Short arc ephemeris determination by a coplanar angle sensing tracker

A problem of some interest concerns the timely ephemeris determination of a space object relative to a known satellite able to detect its line of sight through use of an angles sensing tracker. This can usually be accomplished with three independent angular elevation and azimuth readings, or similarly, readings at a particular time epoch of elevation and azimuth and their time rates and accelerations. This process breaks down under certain geometric conditions, the most severe occurring whenever the object and sensing satellite follow coplanar trajectories. To provide an ephemeris solution in this case, a fourth elevation input is required, or equivalently the elevation acceleration rate (or jerk) at the time epoch. This paper generalizes the simple equations normally used for object ephemeris determination to the more complex set required to also provide solutions for the coplanar sensor-object case. Several examples are provided illustrating the use of these equations. While the coplanar singularity can now be avoided, target ephemeris solutions are generally not unique, and are very sensitive to angular sensor inaccuracies for short tracking arcs. Nevertheless, the solution of these more general equations can often provide useful initial conditions for the recursive ephemeris estimator normally used to precisely locate space objects.