We describe the strategy of the track reconstruction with the Kalman filter in the forward region of the DELPHI experiment. We point out various mathematical and technical problems which arise in an environment characterized by high track multiplicities and low density of measurements, and we present the solutions which we have adopted. It is shown using simulated data that the outlier algorithm developed in this context, in combination with an appropriate decision logic, leads to a considerable improvement in the reconstruction of the global event topology.