Time-Varying Directional State Transition Tensor for Orbit Uncertainty Propagation

TL;DR

This paper introduces a time-varying directional state transition tensor (TDSTT) for orbital uncertainty propagation, enabling analysis at any time with high accuracy and significantly improved computational efficiency over existing methods.

Contribution

The paper proposes a novel TDSTT that computes sensitive directions dynamically, enhancing the accuracy and speed of orbital uncertainty propagation compared to static DSTT and traditional STT methods.

Findings

TDSTT achieves nearly the same accuracy as STT and DSTT.

TDSTT is approximately 94% faster than STT.

TDSTT offers hundreds of times speed improvement over DSTT.

Abstract

The directional state transition tensor (DSTT) reduces the complexity of state transition tensor (STT) by aligning the STT terms in sensitive directions only, which provides comparable accuracy in orbital uncertainty propagation. The DSTT assumes the sensitive directions to be constant during the integration and only works at a predefined epoch. This paper proposes a time-varying STT (TDSTT) to improve the DSTT. The proposed TDSTT computes the sensitive directions with time; thereby, it can perform uncertainty propagation analysis at any point instead of only a predefined epoch as the DSTT does. First, the derivatives of the sensitive directions are derived. Then, the differential equations for the high-order TDSTTs are derived and simplified using the orthogonality of sensitive directions. Next, complexity analysis is implemented to show the advantages of the proposed TDSTT over the STT. Finally, the TDSTT is applied to solve orbital uncertainty propagation problems in highly nonlinear three-body systems. Numerical results show that the proposed TDSTT can yield nearly the same level of accuracy as the STT and DSTT. It is approximately 94% faster than the STT and has hundreds of improvements in speed over the DSTT when one wants to investigate the evolutions of orbital uncertainties.