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 utilizes Gaussian mixtures 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 mixtures and binary hypothesis testing is developed. 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 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.

Optimized Measurement Timing for In-Space Thrust Inference

“…Alternative approaches utilize different assumptions regarding the maneuver optimality or functional form to improve the detection and characterization process. Optimal control distance metrics enable improved correlation between object observations and inherently detect and characterize the maneuver if the spacecraft is assumed to perform maneuvers in an energy-optimal manner [13][14][15]. Filter-based approaches represent an unknown maneuver using a finite Fourier series [16] or polynomial approximation [17] and represent the unknown function coefficients as state variables.…”

Cognitive Systems Engineering Applied to Decision Support in Space Situational Awareness

“…The sensor tasking problem is a high-dimensional, multiobjective, mixed-integer, nonlinear optimization problem, and current approaches focus on tractable subproblems (e.g., single objectives, limited target objects, limited sensors). Potential SSA sensor tasking needs include maintaining catalogs of space object state observations (DeMars, Hussein, Frueh, Jah, & Scott Erwin, 2015; Hobson, 2014), detecting maneuvers or other anomalies (Jaunzemis, Mathew, & Holzinger, 2016), and estimating control modes or behavior (Coder, Holzinger, & Linares, 2018; Hart et al, 2016; Holzinger, Wetterer, Luu, Sabol, & Hamada, 2014). These objectives are generally not complementary, especially given limited sensor resources, and the different objectives require different tasking approaches; for instance, characterization (e.g., anomaly detection) prefers many observations of a small subset of the catalog, whereas catalog maintenance prefers a diverse set of observations from as many objects as possible.…”