Jeffrey M. Aristoff (Numerica Corporation), Joshua T. Horwood (Numerica Corporation), Aubrey B. Poore (Numerica Corporation)
Keywords: SSA
Abstract:
Accurate and efficient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. Existing numerical methods used for orbit propagation are explicit. As such, they cannot exploit the proximity of nearby orbits when propagating uncertainty in the state of an orbiting object (satellite, debris, etc.), for example, as part of the prediction step of the unscented Kalman filter (UKF). As surveillance demands continue to increase, owing in part to improved sensors and the continuously growing amount of space debris, alternative numerical methods should be considered that are able to efficiently propagate uncertainty, as well as take advantage of modern computing architectures.
We have developed an adaptive, implicit Runge-Kutta-based method for uncertainty propagation that is superior to existing explicit methods, even before the algorithm is potentially parallelized. Specifically, we demonstrate the reduction in the computational cost of propagating the 13 sigma points needed to represent uncertainty (of a six-dimensional Gaussian state) in the UKF. For a typical low Earth orbit, the new propagator is able to reduce the computational cost by 70-90% in a serial computing environment, compared to that using Adams-Bashforth-Moulton (an explicit multi-step method) and Dormand-Prince 8(7) (an explicit Runge-Kutta method). In a parallel computing environment, we are able to reduce the cost by 97-99%. Thus, in some cases we can propagate uncertainty via the UKF at no additional computational cost compared to that of propagating a single orbital state, even when restricted to a serial processor. The new propagator is applicable to all regimes of space, and additional features include its ability to estimate and control the truncation error, exploit analytic and semi-analytic approximations to the dynamics, and provide accurate ephemeris data via built-in interpolation.
Date of Conference: September 11-14, 2012
Track: Poster