Maneuver-free approach to range-only initial relative orbit determination for spacecraft proximity operations

Range-only relative orbit determination for spacecraft proximity operations suffers from a well-known mirror solution problem in the context of Clohessy-Wiltshire dynamics during coasting flight. One approach proposed in previous work is to perform specific orbital maneuvers so as to avoid ambiguous relative state estimates. Alternatively, if the range-sensor offset from the spacecraft center-of-mass (COM) is considered, the relative orbit may be determined by using range-only measurements. This research developed a maneuver-free analytic solution to the range-only initial relative orbit determination (TROD) problem for close-in proximity operations by utilizing the range-sensor offsetting for enhanced observability to exclude mirror solutions. As a result, the initial relative orbit determination is reduced to a problem of solving linear equations. Based on these equations, the relative state observability is explored and observable conditions with respect to the range-sensor offset are obtained. The uncertainty of the relative orbit estimation is also derived, given as approximate analytic mean and covariance solutions. Overall, it has been strictly theoretically proven the range-only problem of non-periodic coasting close-in operations can be analytically solved. All these theoretical results are verified by a set of numerical simulation examples.