Least squares orbit estimation including atmospheric density uncertainty consideration

Abstract

Density uncertainty is the major driver of unrealistic covariances for objects in low Earth orbits. The analytic propagation of uncertainties in the neutral atmospheric density to resulting uncertainties in the orbital position and velocity has only received little attention in the literature so far.The main contribution of the paper at hand is the analytic development of an orbital state-vector error variance-covariance matrix that models the propagation of uncertainties in atmospheric density to the orbital state-vector error in the Geocentric Celestial Reference Frame (GCRF). Also extensions of the classical batch weighted least squares (WLS) and the sequential batch weighted least squares algorithms, which allow to incorporate this covariance matrix as process-noise, are presented.Numerical simulations with three different semi-empirical models are provided to validate the derivations. It is shown that the extension of the WLS-algorithm in combination with the density uncertainty GCRF covariance matrix is able to consistently perform orbit and covariance estimation, which is not the case without density uncertainty consideration in a classical WLS algorithm.