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Session D1: Space Navigation and Observation

Systematic Error Analysis of Calculation Error of Starlight Refraction Angle
Zhang Shaoxiong, Beihang University, China
Location: Galleria I/II
Alternate Number 3

Satellite positioning based on starlight refraction angle is a well-received method navigation method started decades ago. Compared with other navigation methods such as radio navigation and horizon-based navigation, starlight refraction has the advantages of lower hardware costs, independent of the outside support, low possibility to be interfered with and the potential of exoplanet navigation and so on. The prerequisite of atmospheric starlight refraction navigation is to obtain the relationship between starlight refraction angle and atmospheric state or apparent altitude, However, both the analytical formula, empirical formula and trained neural network ignore the comprehensive influence of atmosphere on the whole refraction path. There is no doubt that these preconditions will eventually show up in navigation errors. In view of the above problems, this paper focuses on the error analysis of the original starlight refraction formula. And studies the formula the influence of different mathematical simplification methods on the calculation result of refraction angle during the process of obtaining the formula, so as to better analysis the size of the navigation error of the system. It is found that three simplified assumptions are introduced in the derivation of the formula of refraction angle, which are spherical distribution of atmosphere, approximate treatment and isothermal atmosphere model. The three are in a progressive relationship. Firstly, we separate the three hypotheses and analyze the change of the formula for calculating the refraction angle after stripping one hypothesis. Then, we obtain the continuous variation of atmospheric data by interpolation based on exponential function. Thirdly, the atmospheric data obtained are substituted into different formulas for calculating the refraction angle, and the results are compared. Analysis show that among the three simplification measures, approximate treatment has the largest impact, about 10%.

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