Geometric Error Analysis And Modeling Of Solar Differential Navigation

In traditional astronomical navigation methods,solar spectrum is usually used for Doppler velocity measurement.However,when the solar flare or sunspot and other activities occur,the solar spectrum will change dynamically,which reduce the accuracy of velocity measurement.In order to solve this problem,the solar differential navigation method has been proposed and received extensive attention.Among them,the solar Doppler differential velocity measurement navigation method is based on the Doppler velocity difference between the direct light and the reflected light,and the solar arrival time difference method is based on the arrival time difference between the direct light and the reflected light to carry out differential ranging.Both of these two differential navigation methods can solve the optical errors caused by the instability of the sunlight.However,there are still error factors that have not been analyzed in the differential solar navigation method.Therefore,further study on the impact factors of the differential solar navigation method is of great significance to improve the accuracy of the method.In the solar differential navigation system composed of the sun,the target celestial body and the spacecraft,the accuracy of the measurement model directly determines whether the spacecraft can successfully complete the detection mission.Solar direct spectrum and reflection spectrum are the key measurement values of differential navigation method,so the factors that cause the variation of solar spectrum may reduce the accuracy.For this reason,this paper analyzes two major geometric error factors that lead to the variation of solar spectrum and then affect the navigation accuracy: light reflectivity and Doppler frequency shift caused by the movement of the target object,and does the corresponding work:(1)Taking Mars as the target celestial body,the light reflectance analysis model of differential solar navigation is proposed.In the solar difference navigation system composed of the sun,Mars and spacecraft,light reflectance on the Martian surface to the photon on the solar surface is a significant factor that has a bearing on the solar difference navigation,which changes under the restriction of geometric relationship.To analyze the impact of light reflectance on difference navigation,a model of light reflectance analysis is proposed in this paper.With Mars regarded as a reflector,the ratio of the photon’s incident area to the reflection area is used as the light reflectance,and a basic model of light reflectance analysis is established through integral calculus and stereometry.To lower the computational complexity of the basic model,simplified model of light reflectance analysis can be simulated from the maximum and minimum reflectance through optimized calculation.Simulation results show that light reflectance is mainly affected by geometric distribution parameters in the difference navigation system,and the analysis model can provide the basis for the accuracy computation of solar difference navigation.(2)Taking the moon as the target celestial body,the Doppler frequency shift of the reflected light of the differential solar navigation with the motion of the moon is analyzed.Due to the movement of the moon,Doppler frequency shift of reflected light will happen during the process from emitted to received by the spacecraft,which will affect the analysis of the received spectrum on the spacecraft.In order to analyze the Doppler shift distribution caused by the motion of the moon,the velocity of the reflecting point under different lunar rotation axes is analyzed,and the formula for calculating the Doppler red shift value caused by the motion of any reflecting point on the moon surface is derived based on the Doppler shift principle of the motion of the reflector,then the Doppler shift distribution of the reflected light caused by the motion of the moon is simulated by experiments.The experiments show that the moon-spacecraft distance,the sun-moon-spacecraft angle and the velocity of the moon affect the Doppler shift distribution,which can provide compensation for the analysis of the reflected light in the solar differential navigation measurement model.