Optimal Design of Satellite Formation Relative Motion Orbits Using Least-Squares Methods

Formation flying relative orbit design can he achieved by determining six initial conditions in the local-vertical-local-horizontal frame or, equivalently, six differential orbital elements. In this paper, two novel approaches are proposed to design perturbed satellite formation relative motion orbits rising least-squares techniques. First, it is shown that the initial conditions required to approximate a desired formation geometry can be analytically solved for by using the Gim-Alfriend state transition matrix in conjunction with a linear least-squares approach. An improvement to this method is obtained by using the Gaussian least-squares differential correction approach and numerical integration or the equations of motion or the two satellites. Numerical results are presented to demonstrate the applications of the two approaches.