A random error estimation method for satellites being launched into orbit based on ellipsoid theory

Abstract

Accurate and fast random error estimation is essential to improve satellite control. In this paper, the random error of the satellite being launched into orbit is explored. According to the uncertainty matrix of six satellite orbit parameters associated with the project, the uncertainty of the orbit position in the three axes of the geocentric inertial frame of reference is calculated via the propagation rate of the covariance matrix. Then, the random error probability density of the satellite position is constructed for normal distribution. The surface of the error with the same probability density is approximated as an ellipsoid, the size is deduced along with the ellipsoid's shape and direction, and the satellite's spatial position probability is obtained. Monte Carlo method and STK software were employed to simulate low-earth orbit micro-nano satellite launching into the same orbital position. It is confirmed that the results obtained via the theoretical model are in line with practice. Therefore, the ellipsoid theory proposed in this paper can be used to describe the satellite random position error.