Geometry Error Analysis in Solar Doppler Difference Navigation for the Capture Phase

Deep space exploration missions continue to become more ambitious, driving the need to investigate autonomous navigation systems that are accurate and timely. The solar Doppler difference navigation is a newly developed and promising celestial autonomous navigation method for use, particularly, in the crucial capture period. In this paper, we present novel analyses for three error sources for the solar Doppler difference navigation from the perspective of geometry, motivated with a Mars deep space exploration example. The geometry error sources include the area overlap rate of the direct and the reflected solar light sources, the spread effects related to the time difference of arrival (TDOA) of light, and the solar rotation Doppler difference error. The area overlap rate and the spread effects of the TDOA can be utilized to assess the overlap degree of the direct source and the reflected source in both space and time. Theoretical analyses and simulation results demonstrate that the direct and the reflected light sources can be accurately approximated as the same source. The solar rotation Doppler difference error is explored using a velocity error model. This model forms a hemi-ellipsoid that can be utilized to compensate the Doppler error caused by the solar rotation. The three errors decline with the deep space explorer approaching Mars, which means that the performance of the solar Doppler difference navigation method continuously improves in the critical capture period. These results can offer a reference for the system design of the solar Doppler difference navigation.