Precise short- and long-term propagation of orbits and uncertainties using the Hermite integration scheme for LEO space debris objects

Kurzfassung

The Institute of Technical Physics of the German Aerospace Center (DLR) is actively developing laser-based optical tracking methods to determine 3D positions of LEO space debris objects to within 10 metres to support several SSA-related use cases, e.g. conjunction assessment, maneuver detection, or analysis of re-entry events. For the purpose of precise orbit determination and the subsequent propagation of states and their uncertainties, an accurate, fast, and versatile integration method is needed. We will present a numerical integration technique based on the Hermite scheme, a self-starting, implicite predictor-corrector method originally developed and widely used for gravitational N-body systems. The Hermite scheme uses the acceleration and its first time derivative to predict future position and velocity vectors from previous values. The gist of the method relies on the fact that the second and third derivatives can be explicitly calculated from the acceleration and its first derivative alone. These are then used iteratively to correct the object's state vector, yielding an integration method with fourth-order global error. The method can be used with constant or variable timesteps. In the case of constant timesteps, the Hermite integrator is time-symmetric and shows no secular error in the semi-major axis and eccentricity, which makes the integrator extremely useful for long-term dynamical simulations. The code can integrate an ensemble of objects in parallel, with either shared or individual timesteps. It can therefore be applied to propagate a catalogue of space objects and/or to perform realistic uncertainty propagation via Monte-Carlo or sigma-point methods. We will show current results from our orbit propagator development which is geared towards LEO space debris objects and discuss the implementation of the force model.