  In this note we present a mathematical framework for a rigorous approach to a
common track fit for trackers located in the inner region of the ZEUS detector.
The approach makes use of the Kalman filter and offers a rigorous treatment of
magnetic field inhomogeneity, multiple scattering and energy loss. We describe
mathematical details of the implementation of the Kalman filter technique with
a reduced amount of computations for a cylindrical drift chamber, barrel and
forward silicon strip detectors and a forward straw drift chamber. Options with
homogeneous and inhomogeneous field are discussed. The fitting of tracks in one
ZEUS event takes about of 20ms on standard PC.
