  We present a procedure for determination of positions and orbital elements,
and associated uncertainties, of outer Solar System planets. The orbit-fitting
procedure is greatly streamlined compared to traditional methods because
acceleration can be treated as a perturbation to the inertial motion of the
body. These techniques are immediately applicable to Kuiper Belt Objects, for
which recovery observations are costly. Our methods produce positional
estimates and uncertainty ellipses even in the face of the substantial
degeneracies of short-arc orbit fits; the sole a priori assumption is that the
orbit should be bound or nearly so. We use these orbit-fitting techniques to
derive a strategy for determining Kuiper Belt orbits with a minimal number of
observations.
