An initial orbit determination method from relative position increment measurements

摘要

Both Global Navigation Satellite Systems and X-ray pulsar-based navigation system use relative position information to provide accurate spacecraft navigation. To supplement that navigation information, an absolute reference position from other types of measurements should be provided; however, that may increase the complexity or decrease the autonomy of the navigation system. To overcome those drawbacks, this paper proposes an initial orbit determination method using only relative position increment measurements and their corresponding epoch. The proposed method can be summarised as three steps: first, determining the orbital plane from a set of relative position vectors; next, determining the shape of the orbit by solving an ellipse fitting problem in two dimensions; finally, estimating the absolute position and all six orbital elements according to Kepler's equation and geometric relations. Monte Carlo simulations were done to analyse the feasibility and features of the proposed method. The results show that the algorithm we used does not need an initial guess and is robust. It can obtain an acceptable result from a 20% portion of an orbit when the signal-to-noise ratio is set at 15dB with determining the inclination and right ascension of the ascending node quickly and accurately.