The paper deals with the problem of identification of linearly varying frequency of sinusoidal signal with unknown amplitude and phase. Identification task for linearly varying frequency occurs, for example, during telescope operation control and it is of practical interest. Existing synthesis methods for identification algorithms of linearly varying frequency of sinusoidal signal use unlimited functions of time that is not attractive from a technical point of view, since the measurement noise multiplied by an unlimited function tends to give extremely poor estimates of the tunable parameter. This paper proposes a new approach for identification of linearly varying frequency comprising iterative filtering of measured sinusoidal signal (with the use of linear first order stable components), which in turn gives the possibility to obtain a simple linear regression model with one unknown constant parameter. We present computer simulation results, illustrating the performance of the proposed identification algorithm. Computer modeling was performed both in the presence and absence of the measurement noise. Also, comparative analysis of the proposed approach with the previously obtained methods was carried out within the framework of computer simulation. It was shown that the presented solution provides a significant improvement in the accuracy of an unknown frequency identification in the noise presence.