Estimating the unknown parameter vector of the system model is the most important problems in system identification. Especially in cases where the system's parameters are time-variable, it is observed that estimations obtained using estimator have deviated from the actual values, and therefore that the estimator must be corrected to some extent. In this paper, some methods for the parameter estimation in cases where a system is modelled with ARX Autoregressive Exogenous Input) are considered. After reviewing the problems, a simulation study has been made on comparing different estimation methods. Corrected (Adaptive) Kalman Filter (CKF) gives results more accurately than Normal Kalman Filter (NKF) for time varying parameter estimation. Moreover, after an introduction to the method of minimum variance feed-back control, using this method and CKF, a heating control is done in computer aided experimental study. CKF ensures that the system is kept under control by correctly estimating the parameter that changes over time.