A simultaneous track finding / fitting procedure based on Kalman filtering approach has been developed for the forward muon spectrometer of ALICE experiment. In order to improve the performance of the method in high-background conditions of the heavy ion collisions the "canonical" Kalman filter has been modified and supplemented by a "smoother" part. It is shown that the resulting "extended" Kalman filter gives better tracking results and offers higher flexibility. To further improve the tracking performance in a high occupancy environment a new algorithm for cluster / hit finding in cathode pad chambers of the muon spectrometer has been developed. It is based on the expectation maximization procedure for a shape deconvolution of overlapped clusters. It is demonstrated that the proposed method allows to reduce the loss of the coordinate reconstruction accuracy for high hit multiplicities and achieve better tracking results. Both the hit finding and track reconstruction algorithms have been implemented within the AliRoot software framework.