Determination of relative motion of a space object from simultaneous measurements of range and range rate

This tutorial paper considers determination of instantaneous relative motion of a space object, from line-of-sight range and range rate measurements made by sensors fixed to a spacecraft in its proximity. Practical applications of this relative motion determination problem include uncooperative rendezvous prior to docking between space vehicles, capture of out-of-control spacecraft, capture of space debris and asteroids, locating and determining the attitude of space objects, and proximity operations near asteroids and comets. It is shown that the relative attitude of the space object with respect to the observing spacecraft can be determined from line-of-sight range measurements to at least three points on the object being observed, which requires three lidar or radar Doppler sensors. Determining the instantaneous relative translational and angular velocities of the space object also requires range and range rate measurements for at least three distinct points on the object, provided that certain conditions on the locations of the corresponding sensors and directions of their lines of sight are met.