Rotation based analytic range-only initial relative orbit solution for natural periodic motion

Range-only Initial relative orbit determination (IROD) for natural-periodic relative motion (periodically coasting flight) during close-in proximity suffers from a mirror-solution (also named orbital ambiguity) problem if linear relative dynamics is used to propagate the orbit. Approaches proposed in previous work were to perform specific orbital maneuvers, measure by double range-sensor or utilize prior information so as to avoid mirror solutions. Alternatively, if the range-sensor offset from the vehicle center-of-mass (COM) is included, the range-only IROD problem may be uniquely solved. This research develops a novel solution to the range-only IROD problem for natural periodic motion in the context of Clohessy-Wiltshire dynamics, where the range-sensor offset is included to provide state observability to exclude the mirror solutions and certain attitude maneuver is introduced to construct analytic solution. Therefore, the range-only IROD is reduced to a problem of solving linear equations. The uniquely analytic solution is achieved based on these equations. Three rotation schemes for attitude maneuver are analyzed among which the y-mirror rotation scheme is proven to be effective for de-ambiguity. The proposed algorithm is verified and tested by a set of Monte Carlo simulations. The sensitivity of the solution accuracy to different orbits, range-sensor offset, ranging accuracy, rotating accuracy and measurement span is presented and discussed.