A Celestial Navigation Method for Endo-atmospheric Flight Vehicle Using Starlight Refraction

For vehicles flying in the atmosphere, the traditional positioning method based on stellar refraction has a large error, as the measured starlight does not exit the atmosphere and its path does not meet the symmetry requirement. To reduce the error, this paper presents a new starlight refraction positioning method, which is applicable to the endo-atmospheric flight. First, based on the standard atmospheric model, the exponential atmospheric refractive index model is introduced, and an integral formula of the starlight refractive angle based on that model is derived. In view of the singularity of the integrand, we use the properties of the improper integral to prove that the limit of the integral formula is not divergent. Then, the relationship among the observed starlight refraction angle, refraction apparent height, and the vehicle’s position vector are found by utilizing the integral formula for starlight refraction. Finally, the vehicle’s position can be determined by using the least square method to solve the equations established using that relationship. The simulation results show that this method can significantly improve the positioning accuracy when the vehicle is in the atmosphere.