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.

中文翻译：

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考虑太阳特征的天多普勒差分测速导航建模与分析

传统方法将太阳视为刚性球体和漫反射器，而忽略了太阳特性。然而，这导致测量模型中的高偏差。在这项研究中，为了建立更现实的偏差模型和噪声统计模型，作者考虑了三个太阳特征，包括太阳差旋转，兰伯特辐射器和小规模太阳活动。经过数学推导，建立了考虑太阳差旋转和兰伯特辐射器的太阳多普勒差测量的偏差模型。仿真结果表明，所提出的偏差模型与传统偏差模型之间的差异约为0.1-1 m / s，这是缓慢变化且不可忽略的。因此，考虑太阳差旋转和兰伯特辐射器的偏差模型是有意义的。经过数学分析，他们还发现小规模的太阳活动在太阳多普勒差异测量中引起极低的误差。而且，多普勒差的噪声在2m / s以内。由于小规模太阳活动的随机性，由活动引起的极低误差可被视为噪声。这些结果为太阳多普勒差分测速导航的测量建模提供了参考。