A method for calculating inter-satellite cross-calibration coefficients according to particle phase space density correlation characteristics

Abstract

The application discloses a method for calculating an interplanetary cross scaling coefficient according to particle phase space density correlation characteristics, comprising the following steps: obtaining particle flux sequences of a standard A star and a to-be-scaled B star; under a T89c external magnetic field model, respectively calculating a modified third adiabatic invariant and a second adiabatic invariant of the A star and the B star, and calculating a local magnetic field intensity; performing uniform grid division on time and the third adiabatic invariant, and performing logarithmic uniform grid division on the first adiabatic invariant and the second adiabatic invariant; obtaining a local pitch angle and energy in the grid; screening out points with data in the same grid to obtain particle phase space densities of the A star and the B star respectively; calculating a particle phase space density average in the grid; respectively establishing particle phase space density matrices of the A star and the B star; screening out points with data in the same grid of the particle phase space density matrices of the two stars to obtain a cross scaling coefficient of the B star.

Description

Technical Field

[0001] This invention belongs to the field of space data processing technology, and in particular relates to a method for calculating interstellar cross-calibration coefficients based on the spatial density correlation characteristics of particle phases. Background Technology

[0002] Earth's radiation belts pose a serious threat to human space exploration, and our knowledge of them relies primarily on the joint analysis of multi-satellite, in-situ observation data. However, inconsistencies in data standards across different satellites and instruments can easily mislead our understanding of the radiation belts. Cross-calibration is an internationally recognized and widely adopted method for addressing such problems. Traditional cross-calibration techniques require finding intersection points between satellites in different orbits in three-dimensional Earth space. However, due to orbital differences, readily available points for cross-comparison between two satellites are often very scarce. Therefore, a method is urgently needed to correlate seemingly disjoint data in actual three-dimensional space using particle motion characteristics, thereby calculating the cross-calibration coefficients between observations from two satellites. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and to propose a method for calculating interstellar cross-calibration coefficients based on the particle phase space density correlation characteristics.

[0004] In view of this, the present invention proposes a method for calculating interstellar cross-calibration coefficients based on particle phase space density correlation characteristics, comprising:

[0005] Step 1: Obtain the particle flux sequences of standard A-star and B-star to be calibrated. The particle flux sequences include: time, position, energy, local pitch angle, and particle differential flux.

[0006] Step 2: Based on the data from Step 1, under the T89c external magnetic field model, calculate the corrected third adiabatic invariant and the second adiabatic invariant for both A and B stars, and calculate the local magnetic field strength.

[0007] Step 3: Perform uniform meshing on the time and the modified third adiabatic invariant, and perform logarithmic uniform meshing on the first adiabatic invariant and the modified second adiabatic invariant;

[0008] Step 4: Within the grid of adjacent times and the third adjacent adiabatic invariant, calculate the local throw angle and energy;

[0009] Step 5: Combining the data from Step 1 and Step 4, within the grid of adjacent times and adjacent third adiabatic invariants, select the points that have data in the same grid, and obtain the particle phase space density of star A and star B respectively.

[0010] Step 6: For a given grid containing multiple particle phase spatial densities spanning different orders of magnitude, calculate the mean particle phase spatial density within that grid.

[0011] Step 7: Repeat steps 4-6, calculate the logarithm based on the mean particle phase space density in each grid, and then establish the particle phase space density matrices for star A and star B respectively.

[0012] Step 8: Filter out the points where the particle phase space density matrices of stars A and B both contain data in the same grid, and calculate the inter-star cross-calibration coefficients of star B.

[0013] Preferably, the energy sequence in step 1 includes: time t, position r, energy E, and local throwing angle α. local and particle differential flux J(t,α) local E).

[0014] Preferably, step 2 includes:

[0015] Based on the time t, position r, and local throwing angle α of satellites A and B respectively local Using the ONERA-DEEP library, the path integral invariant I and the local magnetic field strength B were calculated under the T89c external magnetic field model. local Magnetic field strength B at the magnetic mirror point mirror and the third adiabatic invariant L * Based on I and B mirror The modified second adiabatic invariant K of the particle is obtained according to the following formula:

[0016]

[0017] Preferably, step 4 includes:

[0018] At adjacent time t i and t i+1 The adjacent third adiabatic invariant L * j and L * j+1 Within the grid cells, find the corrected second adiabatic invariant K = K n , μ=μ m Local throwing angle α at time q ;

[0019] Substituting into the following formula, we obtain the energy E. q :

[0020]

[0021] Where E0 is the particle's rest energy, K n and μ m These are the corresponding settings.

[0022] Preferably, step 5 includes:

[0023] Assuming the particle flux J follows an exponential distribution with energy E and a variable change with the throwing angle α, local The particle differential flux J exhibits a power-law distribution and satisfies the following equation:

[0024] J = Ae -B·E sin n α local

[0025] Where A, B and n are coefficients;

[0026] For ln(J(t,α) local Bilinear interpolation is performed using E and ln(sin(α)). local Using )) as the independent variable, we obtain the result at the interpolation point (E) q ,α q The differential flux of particles at point J q According to the following formula:

[0027]

[0028] The particle phase spatial density f is obtained q .

[0029] Preferably, step 6 includes:

[0030] The phase space density f of the (N+1)th particle q The logarithmically updated particle phase space density is updated according to the following formula:

[0031]

[0032] Among them, w new and w old , respectively, are the logarithmically transformed particle phase space densities before and after the update, and N is the number of data points within the same grid cell.

[0033] Preferably, step 8 includes:

[0034] The particle phase space density matrix F of stars A and B was selected. A and F B Points that all contain data within the same grid are represented by array P. A and P B According to the following formula:

[0035]

[0036] The cross-calibration coefficient c of star B is obtained.

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] For the first time, a particle motion correlation feature that remains unchanged when the particle phase space density is the same under three adiabatic invariants is proposed to cross-calibrate satellite observation data. Compared with searching for correlation data in actual three-dimensional Earth space, this calculation scheme can greatly increase the number of comparable data and improve the reliability of the calculation results. Attached Figure Description

[0039] Figure 1 This is a flowchart of a method for calculating interstellar cross-calibration coefficients based on particle phase spatial density correlation characteristics according to the present invention;

[0040] Figure 2 This is a schematic diagram illustrating the calculation of cross-calibration coefficients using the method of this invention. Detailed Implementation

[0041] This application proposes a novel method for calculating cross-calibration coefficients, which is based on Liouville's theorem—particles with the same adiabatic invariant also have the same phase space density. The method correlates the data that do not intersect in actual three-dimensional space using the motion characteristics of the particles, thereby calculating the cross-calibration coefficients between the observation data of two satellites.

[0042] like Figure 1 As shown, the scheme for calculating the inter-satellite cross-calibration coefficients is as follows:

[0043] (1) Obtain the time t, position r, energy E, and local throwing angle α of the standard star A and the target star B. local and particle differential flux J(t,α) local E).

[0044] (2) Based on the MAKE_LSTAR_SHELL_SPLITTING function of the ONERA-DESP library in version V4.2, input the t, r and α of the binary star. local Calculate the path integral invariant I and the local magnetic field strength B for the corresponding input parameters under the T89c external magnetic field model. local Magnetic field strength B at the magnetic mirror point mirror and L * Based on I and B mirror The modified second adiabatic invariant of the particle can be obtained.

[0045] (3) For t and L * Perform uniform mesh generation, and perform logarithmic uniform mesh generation for μ and K.

[0046] (4) At adjacent time t i and t i+1 Adjacent third adiabatic invariant L *j and L * j+1 Within the grid cell, find K = K n , μ=μ m Local throwing angle α at time q and energy E q Using the (α) calculated in the previous step local For K), we get K = K n Local throwing angle α at time q The local throwing angle α q And B calculated in the previous step local and μ = μ m Substitute into the expression for particle energy Where E0 = m0c 2 Let m0 be the rest energy of the particle, m0 be the mass of the particle, and c be the speed of light.

[0047] (5) At time t i and t i+1 Space L * j and L * j+1 Within the grid cell, find the corresponding local throwing angle α. q and energy E q Particle phase space density f at the location q Assuming the particle flux follows an exponential distribution with energy and a power-law distribution with the throwing angle, the differential flux of the particle can be expressed as: J = Ae^(-J / A ... -BE sin n α local A, B, and n are coefficients, E is energy, and α is... local For the local throwing angle. For ln(J(t,α) local Perform bilinear interpolation on E), where E and ln(sin(α) are used. local Using )) as the independent variable, we obtain the result in (E) q ,α q The differential flux of particles at point J q The expression for calculating the particle phase space density is:

[0048] (6) At t i and t i+1 L * j and L * j+1 K = K n and μ=μ m Within a grid cell, there may be multiple f values ​​spanning several orders of magnitude. q Using the (N+1)th f q The formula for updating the mean density of the particle phase space is: Where w is the logarithmic particle phase space density, and N is the number of data points within the same grid cell.

[0049] (7) Establish the particle phase space density matrix F(t,L*,μ,K), and store the logarithmized particle phase space density obtained in step (6) into the F matrix to obtain F(t). i ,L * j ,μ m ,K n ) = 10 W Meanwhile, repeat steps (4) to (6).

[0050] (8) Select the particle phase space density matrix F obtained from the data of star A and star B respectively. A and F B Points that have data within the same grid, F A and F B The arrays of points that meet the requirements are P. A and P B Because of P A and P B Spanning several orders of magnitude, the formula for calculating the inter-satellite cross-calibration coefficients, obtained by first logarithmicizing and then exponentializing, is as follows:

[0051] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0052] Example

[0053] Embodiments of the present invention propose a method for calculating interstellar cross-calibration coefficients based on particle phase space density correlation characteristics, specifically:

[0054] Given the time, position, energy, local ejection angle, and differential particle energy flux of standard A, and the time, position, energy, local ejection angle, and differential particle energy flux of the target B, the four-dimensional (t, L) values ​​of A and B are calculated according to the technical scheme procedure. * The particle phase space density matrices of μ and K are obtained. Points with data in the same grid of both matrices are selected to obtain the particle phase space density arrays of the standard star A and the star to be calibrated B. If the data of the two stars are positively correlated but differ by a certain systematic deviation in the Y direction, this coefficient deviation, i.e., the cross-calibration coefficient, can be obtained by using the cross-calibration coefficient calculation formula in step (9) of the technical solution.

[0055] In terms of data time range selection, it is advisable to use data from the solar activity peak year, as the particle flux value is relatively large at this time, which can reduce the interference and impact of small flux data close to the detector threshold.

[0056] Technical effects:

[0057] This application uses the particle motion correlation feature, in which the particle phase spatial density remains unchanged when the three adiabatic invariants are the same, to cross-calibrate the satellite observation data. This method enables cross-calibration of data from two satellites that do not have orbital intersections in actual three-dimensional Earth space and increases the number of comparable satellite data.

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating interstellar cross-calibration coefficients based on particle phase space density correlation characteristics, comprising: Step 1: Obtain the particle flux sequence of standard A-star and B-star to be calibrated. The particle flux matrix includes: time, position, energy, local pitch angle and particle differential flux. Step 2: Based on the data from Step 1, under the T89c external magnetic field model, correct the third and second adiabatic invariants of satellites A and B respectively, and calculate the local magnetic field strength. Step 3: Perform uniform meshing on the time and the modified third adiabatic invariant, and perform logarithmic uniform meshing on the first adiabatic invariant and the modified second adiabatic invariant; Step 4: Within the grid of adjacent times and the third adjacent adiabatic invariant, calculate the local throw angle and energy; Step 5: Combining the data from Step 1 and Step 4, within the grid of adjacent times and adjacent third adiabatic invariants, select the points that have data in the same grid, and obtain the particle phase space density of star A and star B respectively. Step 6: For a given grid containing multiple particle phase spatial densities spanning different orders of magnitude, calculate the mean particle phase spatial density within that grid; specifically including: The phase space density of the (N+1)th particle The logarithmically updated particle phase space density is updated according to the following formula: ； in, and These are the logarithmically optimized particle phase space densities before and after the update, respectively. N The number of data items within the same grid cell; Step 7: Repeat steps 4-6, calculate the logarithm based on the mean particle phase space density in each grid, and then establish the particle phase space density matrices for star A and star B respectively. Step 8: Select the particle phase space density matrix F of stars A and B. A and F B Points that all contain data within the same grid are represented by array P. A and P B According to the following formula: ； Obtain the cross-calibration coefficients of star B. .

2. The method for calculating interstellar cross-calibration coefficients based on particle phase spatial density correlation characteristics according to claim 1, characterized in that, The particle flux sequence in step 1 includes: time t, position r, energy E, and local throw angle. and particle differential flux .

3. The method for calculating interstellar cross-calibration coefficients based on particle phase spatial density correlation characteristics according to claim 1, characterized in that, Step 2 includes: Based on the time t, position r, and local throwing angle of satellites A and B respectively Using the ONERA-DEEP library, the path integral invariant I and the local magnetic field strength were calculated under the T89c external magnetic field model. Magnetic field strength at the magnetic mirror point and the third adiabatic invariant L * Based on I and The modified second adiabatic invariant of the particle is obtained according to the following formula. : 。 4. The method for calculating interstellar cross-calibration coefficients based on particle phase spatial density correlation characteristics according to claim 1, characterized in that, Step 4 includes: At adjacent time t i and t i+1 The adjacent third adiabatic invariant L * j and L * j+1 Within the grid cells, find the corrected second adiabatic invariant. , Local throwing angle at time α q ; Substituting into the following formula, we obtain the energy. : ； in, The rest energy of the particle. and These are the corresponding settings.

5. The method for calculating interstellar cross-calibration coefficients based on particle phase spatial density correlation characteristics according to claim 1, characterized in that, Step 5 includes: Assume that the particle flux J follows an exponential distribution with respect to energy E, and varies with the throwing angle. The particle differential flux J exhibits a power-law distribution and satisfies the following equation: ； in, A,B and n For coefficients; right Perform bilinear interpolation with E and ln(sin( Using )) as the independent variable, we obtain the result at the interpolation point ( E q , α q Particle differential flux at ) J q According to the following formula: ； Obtain the particle phase space density .

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