Control Cost and Mahalanobis Distance Binary Hypothesis Testing for Spacecraft Maneuver Detection

Abstract

An anomaly hypothesis testing technique using the minimum-fuel control distance metric is extended to incorporate non-Gaussian boundary-condition uncertainties and employ binary hypothesis testing. The adjusted control distance metric uses Gaussian-mixture models to model non-Gaussian boundary conditions, and binary hypothesis testing allows inclusion of anomaly detection thresholds and allowable error rates. An analogous framework accommodating Gaussian-mixture models and binary hypothesis testing is developed using Mahalanobis distance. Both algorithms are compared using simulated and empirical satellite maneuver data. The north–south station-keeping scenario shows control distance to be less sensitive with increased uncertainty than Mahalanobis distance but more consistent with respect to observation gap duration, a trend which is corroborated using available real-world data. The same consistency with respect to observation gap is observed in East–west station-keeping while also showing the control distance metric to be more sensitive for shorter observation gaps. In the non-Gaussian boundary-condition case, control distance outperforms Mahalanobis distance in both detection and computational complexity. A synergistic operational application of these methods is presented.