Development of a state transition matrix for relative motion using the unit sphere approach
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With the desire to be able to have accurate solutions for relative motion, Hill's equations are insufficient for long-term prediction due to the spherical Earth, circular reference orbit and linearization assumptions. Using differential orbital elements, the Gim-Alfriend state transition matrix (STM) incorporates 1 st order J 2 and eccentricity effects in the equations with the assumption of linearization. In this paper, we use the unit sphere method to get the exact kinematic description for relative positions and develop a high accuracy STM for relative motion.
author list (cited authors)
Yan, H., Sengupta, P., Vadali, S., & Alfriend, K. T.