Catalog-Based Atmosphere Uncertainty Quantification

Abstract

Due to the ever-increasing space objects population, space situational awareness products and services have become the cornerstone for the safety and sustainability of spacecraft operations. Most of these services rely on the characterization of the uncertainty of the system, which is known as uncertainty quantification. In many applications the uncertainty of the orbit state is represented by the covariance matrix, obtained from an orbit determination (OD) process. However, typical OD processes usually consider the measurements noise as the only source of uncertainty. An unrealistic characterisation of the uncertainty of dynamical and observations models leads to a degradation of the realism of the covariance, and jeopardizes spacecraft operations. In this work, we apply our recent methodology for covariance realism improvement, based on the consider parameter theory of batch least-squares methods, to a catalog scenario to derive the uncertainty of the atmospheric drag model. This methodology infers the variance of consider parameters based on the observed distribution of the Mahalanobis distances of the orbital differences between predicted and estimated orbits, which theoretically should follow a chi-square distribution under Gaussian assumptions. Empirical distribution function statistics such as the Cramer-von-Mises or the Kolmogorov-Smirnov distances are used to determine optimum variances of such parameters for covariance realism. The main objective of this work is to adapt and test the previously developed methodology to a LEO catalog scenario, in which the evolution of the density uncertainty for multiple objects can be analysed together by modelling such uncertainty as a consider parameter. Thus, instead of estimating the variances of the consider parameters tailored to a single object during a long period, the objective of this work is to determine variances of parameters of an parametric model for the atmospheric density uncertainty, improving the covariance realism for different clusters of cataloged objects (i.e. different altitudes or ballistic coefficient). Altitude-dependent models of the atmospheric density uncertainty, based on statistical analysis of historic space weather data, are applied for realistic simulations together with space-correlated density perturbations. Results are presented focusing on the physical interpretation of the determined consider parameter model variances and their effectiveness for improving the covariance realism of the considered catalog of objects.