A real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints

Abstract

The present invention discloses a real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints. The method comprises the following steps: determining the corresponding historical constrained year, month, and universal time using the real-time year, month, and universal time; dividing the historical CODE-TEC data by year and month based on the historical CODE-TEC data, taking the average hourly TEC value over 24 hours per month, and determining the historically constrained CODE-TEC based on the historically constrained year, month, and universal time; obtaining the global historically constrained CODE-TEC using the real-time year, month, and universal time, combining it with the real-time observed local TEC data to obtain real-time coefficients through spherical harmonic fitting; and substituting the real-time coefficients into the spherical harmonics to construct a real-time ionospheric TEC model for the local area. The method can quickly and accurately construct a regional ionospheric TEC model, which is of great value to both ionospheric scientific research and space weather monitoring.

Description

Technical Field

[0001] The present invention belongs to the technical field of ionospheric TEC modeling, and in particular relates to a spherical harmonic function real-time ionospheric TEC modeling method based on historical data constraints. Background Art

[0002] As one of the key parameters describing ionospheric variability, state, and structure, the total electron content (TEC) has long been a crucial parameter in satellite navigation and positioning. Research and construction of real-time ionospheric TEC models based on the temporal and spatial variations of the ionosphere is of great value in both theoretical research on ionospheric TEC and the application of satellite navigation and positioning corrections. Ionospheric TEC models can be categorized by coverage: single-station, regional, and global. Regional ionospheric TEC models primarily include polynomial models, trigonometric series models, spherical cap harmonic models, empirical orthogonal function models, grid models, and spherical harmonic function models. Different regional ionospheric TEC models have distinct characteristics: polynomial models exhibit "edge effects" when modeling larger regions; trigonometric series models are suitable for modeling small, localized regions; spherical cap harmonic models are suitable for modeling large regions and provide relatively uniform distribution in time and space; empirical orthogonal function models offer rapid convergence and the ability to separate different physical contributions; and ionospheric TEC models constructed using spherical harmonic functions offer high accuracy, but require uniform global observational data for their construction. Summary of the Invention

[0003] To solve the above technical problems, the present invention proposes a real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints, which can quickly and accurately construct a regional ionospheric TEC model and has important value for ionospheric scientific research and space weather monitoring.

[0004] To achieve the above object, the present invention provides a real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints, comprising the following steps:

[0005] Determine the corresponding historical constraint year, month and universal time through the real-time year, month and universal time;

[0006] Based on historical CODE-TEC data, divide the historical CODE-TEC data by year and month, take the average value of TEC per hour in 24 hours per month, and determine the historical constraint CODE-TEC based on the historical constraint year, month and universal time;

[0007] The CODE-TEC with global historical constraints is obtained by real-time year, month and universal time. The real-time coefficients are obtained by spherical harmonic function fitting based on the real-time observed local TEC data.

[0008] The real-time coefficients are substituted into the spherical harmonic function to construct a real-time ionospheric TEC model of the local area.

[0009] According to the spherical harmonics real-time ionospheric TEC modeling method based on historical data constraints provided by the present invention, the method for determining the corresponding historical constraint year is:

[0010] IGIMYear=mod(NowYear-StartYear,11)+StartYear

[0011] Among them, NowYear is the current input year, StartYear is the year when the historical data starts, IGIMYear is the historical constraint year corresponding to NowYear, and mod is the modulo operation.

[0012] According to the spherical harmonics real-time ionospheric TEC modeling method based on historical data constraints provided by the present invention, the method for determining the corresponding historical constraint month is:

[0013] IGIMMonth=NowMonth

[0014] Among them, NowMonth is the currently input month, and IGIMMonth is the historical constraint month corresponding to NowMonth.

[0015] According to the spherical harmonics real-time ionospheric TEC modeling method based on historical data constraints provided by the present invention, the method for determining the corresponding historical constrained universal time is:

[0016] IGIMUT=NowUT

[0017] Among them, NowUT is the current input world time, IGIMUT is the world time of the historical constraint corresponding to NowUT

[0018] According to the spherical harmonics real-time ionospheric TEC modeling method based on historical data constraints provided by the present invention, the historical CODE-TEC data are divided by year and month, and the average value of TEC per hour in 24 hours per month is obtained as follows:

[0019]

[0020] Where y is year, l is month, i is universal time, j is geographic longitude, k is geographic latitude, t is day, and N0 is the maximum number of days in a month. is the monthly mean vertical TEC of month 1 in year y at geographic longitude j and geographic latitude k with universal time i.

[0021] According to the spherical harmonics real-time ionospheric TEC modeling method based on historical data constraints provided by the present invention, the method for obtaining real-time coefficients by spherical harmonics fitting is:

[0022]

[0023] Where IPPTECV(jI,kI) is the value of CODE-TEC based on historical constraints and the vertical TEC of the local area observed in real time at geographic latitude jI and geographic longitude kI, jI and kI are the geographic latitude and longitude of the penetration point, N is the maximum degree of the spherical harmonic function, P nm is the normalized Legendre function of degree n and order m, C nm and S nm are the real-time coefficients to be determined.

[0024] According to the spherical harmonic function real-time ionospheric TEC modeling method based on historical data constraints provided by the present invention, the method of substituting the real-time coefficients into the spherical harmonic function to construct a real-time ionospheric TEC model for a local area is as follows:

[0025]

[0026] Among them, GridTECV(jG,kG) is the real-time vertical TEC value at geographic latitude jG and geographic longitude kG obtained by real-time data construction, jG and kG are the geographic latitude and longitude on the grid point respectively, N is the maximum degree of spherical harmonics, P nm is the normalized Legendre function of degree n and order m, C nm and S nm are the real-time coefficients that have been calculated respectively.

[0027] Technical effect of the invention: The present invention discloses a real-time ionospheric TEC modeling method based on spherical harmonic functions constrained by historical data. The historically constrained CODE-TEC is obtained through real-time year, month and universal time. When there is a lack of real-time global TEC data, real-time local TEC data can be used to drive the construction of a constrained, high-precision real-time local ionospheric TEC model, providing important technical support for the monitoring of space weather events. At the same time, it has important value in both ionospheric theory research and satellite navigation positioning correction application research. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0029] Figure 1 Schematic diagram of a flow chart of a real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints according to an embodiment of the present invention;

[0030] Figure 2This is a schematic diagram of the absolute and relative error distribution between the model value and the observation value at 07:00 UTC on March 20, 2021 in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0032] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0033] like Figure 1 As shown, this embodiment provides a real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints, including:

[0034] Determine the corresponding historical constraint year, month and universal time through the real-time year, month and universal time;

[0035] Based on historical CODE-TEC data, divide the historical CODE-TEC data by year and month, take the average value of TEC per hour in 24 hours per month, and determine the historical constraint CODE-TEC based on the historical constraint year, month and universal time;

[0036] The CODE-TEC with global historical constraints is obtained by real-time year, month and universal time. The real-time coefficients are obtained by spherical harmonic function fitting based on the real-time observed local TEC data.

[0037] The real-time coefficients are substituted into the spherical harmonic function to construct a real-time ionospheric TEC model of the local area.

[0038] Furthermore, the method for determining the corresponding historical constraint year is:

[0039] IGIMYear=mod(NowYear-StartYear,11)+StartYear

[0040] Among them, NowYear is the current input year, StartYear is the year when the historical data starts, IGIMYear is the historical constraint year corresponding to NowYear, and mod is the modulo operation.

[0041] The method for determining the corresponding historical constraint month is:

[0042] IGIMMonth=NowMonth

[0043] Among them, NowMonth is the currently input month, and IGIMMonth is the historical constraint month corresponding to NowMonth.

[0044] The method to determine the corresponding historical constraint world time is:

[0045] IGIMUT=NowUT

[0046] Among them, NowUT is the current input world time, IGIMUT is the world time of the historical constraint corresponding to NowUT

[0047] Furthermore, the historical CODE-TEC data is divided into years and months, and the average value of TEC per hour in each 24 hours of each month is obtained as follows:

[0048]

[0049] Where y is year, l is month, i is universal time, j is geographic longitude, k is geographic latitude, t is day, and N0 is the maximum number of days in a month. is the monthly mean vertical TEC of month 1 in year y at geographic longitude j and geographic latitude k with universal time i.

[0050] Furthermore, the method for obtaining real-time coefficients by spherical harmonic fitting is:

[0051]

[0052] Where IPPTECV(jI,kI) is the value of CODE-TEC based on historical constraints and the vertical TEC of the local area observed in real time at geographic latitude jI and geographic longitude kI, jI and kI are the geographic latitude and longitude of the penetration point, N is the maximum degree of the spherical harmonic function, P nm is the normalized Legendre function of degree n and order m, C nm and S nm are the real-time coefficients to be determined.

[0053] Furthermore, the method of substituting the real-time coefficients into the spherical harmonic function to construct a real-time ionospheric TEC model for a local area is:

[0054]

[0055] Among them, GridTECV(jG,kG) is the real-time vertical TEC value at geographic latitude jG and geographic longitude kG obtained by real-time data construction, jG and kG are the geographic latitude and longitude on the grid point respectively, N is the maximum degree of spherical harmonics, P nm is the normalized Legendre function of degree n and order m, C nm and S nmare the real-time coefficients that have been calculated respectively.

[0056] Specific application examples:

[0057] Taking the global ionospheric TEC data released by CODE from 2010 to 2020 as historical data and the vertical TEC data observed by a certain observation network at a penetration point in a certain region at 07:00 UTC on March 20, 2021 as real-time observation data, the two are substituted into the spherical harmonic function for fitting, and the regional ionospheric TEC model is obtained as an example. The execution steps are as follows:

[0058] Step 1: Take the historical constraints of 07:00 UTC on March 20, 2021 as an example;

[0059] IGIMYear=mod(NowYear-StartYear,11)+StartYear

[0060] Where NowYear is 2021, StartYear is 2010, and the calculated IGIMYear is 2010, that is, CODE-TEC at 07:00 UTC in March 2010 is taken as the historical constraint.

[0061] Step 2: Taking the CODE-TEC at the penetration point of 100°E and 15°N at 07:00 UTC on March 2010 as an example, the calculation process is as follows:

[0062]

[0063] Calculated It is 9.3710TECU.

[0064] Step 3: Fit the coefficients of historical constraint data with real-time observation data. The CODE-TEC at the penetration point at 100°E and 15°N at 07:00 UTC on March 2010 is used as an example, and the corresponding TEC value is 39.0419 TECU. The vertical TEC data at 105.2901°E and 15.5314°N at 07:00 UTC on March 2021 is used as an example, and the corresponding TEC value is 40.7668 TECU. The two are combined to fit the real-time coefficient C. nm and S nm .

[0065]

[0066] Wherein, N=25, and the coefficients when n=0, 1, and 2 are shown in Table 1.

[0067] Table 1

[0068]

[0069]

[0070] Step 4: Using the real-time coefficients obtained in Step 3, the calculation process is as follows, taking the ionospheric TEC model values ​​constructed at 105°E and 15°N at 07:00 UTC on March 2021 as an example:

[0071]

[0072] The calculated GridTECV(15,105) is 40.1926TECU.

[0073] like Figure 2 The absolute and relative error distributions between the model value and the observed value at 07:00 UTC on March 20, 2021, calculated by the method provided by the present invention.

[0074] The present invention discloses a real-time ionospheric TEC modeling method based on spherical harmonic functions constrained by historical data. The historically constrained CODE-TEC is obtained through real-time year, month and universal time. When there is a lack of real-time global TEC data, real-time local TEC data can be used to drive the construction of a constrained, high-precision real-time local ionospheric TEC model. This provides important technical support for the monitoring of space weather events and is of great value in both theoretical research on the ionosphere and applied research on satellite navigation positioning correction.

[0075] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints, characterized by: The following steps are involved: Determine the corresponding historical constraint year, month and universal time through the real-time year, month and universal time; Based on historical CODE-TEC data, the historical CODE-TEC data is divided into years and months, and the TEC corresponding to the 24 hours of Universal Time for all days of each month is averaged. The historically constrained CODE-TEC is determined based on the historically constrained year, month, and Universal Time. The CODE-TEC with global historical constraints is obtained by real-time year, month and universal time. The real-time coefficients are obtained by spherical harmonic function fitting based on the real-time observed local TEC data. The real-time coefficients are substituted into the spherical harmonic function to construct a real-time ionospheric TEC model of the local area.

2. The spherical harmonics real-time ionospheric TEC modeling method based on historical data constraints according to claim 1, characterized in that: The method for determining the corresponding historical constraint year is: IGIMYear=mod(NowYear-StartYear,11)+StartYear Among them, NowYear is the current input year, StartYear is the year when the historical data starts, IGIMYear is the historical constraint year corresponding to NowYear, and mod is the modulo operation.

3. The real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints according to claim 1 is characterized in that: The method for determining the corresponding historical constraint month is: IGIMMonth=NowMonth Among them, NowMonth is the currently input month, and IGIMMonth is the historical constraint month corresponding to NowMonth.

4. The real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints according to claim 1 is characterized in that: The method to determine the corresponding historical constraint world time is: IGIMUT=NowUT Among them, NowUT is the current input world time, and IGIMUT is the world time of the historical constraint corresponding to NowUT.

5. The real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints according to claim 1 is characterized in that: The historical CODE-TEC data are divided into years and months, and the TEC corresponding to the 24 full hours of the Universal Time for all days of each month are averaged. The monthly average vertical TEC at the Universal Time i at the geographical longitude j and geographical latitude k in year y and month l is obtained as follows: Where y is year, l is month, i is universal time, j is geographic longitude, k is geographic latitude, t is day, and N0 is the maximum number of days in a month. is the monthly mean vertical TEC of month 1 in year y at geographic longitude j and geographic latitude k with universal time i.

6. The real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints according to claim 1, characterized in that: The method for obtaining real-time coefficients through spherical harmonic fitting is: Where IPPTECV(jI,kI) is the value of CODE-TEC based on historical constraints and the vertical TEC of the local area observed in real time at geographic latitude jI and geographic longitude kI, jI and kI are the geographic latitude and longitude of the penetration point, N is the maximum degree of the spherical harmonic function, P nm is the normalized Legendre function of degree n and order m, C nm and S nm are the real-time coefficients to be determined.

7. The real-time ionospheric TEC modeling method based on spherical harmonics and historical data constraints according to claim 1, wherein: The method of substituting the real-time coefficients into the spherical harmonic function to construct the real-time ionospheric TEC model of the local area is: Among them, GridTECV(jG,kG) is the real-time vertical TEC value at geographic latitude jG and geographic longitude kG obtained by real-time data construction, jG and kG are the geographic latitude and longitude on the grid point respectively, N is the maximum degree of spherical harmonics, P nm is the normalized Legendre function of degree n and order m, C nm and S nm are the real-time coefficients that have been calculated respectively.

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