Method and system for analyzing ionospheric interpolation uncertainty of slant path

Abstract

The application provides a slant path ionosphere interpolation uncertainty analysis method and system, comprising: acquiring interpolation results corresponding to different interpolation methods in a selected area; analyzing and processing the interpolation method results respectively through time, distance and high angle relationship; establishing a corresponding mathematical function expression according to the analysis and processing results; obtaining more reasonable uncertainty parameters according to the data function expression at the user end as the variance of ionosphere correction number. The application analyzes the relationship between the slant path ionosphere interpolation results and the interpolation method, time, satellite elevation angle and station distance, and fits the corresponding mathematical function expression. Then the function expression is applied to the user end to obtain the uncertainty parameters of the ionosphere correction number information after interpolation. The application provides a train of thought for the difficulty of setting the ionosphere correction number uncertainty, thereby improving the robustness of the PPP-RTK positioning result.

Description

Technical Field

[0001] This invention relates to the field of satellite system technology, specifically to a method and system for analyzing slant path ionospheric interpolation uncertainty. More particularly, it relates to an slant path ionospheric interpolation uncertainty analysis and its application in PPP-RTK. Background Technology

[0002] The oblique path ionospheric delay model is a developing trend in the accurate correction of ionospheric delay in high-precision satellite positioning. Compared with the traditional vertical ionospheric model, the oblique path ionospheric model can effectively suppress projection errors and improve the accuracy of the corrected ionospheric delay error to the centimeter level.

[0003] However, the uncertainty of existing slant path models is difficult to describe accurately, which leads to problems such as the inability to fully utilize ionospheric information and convergence errors in the process of ionospherically enhanced user-end positioning.

[0004] For PPP-RTK technology, obtaining high-precision ionospheric corrections is crucial, and at the same time, it is equally important to reasonably evaluate the accuracy of ionospheric corrections. Setting the uncertainty too tightly (i.e., setting a very small uncertainty) will lead to positioning convergence errors; conversely, setting the uncertainty too conservatively (i.e., setting a very large uncertainty) will prevent the full utilization of external ionospheric correction information.

[0005] Therefore, in her paper "PPP-RTK considering the ionosphere uncertainty with cross-validation," Li Pan analyzed the uncertainty of the ionospheric correction obtained by inverse distance-weighted interpolation. The analysis showed a linear relationship between the uncertainty and the station distance, and this linear model was applied to PPP-RTK positioning. However, her analysis only focused on a single and common linear interpolation method, which has low accuracy, and did not further analyze and compare the uncertainty characteristics and differences of other advanced interpolation methods. Because different interpolation methods have different uncertainties, this method cannot be extended to other interpolation methods, potentially leading to slow convergence and convergence errors in user-end ionospheric augmentation positioning. Summary of the Invention

[0006] In view of the deficiencies in the prior art, the purpose of this invention is to provide a low-cost verification test method for cooling coatings.

[0007] A method for analyzing the uncertainty of oblique path ionospheric interpolation according to the present invention includes:

[0008] Step S1: Obtain the interpolation results corresponding to different interpolation methods in the selected area;

[0009] Step S2: Analyze and process the interpolation results using time, distance, and elevation angle relationships;

[0010] Step S3: Establish the corresponding mathematical function expression based on the results of the analysis and processing;

[0011] Step S4: Obtain a more reasonable uncertainty parameter on the user end based on the data function expression, which serves as the variance of the ionospheric correction.

[0012] Preferably, the interpolation method includes IDW, radial basis functions, and kriging.

[0013] Preferably, step S2 includes:

[0014] Step S2.1: Analyze the time series diagram of the interpolation results. Divide the interpolation results of IDW into two time periods: ionospheric active and quiescent, and analyze them separately. These are denoted as the first inverse distance weighted average and the second inverse distance weighted average, respectively.

[0015] Step S2.2: Analyze the relationship between the interpolation results and the elevation angle and distance for each time period;

[0016] Step S2.3: Combine the relationship variables of elevation angle and distance corresponding to all interpolation methods to obtain the corresponding combined variables.

[0017] Step S2.4: Analyze the relationship between the interpolation results and the combined variables.

[0018] Preferably, step S2.1 includes:

[0019] Step S2.2.1: Analyze the relationship between the interpolation results and the satellite elevation angle;

[0020] Step S2.2.2: Analyze the relationship between the interpolation results and the average distance between the user station and the reference station.

[0021] Preferably, for IDW, the functional relationship is as follows:

[0022] rms=β(d / sinel)+a0

[0023] For radial basis functions and Kriging, the functional relations are as follows:

[0024] rms=β*d*(π / 2-el)+a0

[0025] Where rms represents the root mean square value, β represents the slope of the line, d represents the average distance between the user station and the reference station, a0 represents the intercept, and el represents the satellite elevation angle.

[0026] A system for analyzing the uncertainty of slant path ionospheric interpolation according to the present invention includes:

[0027] Module M1: Obtains the interpolation results of different interpolation systems in the selected area;

[0028] Module M2: Analyzes and processes the interpolation system results using time, distance, and elevation angle relationships, respectively;

[0029] Module M3: Establishes the corresponding mathematical function expression based on the results of the analysis and processing;

[0030] Module M4: At the user end, a more reasonable uncertainty parameter is obtained based on the data function expression, which serves as the variance of the ionospheric correction.

[0031] Preferably, the interpolation system includes IDW, radial basis functions, and kriging.

[0032] Preferably, the module M2 includes:

[0033] Module M2.1: Analyze the time series diagram of the interpolation results, divide the IDW interpolation results into two time periods, one active and one quiescent, and analyze them separately, denoted as the first inverse distance weighted and the second inverse distance weighted, respectively;

[0034] Module M2.2: Analyzes the relationship between the interpolation results and elevation angle and distance for each time period;

[0035] Module M2.3: Combines the relationship variables of elevation angle and distance corresponding to all interpolation systems to obtain the corresponding combined variables.

[0036] Module M2.4: Analyze the relationship between interpolation results and combined variables.

[0037] Preferably, module M2.1 includes:

[0038] Module M2.2.1: Analyze the relationship between interpolation results and satellite elevation angle;

[0039] Module M2.2.2: Analyze the relationship between the interpolation results and the average distance between the user station and the reference station.

[0040] Preferably, for IDW, the functional relationship is as follows:

[0041] rms=β(d / sinel)+a0

[0042] For radial basis functions and Kriging, the functional relations are as follows:

[0043] rms=β*d*(π / 2-el)+a0

[0044] Where rms represents the root mean square value, β represents the slope of the line, d represents the average distance between the user station and the reference station, a0 represents the intercept, and el represents the satellite elevation angle.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] This invention analyzes the relationship between oblique path ionospheric interpolation results and interpolation methods, time, satellite elevation angle, and station distance, and fits a corresponding mathematical function expression. This function expression is then applied to the user terminal to obtain the uncertainty parameters of the interpolated ionospheric correction information. This provides a solution to the difficulty of setting ionospheric correction uncertainty and improves the robustness of PPP-RTK positioning results. Attached Figure Description

[0047] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0048] Figure 1 This is a schematic flowchart of the method of the present invention;

[0049] Figure 2 This is an interpolation timing diagram of the three interpolation methods in this invention within the Shanghai reference network;

[0050] Figure 3 The interpolation timing diagrams for the three interpolation methods in this invention are shown in the Hong Kong Reference Network.

[0051] Figure 4 This is a graph showing the relationship between the interpolation error of the three interpolation methods in this invention and the satellite elevation angle within the Shanghai reference network;

[0052] Figure 5 This is a graph showing the relationship between the interpolation error of the three interpolation methods in this invention and the satellite elevation angle within the Hong Kong reference network.

[0053] Figure 6 This is a graph showing the relationship between the interpolation error and the average distance of the three interpolation methods in this invention within the Shanghai reference network;

[0054] Figure 7 This is a graph showing the relationship between the interpolation error and the average distance of the three interpolation methods in this invention within the Hong Kong reference network.

[0055] Figure 8 This invention provides PPP-RTK localization solutions for the Shanghai area using three interpolation methods.

[0056] Figure 9 This is the PPP-RTK localization solution for the Hong Kong region of China using three interpolation methods in this invention. Detailed Implementation

[0057] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0058] This invention analyzes the interpolation effects and influencing factors of different interpolation methods, including inverse distance weighting, radial basis functions, and kriging, and establishes a mathematical function expression for the interpolation uncertainty in relation to the satellite elevation angle and the station distance. When using the interpolated ionospheric correction information at the user end, a more reasonable uncertainty parameter is obtained based on the empirical expression, which serves as the variance of the ionospheric correction, thereby improving the robustness of PPP-RTK positioning results.

[0059] According to the present invention, a method for analyzing the uncertainty of ionospheric interpolation along a slant path is provided, such as... Figure 1 As shown, it includes:

[0060] Step S1: Obtain the interpolation results for different interpolation methods in the selected region. Interpolation methods include IDW, radial basis function, and kriging. Analyze the time series diagrams of the interpolation results for the three interpolation methods—inverse distance weighted IDW, radial basis function, and kriging—in the Shanghai and Hong Kong regions, as shown below. Figure 2 and Figure 3 As shown, the horizontal axis represents local time, and the vertical axis represents the interpolation error.

[0061] Step S2: Analyze the interpolation results using time, distance, and elevation angle relationships. Step S2 includes:

[0062] Step S2.1: Analyze the time series plot of the interpolation results. It is found that the IDW method is greatly affected by the diurnal variation of the ionosphere. The IDW interpolation results are divided into two time periods: ionospheric activity and quiescence, and analyzed separately, denoted as the first inverse distance weighted average and the second inverse distance weighted average. The time point for the first inverse distance weighted average is 10:00 to 23:00 corresponding to the current region, and the time point for the second inverse distance weighted average is 23:00 to 10:00 corresponding to the current region. Step S2.1 includes the following sub-steps:

[0063] Step S2.2.1: Analyze the relationship between the interpolation results and the satellite elevation angle. Figure 4 and Figure 5 The graph shows the interpolation error and satellite elevation angle, where the horizontal axis represents the satellite elevation angle and the vertical axis represents the interpolation error (left axis) and the root mean square value of the error (right axis).

[0064] As shown in the figure, the higher the elevation angle of the satellite, the smaller the interpolation error. However, the trends differ depending on the interpolation method. For the IDW method, the fitted curve is closer to 1 / sin(elevation angle), while for the radial basis function and Kriging interpolation methods, the fitted curve is closer to a linear function.

[0065] Step S2.2.2: Analyze the relationship between the interpolation results and the average distance between the user station and the reference stations. First, define the average distance as the average distance between the user station and all reference stations involved in the interpolation. For example... Figure 6 and Figure 7 The scatter plot shown represents the interpolation error and average distance. The horizontal axis represents the average distance between the user station and the reference station, and the vertical axis represents the root mean square value of the interpolation error. The analysis shows that the interpolation error and the average distance are linearly related. The greater the distance, the greater the error. Furthermore, the fitting slopes of different methods are not the same.

[0066] Step S2.2: Analyze the relationship between the interpolation results and the elevation angle and distance for each time period.

[0067] Step S2.3: Combine the relationship variables of elevation angle and distance corresponding to all interpolation methods to obtain the corresponding combined variables. The relationship variables of elevation angle and distance corresponding to all interpolation methods refer to d / sinel and d*(π / 2-el) in the following text.

[0068] Step S2.4: Analyze the relationship between the interpolation results and the combined variables.

[0069] Step S3: Establish the corresponding mathematical function expression based on the analysis results. For IDW, the functional relationship is as follows:

[0070] rms=β(d / sinel)+a0

[0071] For radial basis functions and Kriging, the functional relations are as follows:

[0072] rms=β*d*(π / 2-el)+a0

[0073] Where rms represents the root mean square value, β represents the slope of the line, d represents the average distance between the user station and the reference station, a0 represents the intercept, and el represents the satellite elevation angle, which can be understood as the limit of interpolation accuracy when the average distance approaches zero. The fitted slope and intercept are shown in Table 1.

[0074] Table 1

[0075]

[0076] Step S4: At the user end, obtain a more reasonable uncertainty parameter based on the data function expression, which serves as the variance of the ionospheric correction. This can be used to evaluate the subsequent PPP-RTK positioning accuracy. Simultaneously, compare the positioning results with two traditional methods that set smaller and larger empirical constants, as shown below. Figure 8 and Figure 9 As shown in the figure, the horizontal axis represents local time, the vertical axis represents positioning error, the dashed line indicates that the uncertainty is set to a small constant value, the solid line indicates that the uncertainty is set to a large constant value, and the dotted line indicates that the uncertainty is set using a function expression. The data is organized as shown in Table 2.

[0077] Table 2

[0078]

[0079] Analysis shows that the uncertainty function formula proposed in this invention can better reflect the reliability of the ionospheric interpolation correction. When applied to PPP-RTK positioning, it can effectively improve positioning accuracy and convergence speed.

[0080] The present invention also provides a system for analyzing the uncertainty of oblique path ionospheric interpolation. The system can be implemented by executing the process steps of the method for analyzing the uncertainty of oblique path ionospheric interpolation. That is, those skilled in the art can understand the method for analyzing the uncertainty of oblique path ionospheric interpolation as a preferred embodiment of the system for analyzing the uncertainty of oblique path ionospheric interpolation.

[0081] A system for analyzing the uncertainty of slant path ionospheric interpolation according to the present invention includes:

[0082] Module M1: Obtains interpolation results for different interpolation systems in a selected region. Interpolation systems include IDW, radial basis functions, and kriging.

[0083] Module M2: Analyzes the interpolation system results using time, distance, and elevation angle relationships. Module M2 includes: Module M2.1: Analyzes the time series diagram of the interpolation results, dividing the IDW interpolation results into two time periods: ionospheric active and quiescent, and denoted as the first inverse distance weighted and the second inverse distance weighted, respectively. Module M2.1 includes: Module M2.2.1: Analyzes the relationship between the interpolation results and the satellite elevation angle. Module M2.2.2: Analyzes the relationship between the interpolation results and the average distance between the user station and the reference station. Module M2.2: Analyzes the relationship between the interpolation results for each time period and the elevation angle and distance. Module M2.3: Combines the elevation angle and distance relationship variables corresponding to all interpolation systems to obtain the corresponding combined variables. Module M2.4: Analyzes the relationship between the interpolation results and the combined variables.

[0084] Module M3: Establishes the corresponding mathematical function expression based on the analysis results. For IDW, the functional relationship is as follows:

[0085] rms=β(d / sinel)+a0

[0086] For radial basis functions and Kriging, the functional relations are as follows:

[0087] rms=β*d*(π / 2-el)+a0

[0088] Where rms represents the root mean square value, β represents the slope of the line, d represents the average distance between the user station and the reference station, a0 represents the intercept, and el represents the satellite elevation angle.

[0089] Module M4: At the user end, a more reasonable uncertainty parameter is obtained based on the data function expression, which serves as the variance of the ionospheric correction.

[0090] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0091] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for analyzing the uncertainty of ionospheric interpolation along oblique paths, characterized in that, include: Step S1: Obtain the interpolation results corresponding to different interpolation methods in the selected area; Step S2: Analyze and process the interpolation results using time, distance, and elevation angle relationships; Step S3: Establish the corresponding mathematical function expression based on the results of the analysis and processing; Step S4: Obtain a more reasonable uncertainty parameter on the user end based on the mathematical function expression, which serves as the variance of the ionospheric correction number; For IDW, the functional relationship is as follows: rms=β(d / sinel)+a0 For radial basis functions and Kriging, the functional relations are as follows: rms=β*d*(π / 2-el)+a0 Where rms represents the root mean square value, β represents the slope of the line, d represents the average distance between the user station and the reference station, a0 represents the intercept, and el represents the satellite elevation angle.

2. The method for analyzing uncertainty of oblique path ionospheric interpolation according to claim 1, characterized in that, The interpolation methods include IDW, radial basis functions, and kriging.

3. The method for analyzing uncertainty in oblique path ionospheric interpolation according to claim 2, characterized in that, Step S2 includes: Step S2.1: Analyze the time series diagram of the interpolation results. Divide the interpolation results of IDW into two time periods: ionospheric active and quiescent, and analyze them separately. These are denoted as the first inverse distance weighted average and the second inverse distance weighted average, respectively. Step S2.2: Analyze the relationship between the interpolation results and the elevation angle and distance for each time period; Step S2.3: Combine the relationship variables of elevation angle and distance corresponding to all interpolation methods to obtain the corresponding combined variables; Step S2.4: Analyze the relationship between the interpolation results and the combined variables.

4. The method for analyzing uncertainty of oblique path ionospheric interpolation according to claim 3, characterized in that, Step S2.1 includes: Step S2.2.1: Analyze the relationship between the interpolation results and the satellite elevation angle; Step S2.2.2: Analyze the relationship between the interpolation results and the average distance between the user station and the reference station.

5. A system for analyzing uncertainty in oblique path ionospheric interpolation, characterized in that, include: Module M1: Obtains the interpolation results of different interpolation systems in the selected area; Module M2: Analyzes and processes the interpolation system results using time, distance, and elevation angle relationships, respectively; Module M3: Establishes the corresponding mathematical function expression based on the results of the analysis and processing; Module M4: At the user end, a more reasonable uncertainty parameter is obtained based on the mathematical function expression, which serves as the variance of the ionospheric correction. For IDW, the functional relationship is as follows: rms=β(d / sinel)+a0 For radial basis functions and Kriging, the functional relations are as follows: rms=β*d*(π / 2-el)+a0 Where rms represents the root mean square value, β represents the slope of the line, d represents the average distance between the user station and the reference station, a0 represents the intercept, and el represents the satellite elevation angle.

6. The slant path ionospheric interpolation uncertainty analysis system according to claim 5, characterized in that, The interpolation system includes IDW, radial basis functions, and kriging.

7. The slant path ionospheric interpolation uncertainty analysis system according to claim 6, characterized in that, The module M2 includes: Module M2.1: Analyze the time series diagram of the interpolation results, divide the IDW interpolation results into two time periods, one active and one quiescent, and analyze them separately, denoted as the first inverse distance weighted and the second inverse distance weighted, respectively; Module M2.2: Analyzes the relationship between the interpolation results and elevation angle and distance for each time period; Module M2.3: Combines the relationship variables of elevation angle and distance corresponding to all interpolation systems to obtain the corresponding combined variables; Module M2.4: Analyze the relationship between interpolation results and combined variables.

8. The slant path ionospheric interpolation uncertainty analysis system according to claim 7, characterized in that, The module M2.1 includes: Module M2.2.1: Analyze the relationship between interpolation results and satellite elevation angle; Module M2.2.2: Analyze the relationship between the interpolation results and the average distance between the user station and the reference station.

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