomial, and the residual between the predicted value and the actual observed value is calculated. Iterate through all puncture points, calculate the root mean square of the residuals for different orders, and take the order with the smallest root mean square of the residuals as the optimal polynomial order.

[0017] As a further technical solution, the multiple GNSS stations linearly distributed within the target area are selected according to the following principles: The distance between each station is within 100±10 km, and the number of stations is no less than 9.

[0018] According to one aspect of the present invention, a CORS ionospheric modeling apparatus based on linear variation characteristics is provided, comprising: The first main module is used to calculate the oblique total electron content of the ionosphere based on the observation data of multiple GNSS stations linearly distributed in the target area at the same time and satellites at the same elevation angle. Then, the oblique total electron content is projected into the vertical total electron content through a single-layer model. The second main module is used to calculate the ionospheric puncture point of each station when observing the satellite based on a single-layer model, associate the puncture point with the corresponding vertical total electron content, and construct a time-series modeling dataset. The third main module is used to call the international reference ionosphere model to calculate the vertical total electron content at the puncture point as the fitting weight. With the modeling dataset as input, a dynamic order determination strategy is adopted to perform polynomial fitting through weighted least squares to obtain the linear region ionosphere model.

[0019] According to one aspect of the present invention, a CORS ionosphere modeling apparatus based on linear variation characteristics is provided, comprising a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the CORS ionosphere modeling method based on linear variation characteristics.

[0020] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the CORS ionosphere modeling method based on linear variation characteristics.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: The CORS ionospheric modeling method based on linear variation characteristics provided by this invention accurately estimates high-order gradients through dynamic fixed-order polynomial fitting (selecting the order with the smallest fitting error). This method can capture detailed changes in the ionosphere within linear regions, avoiding the accuracy loss caused by traditional low-order fitting or fixed-order fitting. It optimizes the model's ability to characterize TEC distribution, significantly reduces dependence on station density, and reduces the hardware and management costs of reference station construction and maintenance. It is particularly suitable for regions with sparse station resources but a need for ionospheric delay accuracy. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart illustrating the CORS ionosphere modeling method based on linear variation characteristics provided in an embodiment of the present invention.

[0024] Figure 2 This is a schematic diagram of data acquisition provided for an embodiment of the present invention.

[0025] Figure 3 A schematic diagram illustrating the advantages of polynomial fitting provided in an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0027] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0028] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0029] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0030] The following section elaborates on the CORS ionosphere modeling method based on linear variation characteristics, combining the core principles and actual operation procedures of this invention. This ensures that those skilled in the art can reproduce the scheme by following the steps below, without involving specific experimental data, focusing only on the implementation path of the method.

[0031] This invention addresses the problem that existing ionospheric modeling methods fail to fully utilize the physical characteristics of the linear variation of the ionosphere, leading to stringent requirements on station spacing and low and unstable regional modeling accuracy. It provides a CORS ionospheric modeling method based on linear variation characteristics, comprising three core steps: VTEC extraction, dataset construction, and multinomial fitting to build the model. (Refer to...) Figures 1 to 3 As shown, the details are as follows: Step 1: Based on the observation data of multiple GNSS stations linearly distributed in the target area at the same time on satellites at the same elevation angle, calculate the oblique total electron content of the ionosphere, and then project the oblique total electron content into the vertical total electron content through a single-layer model; Step 2: Calculate the ionospheric puncture point for each station when observing the satellite based on the single-layer model, associate the puncture point with the corresponding vertical total electron content, and construct a time-series modeling dataset; Step 3: The total vertical electron content at the puncture point is calculated using the international reference ionosphere model as the fitting weight. The modeling dataset is used as input, and a dynamic order determination strategy is adopted to perform polynomial fitting using the weighted least squares method to obtain the linear ionosphere model.

[0032] Step 1, based on raw GNSS observation data, extracts the slant total electron content (STEC) using the carrier phase-pseudorange method, and then obtains the vertical total electron content (VTEC) through projection using a modified single-layer model (MSLM). The specific implementation process is as follows: Step 1.1: Select linearly distributed GNSS stations in the target area, with a station spacing of up to 100±10km, and a number of no fewer than 9 stations (denoted as SITE1, SITE2, ..., SITE...). n (n ≥ 9); Select a GNSS satellite with an elevation angle > 15° (denoted as S) to ensure that all stations can observe the satellite at the same time t.

[0033] Step 1.2, preprocess the raw GNSS data from the GPS system, including: Periodic jump detection and repair: The phase smoothing pseudorange method is used to identify and correct periodic jumps in carrier phase observations; Gross error removal: Outliers in pseudorange and carrier phase observations are removed based on the 3σ criterion; Data filtering: Only observation data with continuous arc observation time > 30 min and satellite elevation angle > 15° are retained to reduce the impact of multipath effect and observation noise.

[0034] Step 1.3: Calculate STEC, and then project STEC onto the vertical direction to obtain VTEC by improving the single-layer model.

[0035] The STEC along the GNSS signal propagation path is calculated using the following formula: , in: STEC: Total Electron Content in Oblique Direction (unit: TECU); MHz MHz, corresponding to the first and second frequencies of GPS signals; , : , Corresponding carrier phase observations (unit: m); , : , Corresponding pseudorange observations (unit: m); , : Geometric (GF) combinations of L and P respectively; The average value of the sum of pseudorange and phase within a continuous arc segment, where there is no geometrically linear combination. , : Differential code bias (DCB, unit: m) for receiver and satellite, respectively, calculated from the GIM model provided by the European Centre for Determining Orbits (CODE); m / s: speed of light.

[0036] Based on the improved single-layer model, the STEC is projected onto the vertical direction to obtain the VTEC. The projection formula is as follows: , in: The zenith angle at the ionospheric puncture point (IPP) is calculated using the following formula: ; km: Earth's radius; km: Height of a single-layer model shell; Satellite elevation angle (unit: °); : Empirical correction factor.

[0037] In step 2, during the construction of the modeling dataset, the improved single-layer model is used to calculate the SITE for each site. i When observing satellite S at time t, the IPP positions are such that, since the stations are distributed along a fixed linear direction, all IPPs are also distributed along the same direction, forming a linear IPP sequence: .

[0038] The formula for calculating IPP is: , in, , These are the IPP longitude and latitude of the i-th GNSS station at time t, respectively, in degrees; , which is the IPP height, consistent with the shell height of the improved single-layer model.

[0039] Associate the VTEC corresponding to each IPP with the site observation data to construct the time-series data. Modeling dataset The formula is: ,in for The vertical total electron content is calculated from step 1.

[0040] For subsequent moments Repeat step 2 to build. This enables the continuous acquisition of time-series modeling datasets.

[0041] When constructing the ionospheric model in step 3 using polynomial fitting, Using VTEC calculated from the IRI-2016 model as input, and combining it with the fitting weights, a regional ionospheric model is constructed through weighted least squares polynomial fitting. The specific steps are as follows: Calculate the relative distance of each IPP along the distribution direction of the sites, and normalize it to eliminate the influence of dimensions. The formula is as follows: , in: Indicates IPP i The arc length distance (in km) from the reference IPP along the distribution direction; the reference IPP is the IPP at the middle position in the IPP sequence; This represents the normalized relative distance (value range: [0, 1]).

[0042] Each was calculated using the IRI-2016 model. VTEC at the location (denoted as ), which serves as the weight for polynomial fitting, and is the weight coefficient corresponding to the i-th IPP. The calculation is as follows: , VTEC at time t for the k-th IPP calculated for the IRI-2016 model; n is the number of GNSS stations.

[0043] in The following parameters are obtained from the IRI-2016 model input: Solar index: F10.7 daily value, 81-day average, 12-month average, and 12-month average sunspot number; Ionospheric Index: The ionospheric altimeter is based on the 12-month average of the IG index; Geomagnetic index: 3-hour AP index, daily AP index.

[0044] With NormD i VTEC is the independent variable. i Let (t) be the dependent variable. The optimal formula for constructing an m-th order polynomial (m is determined by cross-validation) is as follows: , in IPP for model fitting i VTEC at (t), Let be the polynomial coefficients. The weighted least squares method is used to solve for the coefficients, and the objective function is to minimize the weighted sum of squared residuals: , Solving the coefficient vector using matrix operations The formula is as follows: , in: To design a matrix with dimensions of The i-th line ; This is the weight matrix, which is an n-order diagonal matrix with diagonal elements of 1. ; Let be the observation vector, with dimension . , element is .

[0045] Furthermore, cross-validation is used to determine the optimal polynomial order. The details are as follows: Remove one IPP at a time (e.g.) ), use the remaining One IPP Build according to the above steps Polynomial model of order; Predict using the constructed model place Calculate the predicted value and the actual observed value. The residual; Iterate through all IPPs and calculate different orders. ( The root mean square of the residuals (RMSE) under the given conditions; The order with the smallest RMSE is selected as the polynomial order of the final model.

[0046] Preferably, after completing the construction of the linear ionospheric model, the method further includes: Step 4, interpolation application of the linear ionospheric model. That is, using the established linear ionospheric model, the VTEC value of any point in the region is interpolated, and then a virtual reference station is constructed to generate its pseudorange and phase observation values.

[0047] Step 4.1, interpolate to obtain the target point VTEC. Let the target point be... , Here, longitude and latitude represent the target point, respectively, and its VTEC value can be obtained by interpolation using a pre-constructed linear ionospheric model: First, calculate the normalized distance of the target point along the linear direction to determine the target point. Projection points in the linear direction ;calculate Arc length distance with reference IPP ; Calculate the normalized distance: , Next, VTEC is calculated using the ionospheric model: , in These are the coefficients of the fitted polynomial.

[0048] Step 4.2: Construct virtual base station observations.

[0049] Set the virtual base station coordinates based on the user's location or the center of the service area. , These represent the longitude, latitude, and altitude of the virtual reference station, respectively; typically... The ground elevation can be obtained from DEM data or average elevation.

[0050] Calculate the VTEC of the virtual reference station for each satellite. For each visible satellite... Calculate its IPP position relative to VRS; then interpolate to obtain .

[0051] Step 4.3: Invert the pseudorange and phase observations of the virtual reference station.

[0052] First, calculate STEC: , in For VRS to satellite The IPP zenith angle.

[0053] This step allows the ionospheric delay obtained from modeling linear variation characteristics to be applied to the calculation of virtual observations.

[0054] The observations from the virtual reference station can be represented as: Pseudorange observations (taking L1 frequency as an example): , in: Represents geometric distance; Indicates the clock difference between the receiver and the satellite; Indicates ionospheric delay; Indicates tropospheric delay; This represents pseudorange noise.

[0055] Phase observations: , in: Indicates integer ambiguity; Indicates the wavelength of frequency L1; This represents phase noise.

[0056] Step 4.4: Generate the virtual observation file. Based on the inverted observations, generate a RINEX format observation file containing pseudorange and phase observations for all visible satellites. Optionally, headers such as virtual station coordinates, observation time, and satellite information can be added.

[0057] Step 4.5: Apply virtual observations in the network RTK.

[0058] First, the user receives virtual observation data. The user receives the VRS virtual observation file or RTCM data stream over the network; Next, differential positioning is performed. The user performs double-difference processing using their own observations and VRS virtual observations to eliminate common errors; and uses carrier phase to fix ambiguity, achieving high-precision positioning.

[0059] The method described in this invention first selects multiple GNSS stations distributed linearly, preprocesses the observation data, and calculates the ionospheric oblique total electron content (STEC). Then, by improving the single-layer model, the STEC is projected into the vertical total electron content (VTEC). Next, a VTEC dataset along the target direction at the same time is constructed. The distance of the ionospheric puncture point (IPP) is normalized, and the VTEC reference value calculated by the international reference ionospheric model is used as the fitting weight. A dynamic order determination strategy is adopted to complete the polynomial fitting using the weighted least squares method to obtain the regional ionospheric model. At the same time, the VTEC corresponding to the virtual reference station can be obtained by interpolation to obtain the ionospheric delay, which is further used in the calculation of virtual observation values ​​to achieve high-precision network RTK calculation in linear regions. This invention fully utilizes the physical characteristic of the ionosphere having a regular variation in the longitude / latitude direction, which can significantly improve the accuracy of the regional ionospheric model while relaxing the requirements for station spacing, and further improve the observation accuracy of linear regional network RTK.

[0060] The implementation of the various embodiments of the present invention is based on programmed processing through a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a CORS ionosphere modeling device based on linear variation characteristics. This device is used to execute a CORS ionosphere modeling method based on linear variation characteristics from the above method embodiments.

[0061] The device includes: a first main module, which is used to calculate the oblique total electron content of the ionosphere based on the observation data of multiple GNSS stations linearly distributed in the target area at the same time on satellites at the same elevation angle, and then project the oblique total electron content into the vertical total electron content through a single-layer model;

[0062] The second main module is used to calculate the ionospheric puncture point of each station when observing the satellite based on a single-layer model, associate the puncture point with the corresponding vertical total electron content, and construct a time-series modeling dataset.

[0063] The third main module is used to call the international reference ionosphere model to calculate the vertical total electron content at the puncture point as the fitting weight. With the modeling dataset as input, a dynamic order determination strategy is adopted to perform polynomial fitting through weighted least squares to obtain the linear region ionosphere model.

[0064] This invention provides a CORS ionospheric modeling device based on linear variation characteristics. Addressing the problem that existing ionospheric modeling methods fail to fully utilize the physical characteristics of the ionospheric variation patterns in linear regions, leading to stringent requirements on station spacing and low and unstable regional modeling accuracy, this invention employs several modules to accurately estimate high-order gradients through dynamic fixed-order polynomial fitting. This captures detailed changes in the ionospheric region, avoiding the accuracy loss caused by traditional low-order or fixed-order fitting, optimizing the model's ability to characterize TEC distribution, and significantly reducing dependence on station density.

[0065] It should be noted that the device embodiments provided by the present invention, in addition to implementing the methods in the above method embodiments, are also used to implement the methods in other method embodiments provided by the present invention. The difference lies only in setting corresponding functional modules, and their principles are basically the same as those of the above device embodiments provided by the present invention. As long as those skilled in the art, based on the above device embodiments and referring to the specific technical solutions in other method embodiments, obtain corresponding technical means and technical solutions constituted by these technical means by combining technical features, and improve the device in the above device embodiments while ensuring the practicality of the technical solutions, they can obtain corresponding device-type embodiments for implementing the methods in other method-type embodiments. For example:

[0066] Based on the above-described device embodiments, as a preferred embodiment, the CORS ionosphere modeling device based on linear variation characteristics provided in this invention further includes:

[0067] The fourth main module is used to interpolate the vertical total electron content at any point in the obtained linear ionospheric model; set the coordinates of the virtual reference station, calculate the vertical total electron content of each satellite relative to the virtual reference station, and construct the virtual reference station observation values; based on the virtual reference station observation values, invert the pseudorange and phase observation values ​​of the virtual reference station to form a virtual observation file.

[0068] Furthermore, after obtaining the virtual observation file, differential positioning is performed based on the virtual observation file, and ambiguity is fixed using carrier phase to realize RTK calculation for linear area networks.

[0069] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a CORS ionosphere modeling device based on linear variation characteristics, including a memory and a processor. The memory stores program instructions that are executed by the processor, and the processor calls the program instructions to execute the CORS ionosphere modeling method based on linear variation characteristics.

[0070] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the CORS ionosphere modeling method based on linear variation characteristics as follows:

[0071] Based on the observation data of multiple GNSS stations linearly distributed in the target area at the same time on satellites at the same elevation angle, the oblique total electron content of the ionosphere is calculated, and then the oblique total electron content is projected into the vertical total electron content through a single-layer model;

[0072] Based on a single-layer model, the ionospheric puncture point of each station when observing the satellite is calculated, and the puncture point is associated with the corresponding vertical total electron content to construct a time-series modeling dataset.

[0073] The total vertical electron content at the puncture point was calculated using the international reference ionospheric model and used as the fitting weight. The modeling dataset was used as input, and a dynamic order determination strategy was adopted to perform polynomial fitting using the weighted least squares method to obtain the linear ionospheric model.

[0074] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0075] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0076] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0077] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0078] In summary, this invention aims to address the problem that existing ionospheric modeling methods fail to fully utilize the physical characteristics of the linear variation of the ionosphere, leading to stringent requirements on station spacing and low and unstable regional modeling accuracy. The invention selects linearly distributed GNSS stations in the target area and collects observation data from all stations at the same time for the same high-elevation angle (>15°) GPS satellite. Based on an improved single-layer model, the ionospheric penetration point (IPP) for each station observing the satellite is calculated, and the IPP is associated with the corresponding VTEC to construct a time-series modeling dataset. The distance of the IPP along the station distribution direction is normalized, and the VTEC at the IPP calculated by the international reference ionospheric model is used as the weight. A polynomial fitting model is constructed using the weighted least squares method. Cross-validation is employed to determine the optimal polynomial order, ensuring that the model accurately captures the linear variation of the regional ionosphere, ultimately forming a high-precision regional ionospheric model. While relaxing the station spacing requirements, this invention significantly improves the accuracy of ionospheric modeling, further enhances the accuracy of virtual reference station observations, and improves the observation accuracy of network RTK.

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for ionospheric modeling based on linear variation characteristics of CORS, characterized in that, The method comprises the following steps: Based on the observation data of the same elevation angle satellite at the same time by the multiple GNSS stations in the target area, the slant total electron content of the ionosphere is calculated, and the slant total electron content is projected into the vertical total electron content by the single layer model; Based on the single layer model, the ionospheric piercing point of each station observing the satellite is calculated, the piercing point is associated with the corresponding vertical total electron content, and a time-series modeling data set is constructed; The vertical total electron content at the piercing point is calculated by calling the international reference ionospheric model as the fitting weight, the modeling data set is input, the dynamic order determination strategy is adopted, the weighted least squares method is used for polynomial fitting, and a linear regional ionospheric model is obtained. 2.The method of claim 1, wherein, The method further comprises the following steps: Based on the obtained linear regional ionospheric model, the vertical total electron content of any point in the region is obtained by interpolation; A virtual reference station coordinate is set, the vertical total electron content of each satellite is calculated, and a virtual reference station observation value is constructed; Based on the virtual reference station observation value, the pseudo-range and phase observation value of the virtual reference station are obtained by inversion, and a virtual observation file is formed. 3.The method of claim 2, wherein, After obtaining the virtual observation file, the method further comprises the following steps: Based on the virtual observation file, differential positioning solution is carried out, carrier phase ambiguity is fixed, and linear regional network RTK calculation is realized. 4.The method of claim 1, wherein, Before polynomial fitting, the following steps are further included: The relative distance of each piercing point along the station distribution direction is calculated, and normalization processing is performed.

5. The method of claim 4, wherein the method further comprises: The method further comprises the following steps: An m-order polynomial is constructed with the normalized relative distance as the independent variable and the vertical total electron content at the piercing point as the dependent variable; The weighted least squares method is used to solve the polynomial coefficients, and the objective function is to minimize the weighted residual sum of squares; The optimal polynomial order is determined by dynamic cross-validation.

6. The method of claim 5, wherein the method further comprises: The optimal polynomial order is determined by dynamic cross-validation, which comprises the following steps: One piercing point is removed from the n piercing points each time, and an m-order polynomial is reconstructed with the modeling data set of the remaining n-1 piercing points; The vertical total electron content at the removed piercing point is predicted by using the constructed m-order polynomial, and the residual between the predicted value and the actual observation value is calculated; The root mean square of the residual under different orders is calculated by traversing all the piercing points, and the order with the minimum root mean square of the residual is taken as the optimal polynomial order.

7. The method of claim 1, wherein the method further comprises: The multiple GNSS stations in the target area are selected according to the following principles: The distance between each station is within 100±10 km, and the number is not less than 9.

8. A device for ionospheric modeling based on linear variation features of CORS, characterized in that, The method comprises the following steps: A first main module is used to calculate the slant total electron content of the ionosphere based on the observation data of the same elevation angle satellite at the same time by the multiple GNSS stations in the target area, and the slant total electron content is projected into the vertical total electron content by the single layer model; A second main module is used to calculate the ionospheric piercing point of each station observing the satellite based on the single layer model, associate the piercing point with the corresponding vertical total electron content, and construct a time-series modeling data set; A third main module is used to calculate the vertical total electron content at the piercing point by calling the international reference ionospheric model as the fitting weight, input the modeling data set, adopt the dynamic order determination strategy, perform polynomial fitting by the weighted least squares method, and obtain a linear regional ionospheric model.

9. A device for ionospheric modeling based on linear variation features of CORS, characterized in that, The application relates to a computer readable storage medium, comprising a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor invokes the program instructions to execute the method for modeling the ionosphere of CORS based on linear variation characteristics according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method for modeling the ionosphere of CORS based on linear variation characteristics according to any one of claims 1 to 7.

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