Performance Aspects of Orbit Propagation Using the Unified State Model

The Unified State Model is a method for expressing orbits using a set of seven elements. The elements consist of a quaternion and three parameters based on the velocity hodograph. The equations of this model and the background theory necessary to understand them have been shown here. Numerical simulations comparing the Unified State Model with the traditional Cartesian coordinates have been carried out for perturbed orbits, orbits with low-thrust propulsion, and a solar sailing trajectory. The Unified State Model outperforms Cartesian coordinates for all cases in terms of accuracy and computational speed, except for highly eccentric perturbed orbits. The performance of the Unified State Model is exceptionally better for the case of orbits with continuous low-thrust propulsion with CPU simulation time being an order of magnitude lower than for the simulation using Cartesian coordinates. This makes the Unified State Model especially suited for use in trajectory simulators and optimizers