Cardiac reentrant arrhythmias may be examined by using time-series analysis, where a state variable is plotted against the same variable with an embedded time delay tau to form a phase portrait. The success of this procedure is contingent upon the resultant phase-space trajectories encircling a fixed origin. However, errors in interpreting the dynamics of phase singularities associated with reentry may arise due to the trajectories not encircling the origin or due to a poor choice of tau. We demonstrate an algorithm which is capable of establishing proper orbits without the need to specify tau. We find that phase singularities could be localized closer to the point of initial formation than was possible previously, which is important for the purposes of singularity tracking and investigating electrodynamic interactions.