Kernel-based ensemble gaussian mixture filtering for orbit determination with sparse data

Abstract

In this paper, a modified kernel-based ensemble Gaussian mixture filtering (EnGMF) is introduced to produce fast and consistent orbit determination capabilities in a sparse measurement environment. The EnGMF is based on kernel density estimation (KDE) to combine particle filters and Gaussian sum filters. This work proposes using Silverman’s rule of thumb to reduce the computational burden of KDE. Equinoctial orbital elements are used to improve the accuracy of the KDE bandwidth parameter in the modified EnGMF. A bi-fidelity approach to propagation and an adaptation algorithm for selecting the appropriate number of particles are also applied to the EnGMF to reduce the computational burden with an acceptable loss in accuracy for long time propagation. Through numerical simulation, the proposed implementation is compared to state-of-the-art approaches in terms of accuracy, consistency, and computational speed.