Optimal Design of Satellite Formation Relative Motion Orbits Using Least-Squares Methods Academic Article uri icon


  • Formation flying relative orbit design can be 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 using 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 of the equations of motion of the two satellites. Numerical results are presented to demonstrate the applications of the two approaches. Copyright © 2008 by H. Yan, K. T. Alfriend, S. R. Vadali, and P. Sengupta. Published by the American Institute of Aeronautics and Astronautics, Inc.

author list (cited authors)

  • Yan, H., Alfriend, K. T., Vadali, S. R., & Sengupta, P.

citation count

  • 20

publication date

  • March 2009