A validation framework for orbit uncertainty propagation using real satellite data applied to orthogonal probability approximation

This paper presents a validation framework using data for uncertainty propagation techniques for space situational awareness (SSA) applications. In particular, we validate a novel technique for uncertainty propagation, dubbed here as Orthogonal Probability Approximation (OPA) This technique describes the evolution of state/parameter uncertainties, e.g. initial condition and/or drag coefficient, of nonlinear dynamical systems at a future time. This new uncertainty quantification method employs Liouville’s theorem and Chebyshev polynomial approximation to create a functional representation of the probability density function (PDF) at the future time of interest at a fraction of the computational cost of classical high-fidelity uncertainty propagation methods. OPA is first compared against Polynomial Chaos Expansions and Monte-Carlo simulations to numerically demonstrate the accuracy of the method. For the real data validation, two sources of satellite data are used: GRACE navigation data from the Jet Propulsion Laboratory (JPL) database, and FireOPAL ground-based observer provided by Lockheed Martin. In the presented validation framework, the state/parameter uncertainties of resident space objects (RSOs) are propagated by OPA without using any measurements. The maximum likelihood estimate and the uncertainty bounds of the RSO state from OPA are compared with documented estimates and uncertainty bounds obtained from real satellite/object tracking data as well as other uncertainty propagation methods Results indicate successful validation using GRACE navigation data (precise orbit determination in LEO), and FireOPAL sensor tracking data for Yamal 202 (GEO case) and a rocket body of Block-DM satellite with highly elliptical orbit (HEO). The results show the capability of OPA to accurately estimate the states of RSOs in the absence of continuous measurements, and, in addition, the presented framework can be used to validate any uncertainty propagation technique.