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.

published proceedings


author list (cited authors)

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

citation count

  • 21

complete list of authors

  • Yan, Hui||Alfriend, Kyle T||Vadali, Srinivas R||Sengupta, Prasenjit

publication date

  • March 2009