  We present an alternative implementation of the Kalman filter employed for
track fitting within the LHCb experiment. It uses simple parametrizations for
the extrapolation of particle trajectories in the field of the LHCb dipole
magnet and for the effects of multiple scattering in the detector material. A
speedup of more than a factor of four is achieved while maintaining the quality
of the estimated track quantities. This Kalman filter implementation could be
used in the purely software-based trigger of the LHCb upgrade.
