The Global Positioning System (GPS) satellite constellation has provided long-term observations of energetic electrons in Earth’s radiation belts, but inconsistencies among different satellites limit the direct use of their combined measurements. A comparative analysis of electron flux data from year 2000 to 2020 reveals significant deviations for several satellites, particularly NS41 and NS48 in low-flux regions, as well as scattered observations from satellites such as NS74 and NS69. These discrepancies highlight the necessity of cross-calibration to ensure data consistency. To address this, we conducted the first systematic cross-calibration of energetic electron fluxes from 25 GPS satellites. Taking the 2.0 MeV average unidirectional differential electron fluxes and the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\ge$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≥</mo> </math></EquationSource> </InlineEquation>2.0 MeV omnidirectional integral electron fluxes as examples, we adopted the conjunction method in magnetic coordinates (Lm, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${B/B_0}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <mo stretchy="false">/</mo> <msub> <mi>B</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> ) (Lm: McIlwain L-shell parameter, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${B/B_0}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <mo stretchy="false">/</mo> <msub> <mi>B</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> : magnetic field ratio) and applied cubic polynomial fitting to achieve unified calibration using NS59 as the reference. For the 2.0 MeV differential electron fluxes, the Root-Mean-Square Deviation (RMSD) before calibration is on average 3.08 times larger than that after calibration, while the Correlation Coefficient (CC) increases by a factor of 1.14 on average. For the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\ge$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≥</mo> </math></EquationSource> </InlineEquation>2.0 MeV integral electron fluxes, the corresponding values are 1.68 and 1.01, respectively. This method can be extended to other energy channels and satellites. The calibrated dataset facilitates quantitative analysis and modeling of variations in the high-energy electron distribution in medium Earth orbits.

Cross-calibration and performance analysis of the energetic electron flux data from GPS satellite constellation

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2026年7月6日

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Xiaojing Sun,
Ruilin Lin,
Wenlong Liu,
Siqing Liu,
Bingxian Luo,
Xuan Dong,
Shuai Liu,
Dianjun Zhang

摘要

The Global Positioning System (GPS) satellite constellation has provided long-term observations of energetic electrons in Earth’s radiation belts, but inconsistencies among different satellites limit the direct use of their combined measurements. A comparative analysis of electron flux data from year 2000 to 2020 reveals significant deviations for several satellites, particularly NS41 and NS48 in low-flux regions, as well as scattered observations from satellites such as NS74 and NS69. These discrepancies highlight the necessity of cross-calibration to ensure data consistency. To address this, we conducted the first systematic cross-calibration of energetic electron fluxes from 25 GPS satellites. Taking the 2.0 MeV average unidirectional differential electron fluxes and the $\ge$ $\geq$ 2.0 MeV omnidirectional integral electron fluxes as examples, we adopted the conjunction method in magnetic coordinates (L_m, ${B/B_0}$ $B / B_{0}$ ) (L_m: McIlwain L-shell parameter, ${B/B_0}$ $B / B_{0}$ : magnetic field ratio) and applied cubic polynomial fitting to achieve unified calibration using NS59 as the reference. For the 2.0 MeV differential electron fluxes, the Root-Mean-Square Deviation (RMSD) before calibration is on average 3.08 times larger than that after calibration, while the Correlation Coefficient (CC) increases by a factor of 1.14 on average. For the $\ge$ $\geq$ 2.0 MeV integral electron fluxes, the corresponding values are 1.68 and 1.01, respectively. This method can be extended to other energy channels and satellites. The calibrated dataset facilitates quantitative analysis and modeling of variations in the high-energy electron distribution in medium Earth orbits.