Optimal design of satellite formation relative motion orbits using least squares methods
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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 satellite formation relative motion orbits using least squares techniques. First, it is shown that the initial conditions required to approximate desired formation geometry can be analytically solved for by using the Gim-Alfriend state transition matrix in conjunction with a linear least square approach. An improvement to the first method is obtained by utilizing the Gaussian least squares differential correction approach and numerical integration of the equations of motion of the two satellites. Numerical results demonstrate the applications of the two approaches.
