Improved fkp network rtk regional ionospheric error compensation method and system

Abstract

The application discloses an improved FKP network RTK regional ionospheric error compensation method and system, comprising a data acquisition and preprocessing step, which is used for acquiring global navigation satellite system observation data and ionospheric related parameters from a reference station network; a nonlinear error modeling step, which introduces a nonlinear term in the ionospheric error model to enhance the spatial curvature representation capability; a dynamic elevation angle correction step, which adopts a segmented correction function and dynamically adjusts the correction weight according to the geomagnetic activity index; a kernel function feature extraction step, which uses a kernel function for local weighted regression to improve the local fitting capability; and a weight coefficient calculation step, which optimizes and solves the weight coefficient based on the reference station observation data, outputs an ionospheric error correction model, and realizes ionospheric error compensation. The application solves the problem of the traditional FKP method and is suitable for the field of high-precision GNSS services.

Description

Technical Field

[0001] This invention belongs to the field of high-precision global navigation satellite system (GNSS) real-time dynamic positioning (RTK) technology, specifically involving an improved FKP (Flächenkorrekturparameter, regional correction parameter) network RTK regional ionospheric error compensation technology based on nonlinear modeling, dynamic elevation angle correction and kernel function enhancement. Background Technology

[0002] Traditional FKP methods are based on linear polynomial plane models and assume that regional ionospheric delay error varies linearly with geographic coordinates. They suffer from significant technical limitations in the following scenarios:

[0003] 1) Failure of nonlinear error characterization: In small areas with a sharp gradient in total ionospheric electron content (TEC) (such as the equatorial anomaly zone and urban canyons), the error distribution exhibits significant spatial curvature characteristics. However, traditional linear models can only describe first-order spatial changes, resulting in a quadratic increase in compensation residuals with distance, which severely degrades positioning accuracy.

[0004] 2) Insufficient low elevation angle correction mechanism: When the satellite elevation angle is below 30°, the signal propagation path is significantly extended, and the ionospheric delay can be more than 3 times that in the zenith direction. However, the traditional elevation angle correction factor (HH) adopts a single function form and does not design a segmented optimization strategy for the difference in low elevation angle signal path, resulting in insufficient error suppression effect.

[0005] 3) Poor real-time parameter update: Relying on static models and low-frequency parameter updates, it is difficult to respond in a timely manner to short-term and violent fluctuations in ionospheric TEC (such as TEC sudden changes exceeding 50 TECU during geomagnetic storms), causing positioning drift and loss of lock in dynamic scenarios;

[0006] 4) Strong dependence on reference station density: A dense network of reference stations (spacing <50 km) is required to maintain accuracy. In sparse networks or edge areas, linear interpolation errors accumulate nonlinearly with distance, significantly increasing hardware deployment and maintenance costs.

[0007] 5) Weak anti-interference capability: It lacks a robust data quality control mechanism, and abnormal observations (such as pseudorange jumps caused by multipath effects) directly participate in the solution, resulting in parameter estimation bias.

[0008] Existing improvement schemes (such as patent CN112230261A) enhance accuracy by increasing reference station density or introducing additional observations (such as dual-frequency data), but these methods are costly in terms of hardware and difficult to adapt to dynamic ionospheric environments. Other methods (such as virtual reference station technology) expand coverage but do not address the core issues of nonlinear error and low elevation angle correction. Therefore, there is an urgent need to develop a high-precision, low-cost, and robust ionospheric error compensation method. Summary of the Invention

[0009] The traditional FKP method has significant technical limitations in application, specifically:

[0010] Linear model failure: Error models based on the linear polynomial plane assumption cannot effectively characterize the nonlinear spatial distribution characteristics of drastic fluctuations in the ionosphere in small areas (such as cities and equatorial regions), resulting in a significant decrease in error compensation accuracy in complex terrain or ionospheric disturbance scenarios.

[0011] Low elevation angle correction defects: When the satellite elevation angle is below 30°, the signal path lengthening leads to a doubling of ionospheric delay. However, the traditional elevation angle correction factor (HH) adopts a single function form and does not design a segmented optimization strategy for the differences in low elevation angle signal paths, resulting in insufficient error suppression effect.

[0012] Parameter update lag: Relying on static models and low-frequency parameter updates (usually >10 minutes), it is difficult to respond in a timely manner to short-term and violent fluctuations in ionospheric TEC (such as TEC sudden changes exceeding 50 TECU during geomagnetic storms), resulting in drift of positioning results in dynamic environments;

[0013] Limited spatial resolution: It relies on a high-density reference station network (usually with a spacing of <50 km) to maintain accuracy. In sparse station networks or edge areas, the linear interpolation error increases quadratically with distance, significantly increasing hardware deployment costs.

[0014] Weak anti-interference capability: Lacking a robust data quality control mechanism, abnormal observations (such as pseudorange jumps caused by multipath effects) directly participate in the solution, causing parameter estimation bias.

[0015] These issues collectively lead to traditional methods failing to meet the stringent requirements of high-precision navigation (such as autonomous driving and UAV aerial surveying) in complex ionospheric environments in terms of positioning accuracy, real-time performance, and stability. A breakthrough through multi-dimensional optimization is urgently needed. To improve the accuracy of high-precision error compensation in scenarios with drastic changes in the ionosphere within a small area, this invention systematically solves the aforementioned technical bottlenecks through nonlinear modeling, dynamic correction, and kernel function enhancement, filling the application gap of traditional methods in complex scenarios.

[0016] This invention addresses the aforementioned technical problems by providing an improved ionospheric error compensation method for the RTK region of an FKP network, comprising:

[0017] The data acquisition and preprocessing steps are used to obtain global navigation satellite system observation data and ionospheric parameters from the reference station network;

[0018] The nonlinear error modeling steps introduce nonlinear terms into the ionospheric error model to enhance the ability to represent spatial curvature.

[0019] The dynamic elevation angle correction step employs a piecewise correction function and dynamically adjusts the correction weights based on the geomagnetic activity index.

[0020] The kernel function feature extraction step uses the kernel function to perform locally weighted regression to improve local fitting ability;

[0021] The weighting coefficient calculation steps involve optimizing the solution of the weighting coefficients based on the observation data of the reference station, outputting the ionospheric error correction model, and realizing ionospheric error compensation.

[0022] Furthermore, the data acquisition and preprocessing steps include cycle slip detection and repair of carrier phase observations, fixation of double-difference ambiguity, and weight reduction processing of abnormal observations.

[0023] Furthermore, the nonlinear error modeling step adds north-south and east-west nonlinear correction parameters to the ionospheric error model.

[0024] Furthermore, the piecewise correction function in the dynamic elevation angle correction step is designed with different correction coefficients for cases where the satellite elevation angle is lower than the preset elevation angle, in order to compensate for the ionospheric delay caused by the extended signal path at low elevation angles.

[0025] Furthermore, the kernel function feature extraction step uses a Gaussian kernel or a polynomial kernel to replace the global polynomial, and selects the center point grid of the kernel function through a clustering method.

[0026] Moreover, the weight coefficient calculation step uses the least squares method to solve for the weight vector.

[0027] Furthermore, in the dynamic elevation angle correction step, the operation of dynamically adjusting the correction weight according to the geomagnetic activity index is triggered when the geomagnetic activity index is greater than or equal to the corresponding preset index threshold.

[0028] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the improved FKP network RTK region ionospheric error compensation method as described above.

[0029] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the improved FKP network RTK region ionospheric error compensation method as described above.

[0030] On the other hand, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the improved FKP network RTK region ionospheric error compensation method as described above.

[0031] Based on the above technical solutions, this invention significantly improves the performance of high-precision positioning systems in complex ionospheric environments through multi-dimensional technical optimization. First, by introducing a nonlinear error model, the system can accurately capture the complex spatial variation characteristics of ionospheric delay within a small area, overcoming the failure problem of traditional linear models in regions with drastic curvature changes and greatly improving the precision of error correction. Addressing the challenge of low-elevation satellite signals being susceptible to ionospheric interference, the dynamic segmented elevation angle correction mechanism effectively suppresses signal distortion when the elevation angle is below 30 degrees through differentiated weight adjustment, significantly enhancing the reliability of low-altitude observation data. The introduction of kernel function technology further optimizes local feature extraction capabilities. Through adaptive spatial weight allocation, it avoids the overfitting risk of global multinomial models in complex terrain, enabling the system to flexibly adapt to diverse geographical environments. The real-time parameter update strategy, combined with multi-source data fusion, ensures that the corrected parameters can quickly respond to instantaneous fluctuations in ionospheric activity, maintaining stable centimeter-level positioning accuracy even under extreme space weather events such as geomagnetic storms. In addition, the improved solution reduces the reliance on reference station density, reducing hardware deployment costs while ensuring coverage of areas up to 100 kilometers away, providing a more economical and scalable solution for large-scale high-precision positioning applications such as autonomous driving and precision agriculture.

[0032] Compared with existing technologies, this invention achieves high-precision error compensation through the following core innovations:

[0033] 1) Nonlinear error modeling: A second-order polynomial term is introduced into the ionospheric correlation error model to enhance the ability to represent spatial curvature;

[0034] 2) Dynamic elevation angle correction: Design a piecewise correction function and dynamically adjust the correction weight of low elevation angle satellites in combination with the Kp exponent;

[0035] 3) Kernel function feature extraction: A Gaussian kernel function is used to replace the global polynomial to improve local fitting ability;

[0036] 4) Real-time parameter calculation: For example, based on the sliding window weighted least squares method, the parameters are updated every 5 seconds. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the process of an embodiment of the present invention.

[0038] Figure 2 This is a piecewise function diagram for dynamic elevation angle correction in an embodiment of the present invention. Detailed Implementation

[0039] The following will further explain the concept, specific structure and technical effects of the present invention in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, features and effects of the present invention.

[0040] Example 1

[0041] See Figure 1 This embodiment provides an improved ionospheric error compensation method for RTK regions of FKP networks, comprising the following steps:

[0042] Step 1. Data Acquisition and Preprocessing

[0043] This step acquires global navigation satellite system observation data from the reference station network, including pseudorange measurements, carrier phase observations, and satellite elevation angles, and obtains the total electron content of the ionosphere and the geomagnetic activity index; performs quality control on the observation data, including cycle slip detection and repair, ambiguity fixation, and downweighting of abnormal observations; and obtains relative ionospheric error information between reference stations.

[0044] The preferred implementation method is the following sub-steps:

[0045] Step 1.1 Obtain input data

[0046] In practice, the data processing system can collect GNSS observation data in real time from a network of reference stations within the distribution area. This includes pseudorange measurements, carrier phase observations, and satellite elevation angles (EE) from each reference station. Simultaneously, it obtains the total electron content (TEC) and geomagnetic activity index (Kp) of the ionosphere through ionospheric monitoring stations or space weather data interfaces. The pseudorange and carrier phase data are used to calculate the initial positioning error, the satellite elevation angle (EE) is used for subsequent dynamic correction factor calculations, and the TEC and Kp index serve as key input parameters for ionospheric delay correction, used to adjust the weights of ionospheric-related terms in the error model in real time. All data is transmitted to the central processing server via an encrypted link to ensure data integrity and timeliness.

[0047] Step 1.2 Preprocessing

[0048] Data quality control was performed on the raw GNSS observation data collected from the reference stations. First, a carrier phase cycle slip detection algorithm (such as TurboEdit or the MW combination method) was used to identify and correct cycle slip phenomena in the carrier phase observations to ensure phase continuity. Then, the LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method was used to fix the double-difference ambiguity to integer values, improving the accuracy of the observation model. For the residual analysis results, reference stations with observation residuals exceeding three times the standard deviation were downweighted, with their weight coefficients adjusted to 1 / 10 of their original values ​​to suppress the interference of abnormal observations on parameter calculation. The preprocessed effective data will be used for subsequent nonlinear modeling and parameter calculation to ensure the robustness and reliability of the error correction model.

[0049] Step 1.3 Obtaining the relative ionospheric error between reference stations

[0050] Based on the fixed ambiguities and reference station coordinates, baseline ionospheric error information is extracted. The central station of all reference stations is selected as the primary reference station, and the relative error information of all auxiliary stations is obtained through the overall adjustment algorithm of baseline error corrections.

[0051] The preferred implementation method is divided into four steps: 1) Use the triangular network closure error test to determine whether there are gross errors; 2) Select the central station of all reference stations as the main reference station, and other reference stations as auxiliary stations; 3) Use the error correction of each baseline to perform overall adjustment of the relative error correction; 4) Based on the adjustment results, locate and repair the gross errors and adjust again.

[0052] Step 2. Nonlinear error modeling

[0053] This invention sets up a method by introducing a second-order polynomial term ( , It is used to capture the spatial curvature changes of ionospheric errors and enhance the ability to characterize small-scale ionospheric nonlinear errors.

[0054] The preferred implementation method is the following sub-steps:

[0055] Step 2.1 Error Modeling

[0056] The non-ionospheric error effect is modeled linearly using the original FKP method:

[0057]

[0058] in, It is the correction value for the non-ionospheric error-affected part.

[0059] : Simplified value of the Earth's average radius (6370 km / 1000).

[0060] Ionospheric irrelevant corrections in the north-south and east-west directions (unit: ppm).

[0061] Latitude difference (radians).

[0062] Longitude difference (radians).

[0063] : Latitude of the main reference station.

[0064] Based on the original linear FKP method, this invention proposes to add a nonlinear correction parameter to establish a new ionospheric error (diffuse error) model:

[0065]

[0066] in, Ionospheric irrelevant corrections in the north-south and east-west directions (unit: ppm).

[0067] Ionospheric related error (unit: meters).

[0068] : Simplified value of the Earth's average radius (6370 km / 1000).

[0069] : Dynamic elevation angle correction factor.

[0070] Linear correction parameters for north-south and east-west directions (unit: ppm).

[0071] Nonlinear correction parameters for north-south and east-west directions (unit: ppm / rad²).

[0072] Latitude difference (radians).

[0073] Longitude difference (radians).

[0074] : Latitude of the main reference station.

[0075] Step 2.2 Design matrix extension

[0076] By adding a column of quadratic terms to the original linear terms, a nonlinear design matrix is ​​obtained.

[0077]

[0078] in, Represents the nonlinear design matrix. and The subscripts 1…n are used to represent the corresponding reference station numbers.

[0079] Step 3: Dynamic Elevation Angle Correction

[0080] This invention proposes a piecewise function design for dynamic elevation angle correction, which designs different correction coefficients for cases where the satellite elevation angle is lower than a preset elevation angle threshold, in order to compensate for the ionospheric delay caused by the extended signal path at low elevation angles; and dynamically adjusts the correction coefficients in conjunction with the ionospheric activity index (Kp).

[0081] The preferred implementation method is the following sub-steps:

[0082] Step 3.1 Piecewise Correction Function

[0083] The piecewise correction function preferably uses a first coefficient when the satellite elevation angle is below 30 degrees and a second coefficient when the satellite elevation angle is above or equal to 30 degrees, and the first coefficient is greater than the second coefficient.

[0084] See Figure 2 The preferred piecewise function established in this embodiment of the invention is as follows:

[0085]

[0086] in, It is the satellite's elevation angle, measured in degrees. When the satellite's elevation angle is below 30°, the signal propagation path is significantly prolonged, and the ionospheric delay can be more than three times that at the zenith.

[0087] In the original FKP method, the elevation angle correction function is:

[0088]

[0089] This function clearly does not account for the abrupt change in ionospheric delay content below 30°. Therefore, to differentiate this, in this embodiment of the invention, the coefficient 16 is preferably changed to 10 and 20, respectively. Simultaneously, this piecewise correction function setting ensures that the ionospheric delay correction function value maintains a smooth transition at the high / low elevation angle boundary (30°), and more accurately reflects the significant increase in ionospheric delay under low elevation angle conditions.

[0090] Step 3.2 Ionospheric Activity Index Fusion

[0091] Dynamic adjustment strategy: Obtain the Kp index in real time (via space weather data interface); adjust the coefficient of H according to the range of the Kp index.

[0092]

[0093] in, Adjusting the range of the Kp index When the coefficient Kp is greater than or equal to a preset exponential threshold (preferably set to 3 in this embodiment), the ionosphere is in a more active state. This invention further enhances the elevation angle correction function by increasing the Kp parameter, effectively suppressing the influence of ionospheric irregularities. For example, when Kp=5, the weight of low elevation angle (E=20°) satellites is increased by about 70%, effectively suppressing ionospheric distortion.

[0094] Step 4: Kernel Function Feature Extraction

[0095] This invention proposes that the kernel function feature extraction uses a Gaussian kernel or a polynomial kernel function instead of a fixed polynomial, and the center points are generated through K-means clustering.

[0096] The preferred implementation method is the following sub-steps:

[0097] Step 4.1 Radial Basis Functions (RBF)

[0098] By replacing the fixed polynomial with a Gaussian kernel or a polynomial kernel function, the local fitting ability is enhanced, complex spatial changes are captured flexibly, and global polynomial overfitting is avoided.

[0099]

[0100] In the above formula, The index of the center point For the first The weight coefficients corresponding to each center point This represents the current location (latitude or longitude coordinates). For the first The location of the center point The bandwidth parameter of the Gaussian kernel controls the local influence range of the function.

[0101] In the FKP method of the aforementioned network RTK, a low-order global polynomial model (e.g., a first- or second-order surface) is typically used to fit and interpolate the ionospheric delay error across the entire region. However, when the region is large or ionospheric activity is intense, the spatiotemporal variations of the error are very complex. The global polynomial model, due to its limited degrees of freedom, struggles to accurately fit these variations, easily leading to underfitting (failure to capture detailed changes) or overfitting (excessive sensitivity to noise). The purpose of this invention is to replace the global polynomial calculation in FKP with a locally weighted regression based on a Gaussian kernel function, thereby enhancing the ability to locally fit complex spatial error fields and providing more accurate and robust regional error correction information.

[0102] To further refine the spatial modeling, this invention proposes defining Gaussian kernel functions in both the latitude and longitude directions:

[0103]

[0104]

[0105] In the above formula, The index of the center point in the latitudinal direction. The center point number in the longitude direction. The latitude (in radians) of the reference station.

[0106] and : These represent the RBF kernel values ​​in the latitude and longitude directions, respectively.

[0107] and The difference in latitude and longitude between the reference station and the main reference station.

[0108] and : Latitude and longitude coordinates of the center point of RBF.

[0109] : The bandwidth parameter of the Gaussian kernel.

[0110] and The number of center points in the latitude and longitude directions.

[0111] Step 4.2 Center point selection

[0112] Based on the relative coordinates of the reference station A grid of centroids is generated using K-means clustering.

[0113] Step 5: Calculate the weighting coefficients and output the ionospheric error correction model to achieve ionospheric error compensation.

[0114] The determination of the weight coefficients corresponding to the center point is the core of the entire model, as it determines the shape of the final interpolation surface. This solution process is completed on the server side, and its essence is to determine a set of optimal weights by solving a system of linear equations or an optimization problem based on the known observation data of the reference station network.

[0115] In this invention, the least squares method is preferably used to extract the optimal weight coefficients. The specific steps of the implementation in the embodiment include:

[0116] Step 5.1 Construct the observation equations (linear system)

[0117] In this step, we assume that the reference station network has There are 1 reference station, and the location of each reference station is... The observed ionospheric delay is ;choose The center points of the Gaussian kernel function, each center point The position is For each reference station It can be calculated to all center points based on its location. The Gaussian kernel function values ​​are used to form a design matrix.

[0118]

[0119] Each element in the matrix Indicates the first The first reference station and the first Correlation between the centroids:

[0120]

[0121] Step 5.2 Establish the equation

[0122] Model at reference station The predicted value at this location is:

[0123] The equations from the reference stations are combined to obtain a linear system:

[0124]

[0125] in:

[0126] It is the weight vector to be determined.

[0127] The observation vector of the reference station.

[0128] Step 5.3 Solve for the weight values

[0129] The objective of the least squares solution is to minimize the residual L2 norm. The solution to its normal equation is:

[0130]

[0131] By solving this equation, a set of weights w that minimizes the overall fitting error of the model across all reference stations can be obtained. Then, the ionospheric error correction model can be output to achieve ionospheric error compensation.

[0132] Preferably, error correction parameters are updated periodically to respond to ionospheric changes. For example, based on the sliding window weighted least squares method, the parameters are updated every 5 seconds to achieve real-time parameter calculation and broadcasting. The sliding window weighted least squares method is a technique for point-by-point local polynomial fitting. A fixed-length window slides across the data sequence, and at each position, based on the data points within the window and assigning them different weights, a local polynomial model is fitted. This method effectively adapts to the non-stationary characteristics of the data, maintaining smoothness while better capturing the local trends and fluctuations of the sequence. The optimal weight coefficients obtained through the above steps can significantly improve the performance of the high-precision positioning system in complex ionospheric environments.

[0133] To understand the technical effects of this invention, and addressing the core problems of traditional FKP methods such as linear model failure in scenarios with drastic ionospheric changes in a small area, insufficient error correction for low-elevation satellites, and lagging parameter updates, the following process was implemented to achieve nonlinear error modeling: A second-order polynomial term was introduced to expand the ionospheric error model, accurately representing local nonlinear spatial changes and solving the error compensation failure problem of traditional linear models in complex terrain or ionospheric disturbance areas; Dynamic elevation angle correction: A piecewise correction function was designed, and the correction weights for low-elevation satellites were dynamically adjusted in conjunction with the ionospheric activity index, significantly suppressing low-elevation signal path distortion; Kernel function enhancement: A Gaussian kernel function was used to replace the global polynomial, improving local fitting ability through adaptive spatial weight allocation, avoiding overfitting and reducing the reference station density requirement; Real-time parameter updates: Based on the sliding window weighted least squares method, parameters were updated every 5 seconds to achieve high-frequency dynamic response to short-term ionospheric fluctuations (such as geomagnetic storm events). Experimental results demonstrate that this invention can improve horizontal positioning accuracy to 2-5 cm (RMS) in scenarios with severe ionospheric fluctuations, enhance low-elevation satellite error suppression by over 40%, support coverage at the 100-kilometer level, reduce reference station density by 20%, and significantly optimize hardware costs. It supports high-precision GNSS services in fields with stringent requirements for real-time performance, accuracy, and reliability, such as autonomous driving, precision agriculture, and UAV aerial surveying.

[0134] Example 2

[0135] The present invention also provides a system for implementing the method described in Embodiment 1, comprising a reference station network, a central processing server, and user terminals. The reference station network provides observational data for data processing; the central processing server is responsible for receiving data, completing steps 1-5 of the data processing to obtain and publish regional ionospheric corrections; and the user terminals obtain the regional ionospheric corrections to provide positioning accuracy.

[0136] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0137] The improved FKP network RTK region ionospheric error compensation electronic device provided by the present invention will be described below. The improved FKP network RTK region ionospheric error compensation electronic device described below can be referred to in correspondence with the improved FKP network RTK region ionospheric error compensation method described above.

[0138] The electronic device may include a processor, a communications interface, memory, and a communication bus. The processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute the improved FKP network RTK region ionospheric error compensation method, which mainly includes the software processing part described above.

[0139] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0140] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the software processing part of the improved FKP network RTK region ionospheric error compensation method provided by the above methods.

[0141] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the software processing portion of the improved FKP network RTK region ionospheric error compensation method provided by the above methods.

[0142] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0143] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, 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 can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0144] 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 of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An improved FKP network RTK regional ionospheric error compensation method, characterized in that, Comprise: a data acquisition and preprocessing step for obtaining global navigation satellite system observation data and ionospheric related parameters from a reference station network; a nonlinear error modeling step for introducing nonlinear terms in the ionospheric error model to enhance the spatial curvature representation capability, such as the following formula, wherein, Ionosphere-independent correction in north-south and east-west directions; is the ionospheric related error; R is a simplified value for the mean radius of the earth; where: h = dynamic height angle correction factor; linear correction parameters for north-south and east-west directions; are the nonlinear correction parameters for the north and east directions, respectively; is the difference in latitude; is the difference in longitude; Latitude for primary reference station; a dynamic elevation angle correction step for using a piecewise correction function and dynamically adjusting the correction weight according to the geomagnetic activity index, the piecewise correction function is as follows: wherein is the elevation angle of the satellite; The dynamic adjustment is realized by obtaining the Kp index in real time, and adjusting the coefficient of H according to the Kp index range, wherein, Kp index range adjustment coefficient, when the Kp value is greater than or equal to the preset index threshold, the ionosphere is in an active state, and by increasing the Kp parameter, the elevation angle correction function is further suppressed to suppress the influence of ionosphere irregularities. a kernel function feature extraction step for using a kernel function for local weighted regression to improve local fitting capability; a weight coefficient calculation step for optimizing and solving the weight coefficient based on the reference station observation data, outputting an ionospheric error correction model, and realizing ionospheric error compensation.

2. The improved FKP network RTK regional ionospheric error compensation method according to claim 1, characterized in that: The data acquisition and preprocessing step includes cycle slip detection and repair for carrier phase observation values, double difference ambiguity fixing, and abnormal observation weight reduction processing.

3. The improved FKP network RTK regional ionospheric error compensation method according to claim 1, characterized in that: The nonlinear error modeling step adds nonlinear correction parameters in the north-south direction and the east-west direction in the ionospheric error model.

4. The improved FKP network RTK regional ionospheric error compensation method according to claim 1, characterized in that: The piecewise correction function in the dynamic elevation angle correction step designs different correction coefficients for the case where the satellite elevation angle is lower than the preset elevation angle threshold, to compensate for the ionospheric delay of the signal path lengthening at low elevation angles.

5. The improved FKP network RTK regional ionospheric error compensation method according to claim 1, characterized in that: The kernel function feature extraction step uses Gaussian kernel or polynomial kernel instead of global polynomial, and selects the center point grid of the kernel function through clustering method.

6. The improved FKP network RTK regional ionospheric error compensation method according to claim 1, characterized in that: The weight coefficient calculation step uses least squares method to solve the weight vector.

7. The improved FKP network RTK regional ionospheric error compensation method according to claim 1, characterized in that: In the dynamic elevation angle correction step, the operation of dynamically adjusting the correction weight according to the geomagnetic activity index is triggered when the geomagnetic activity index is greater than or equal to the corresponding preset index threshold.

8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: The processor executes the program to realize the improved FKP network RTK regional ionospheric error compensation method of any one of claims 1 to 7. 9.A non-transitory computer-readable storage medium having stored thereon a computer program. The computer program is executed by the processor to realize the improved FKP network RTK regional ionospheric error compensation method of any one of claims 1 to 7.

10. A computer program product comprising a computer program, characterized in that: The computer program is executed by the processor to realize the improved FKP network RTK regional ionospheric error compensation method of any one of claims 1 to 7.

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