In the paper issues related to the identification of the basic parameters of the two-mass mechanical system are presented. After brief introduction the motivation of the work is introduced. The advanced control structures used in order to damp the torsional vibration are shortly described. Then the mathematical model of the drive is demonstrated. Next the extended Kalman filter is briefly described. Then the concept of multi-layer Kalman filter based estimator is presented. The proposed estimator is used to estimate the mechanical parameters of the drive. Then they are used in order to design the closed-loop control structure. The proposed solution is tested in simulation as well as experimental studies. The main concluding remarks are put at the end of the paper.