Angles-Only Initial Orbit Determination via Multivariate Gaussian Process Regression

Abstract

Vital for Space Situational Awareness, Initial Orbit Determination (IOD) may be used to initialize object tracking and associate observations with a tracked satellite. Classical IOD algorithms provide only a point solution and are sensitive to noisy measurements and to certain target-observer geometry. This work examines the ability of a Multivariate GPR (MV-GPR) to accurately perform IOD and quantify the associated uncertainty. Given perfect test inputs, MV-GPR performs comparably to a simpler multitask learning GPR algorithm and the classical Gauss–Gibbs IOD in terms of prediction accuracy. It significantly outperforms the multitask learning GPR algorithm in uncertainty quantification due to the direct handling of output dimension correlations. A moment-matching algorithm provides an analytic solution to the input noise problem under certain assumptions. The algorithm is adapted to the MV-GPR formulation and shown to be an effective tool to accurately quantify the added input uncertainty. This work shows that the MV-GPR can provide a viable solution with quantified uncertainty which is robust to observation noise and traditionally challenging orbit-observer geometries.