Characterizing orbit uncertainty due to atmospheric uncertainty

Abstract

In orbit prediction, there exists a need for accurate estimates of the accuracy of a prediction, i.e. the covariance. An accurate covariance is required for any number of purposes but, in particular, for probability of collision analysis. An inaccurate drag model, the primary error in dynamic models, typically leads to a covariance which is too conservative. Thus, a potentially catastrophic orbital collision may not be predicted or, on the other hand, a needless debris avoidance maneuver is performed. Currently, USSPACECOM uses a batch least squares orbit prediction method which assumes a perfect dynamic model, and then uses empirical methods to artificially inflate the covariance. However, these techniques often have no physical basis and are merely based upon operator experience. The study presented in this paper compares the batch least squares process used by USSPACECOM to a Kalman filtering method which incorporates the effects of force model errors. A Gauss-Markov colored-noise process is implemented to model errors in the atmospheric density model. This study shows that the Kalman filter computes a believable and more realistic covariance.