  In the future International Linear Collider (ILC) experiment, high
performance tracking is essential to its physics program including precision
Higgs studies. One of major challenges for a detector such as the proposed
International Large Detector (ILD) is to provide excellent momentum resolution
in a magnetic filed with small (but non-negligible) non-uniformity. The
non-uniform magnetic field implies deviation from a helical track and hence
requires the extension of a helical track model used for track fitting in a
uniform magnetic field. In this paper, a segment-wise helical track model is
introduced as such an extension. The segment-wise helical track model
approximates the magnetic field between two nearby measurement sites to be
uniform and steps between the two sites along a helix. The helix frame is then
transformed according to the new magnetic field direction for the next step, so
as to take into account the non-uniformity of the magnetic field. Details of
the algorithm and mathematical aspects of the segment-wise helical track model
in a Kalman-filter-based track fitting in the non-uniform magnetic field are
elaborated. The new track model is implemented and successfully tested in the
framework of the Kalman filter tracking software package, KalTest, which was
originally developed for tracking in a uniform magnetic field.
