Adaptive Gaussian Mixture based orbit determination with combined atmospheric density uncertainty consideration

Abstract

Large initial uncertainties in the semi-major axis or force-model uncertainties, such as atmospheric density uncertainty are key drivers of the along-track uncertainty growth. Long propagation times may result in the need to use filtering algorithms for orbit determination that do not reside to the assumption of Gaussianity for state errors but estimate the entire probability density function. Adaptive Gaussian mixture based filters have shown promising results in the past. Previous research in the field of orbit determination using Gaussian mixture filters has restricted its attention to initial uncertainties in the semi-major axis direction. The present paper focuses on the consequences of including realistic, physics-based descriptions of atmospheric density uncertainty into the covariance propagation of the mixture kernels.It is shown that the neglect of process noise, as has been customary for many years, can lead to undesired characteristics of the probability density function (pdf) estimates and that the inclusion of atmospheric density uncertainty process noise, even in cases where it is not the dominant driver of along-track uncertainty growth, is able to correct these deficiencies. For low orbiting satellites with increased ballistic coefficients or small initial uncertainties in the semi-major axis direction, density uncertainty is the dominant driver of the along-track uncertainty increase. Due to its growth that evolves at least cubic in time, situations may arise which require the usage of Gaussian mixtures also for the process noise when working in Cartesian coordinates. The theoretical foundation for this case is elaborated and an algorithm capable of dynamically switching between a single Gaussian and a Gaussian mixture for the density uncertainty process noise is presented.