A Celestial Analytic Positioning Method by Stellar Horizon Atmospheric Refraction

This article, in allusion to the limitation of conventional stellar horizon atmospheric refraction based on orbital dynamics model and nonlinear Kalman filter in practical applications, proposes a new celestial analytic positioning method by stellar horizon atmospheric refraction for high-altitude flight vehicles, such as spacecraft, airplanes and ballistic missiles. First, by setting up the geometric connexion among the flight vehicle, the Earth and the altitude of starlight refraction, an expression for the relationship of starlight refraction angle and atmospheric density is deduced. Second, there are produced a novel measurement model of starlight refraction in a continuous range of altitudes (CRA) from 20 km to 50 km on the basis of the standard atmospheric data in stratosphere, and an empirical formula of stellar horizon atmospheric refraction in the same altitudes against the tangent altitude. Third, there is introduced a celestial analytic positioning algorithm, which uses the least square differential correction instead of nonlinear Kalman filter. The information about positions of a flight vehicle can be obtained directly by solving a set of nonlinear measurement equations. The stellar positioning algorithm adopts the characteristics of stellar horizon atmospheric refraction thereby removing needs for orbit dynamics models and priori knowledge of flight vehicles. The simulation results evidence the validity of the proposed stellar positioning algorithm.