Towards covariance realism in batch least-squares orbit determination

Abstract

Regular products within the field of Space Surveillance and Tracking (SST) and Space Traffic Management (STM), such as high-risk collisions, upcoming re-entries or fragmentations, rely both on the estimated state and associated uncertainty of detectable resident space objects (RSOs). Classical orbit determination (OD) algorithms provide the required estimations, assuming that the uncertainty in the state of the object is properly characterized by its state vector covariance and assuming Gaussian processes. However, a common problem of classical orbit determination processes is the misrepresentation of the RSOs uncertainty through the estimated covariance. Ultimately, this causes a great impact in the quality and accuracy of SST products as the estimated covariance is overly optimistic (too small) and the true uncertainty of the object is not captured. One of the causes for the unrealism of the estimated covariance is found in the classical OD approaches, as they fail to consider, or properly characterize, the uncertainty of the dynamical models used to describe the motion of the objects, such as the atmospheric drag force or the solar radiation pressure acting on the orbiting RSOs. Because these models provide a deterministic solution to a stochastic phenomenon, an inherent associated uncertainty should be regarded when used during an orbit determination. The aim of this work is to devise a methodology to improve the covariance realism of common OD processes through the classical theory of consider parameters of batch least squares methods. The methodology uses the classical theory of consider parameter to add to the estimated covariance the contribution coming from the uncertainty of the consider parameters. To do so, the variances of the consider parameters are estimated through another least squares process, with which the propagated covariance best fits a so-called observed covariance, previously derived, in a process named covariance determination. The influence of the main sources of dynamic model uncertainty can be evaluated by examining the resulting covariance correction for each uncertainty source (e.g. atmospheric drag force modelling, sensor calibration parameters or solar radiation prediction). This publication focus on studying the effect of the atmospheric drag force and range bias modelling uncertainty in the correction of an estimated covariance. The proposed methodology has been applied to a simulated realistic scenario of measurements and objects to evaluate the consistency of the corrected covariance via Monte Carlo analysis. Thorough analyses are presented to illustrate the effect of dynamic model errors on covariance realism. Copyright © 2019 by the International Astronautical Federation (IAF). All rights reserved.