  The IceCube Neutrino Observatory at the geographic South Pole consists of two
components, a km2 surface array IceTop and a km3 in-ice array between 1.5 and
2.5 km below the surface. Cosmic ray events with primary energy above a few
tens of TeV may trigger both the IceTop and in-ice array and leave a
three-dimensional footprint of the electromagnetic and muonic components in the
extensive air shower. A new reconstruction based on the minimization of a
unified likelihood function involving quantities measured by both IceTop and
in-ice detectors was developed. This report describes the new reconstruction
algorithm and summarizes its performance tested with Monte Carlo events under
two different containment conditions. The advantages of the new reconstruction
are discussed in comparison with reconstructions that use IceTop or in-ice data
separately. Some possible improvements are also summarized.
