Initial Orbit Determination with Sequential Stellar Aberration Measurements

In this work, we develop a solution to the initial orbit determination (IOD) problem from sequential inter-star angle measurements. With the constantly increasing interest in deep space missions, alternative methods of navigation are gaining more and more attention. Scenarios where classic Earth-based navigation sources are not available require new spacecraft to be able to autonomously detect their own orbit using information accessible in unfamiliar environments. Throughout the Solar System, stars are one of the few sources of information which is always available and the effect of stellar aberration may be used to infer the velocity vector of the orbiting body. In the problem analyzed in this work, the spacecraft measures a single inter-star angle at each time, with the star pair potentially changing from observation to observation. The solution is obtained in two steps: the first aims at providing an initial guess of the orbit by modeling the velocity vector with the Lagrange interpolating polynomial. The second step refines the initial guess by accounting for the two-body dynamics through a propagation approach based on Euler's finite rotation formula. This propagation method reveals to be especially convenient in the StarNAV context, where the knowledge of the position vector is superfluous and its propagation can be avoided.