  We describe systematic ranging, an orbit determination technique especially
suitable to assess the near-term Earth impact hazard posed by newly discovered
asteroids. For these late warning cases, the time interval covered by the
observations is generally short, perhaps a few hours or even less, which leads
to severe degeneracies in the orbit estimation process. The systematic ranging
approach gets around these degeneracies by performing a raster scan in the
poorly-constrained space of topocentric range and range rate, while the plane
of sky position and motion are directly tied to the recorded observations. This
scan allows us to identify regions corresponding to collision solutions, as
well as potential impact times and locations. From the probability distribution
of the observation errors, we obtain a probability distribution in the orbital
space and then estimate the probability of an Earth impact. We show how this
technique is effective for a number of examples, including 2008 TC3 and 2014
AA, the only two asteroids to date discovered prior to impact.
