  This paper presents a novel formulation and solution of orbit determination
over finite time horizons as a learning problem. We present an approach to
orbit determination under very broad conditions that are satisfied for n-body
problems. These weak conditions allow us to perform orbit determination with
noisy and highly non-linear observations such as those presented by range-rate
only (Doppler only) observations. We show that domain generalization and
distribution regression techniques can learn to estimate orbits of a group of
satellites and identify individual satellites especially with prior
understanding of correlations between orbits and provide asymptotic convergence
conditions. The approach presented requires only visibility and observability
of the underlying state from observations and is particularly useful for
autonomous spacecraft operations using low-cost ground stations or sensors. We
validate the orbit determination approach using observations of two spacecraft
(GRIFEX and MCubed-2) along with synthetic datasets of multiple spacecraft
deployments and lunar orbits. We also provide a comparison with the standard
techniques (EKF) under highly noisy conditions.
