The IceCube project has transformed 1 km3 of deep natural Antarctic ice into a Cherenkov detector. Muon neutrinos are detected and their direction is inferred by mapping the light produced by the secondary muon track inside the volume instrumented with photomultipliers. Reconstructing the muon track from the observed light is challenging due to noise, light scattering in the ice medium, and the possibility of simultaneously having multiple muons inside the detector, resulting from the large flux of cosmic ray muons. This paper describes work on two problems: (1) the track reconstruction problem, in which, given a set of observations, the goal is to recover the track of a muon; and (2) the coincident event problem, which is to determine how many muons are active in the detector during a time window. Rather than solving these problems by developing more complex physical models that are applied at later stages of the analysis, our approach is to augment the detector's early reconstruction with data filters and robust statistical techniques. These can be implemented at the level of on-line reconstruction and, therefore, improve all subsequent reconstructions. Using the metric of median angular resolution, a standard metric for track reconstruction, we improve the accuracy in the initial reconstruction direction by 13%. We also present improvements in measuring the number of muons in coincident events: we can accurately determine the number of muons 98% of the time.