Magnetospheric relativistic electrons can destroy on-orbit spacecrafts completely by internal charging and discharging effects. As the characteristics and physical mechanism of this space particle are still unclear, magnetospheric relativistic electrons have always been an important object of space environment exploration and space science research. For studying the physical mechanisms and developing models relating to magnetospheric relativistic electrons, it is necessary to use the observations from different satellites and detectors at the same time. Eliminating the systematic deviation between different detection systems to assimilate the observations from different sources is essentially required by such researches. In this work, the on-orbit cross-calibration and assimilation for relativistic electron (> 2 MeV) observations from FengYun 4A and GOES-13 are performed. In this work, only the observations obtained under very quiet geomagnetic conditions ( Kp< 2) are adopted to ensure that the objects of study are the radiation belt particles, which are stably captured by the geomagnetic field. According to the physical characteristics of the radiation belt particles, that is, the three adiabatic invariants, and based on the Liouville theorem, the phase space density of the stably captured particles is unchanged. In this paper, the relativistic electron flux data of energy > 2 MeV and instrument pitch angle are in the east and west direction respectively. If the particles’ energy is the same, then their corresponding μvalues are the same, and their particles’ directions are the same, then their corresponding Jvalues are the same, and the Liouville theorem can be simplified as the drift shell L_mis the same, the fluxes are the same, and the electron fluxes observed by the two satellites are compared in the drift shell L_mcoordinate. The systematic deviation between the two satellites’ relativistic electronic observations can be obtained. According to this result, the data assimilation is carried out, and the results show that the system deviation can be removed well. By this research work, the systematic deviation between two important relativistic electron detection systems in geosynchronous orbit is obtained. Based on the obtained systematic deviations, the assimilations for observations from the two detection systems are achieved. This work lays a solid foundation for the follow-up theoretical and applied researches, and also provides the methods for on-orbit cross-calibration and observation assimilation which could be referred to when other electronic observations on geosynchronous orbit are dealt with.