Modelling and analysis of celestial Doppler difference velocimetry navigation considering solar characteristics

Abstract

The traditional method considers the Sun as a rigid sphere and diffuse radiator, and neglects the solar characteristics. However, this leads to high bias in the measurement model. In this study, to build a more realistic bias model and a statistical model of noise, the authors consider three solar characteristics, including the solar differential rotation, Lambert radiator and small-scale solar activities. After mathematical derivation, the bias model of the solar Doppler difference measurement considering the solar differential rotation and Lambert radiator is built. Simulation results demonstrate that the difference between the proposed bias model and the traditional one is on the order of 0.1–1 m/s, which is slowly-varying and non-ignorable. Therefore, the bias model considering the solar differential rotation and Lambert radiator is meaningful. After mathematical analysis, they also find that small-scale solar activities cause an extremely low error in the solar Doppler difference measurement. Moreover, the noise of the Doppler difference is within 2 m/s. Due to the randomness of small-scale solar activities, the extremely low errors caused by activities can be regarded as noises. These results provide a reference for the measurement modelling of the solar Doppler difference velocimetry navigation.