We consider the problem of estimation of a (linearly) time-varying frequency of a sinusoidal signal with unknown phase and magnitude. Such a problem may arise in control design for optical telescopes that makes it interesting from the practical point of view. The existing methods typically use unbounded functions of time that, being multiplying by the input signal, may yield significant noise amplification and poor estimation performance. In contrast, we present a novel approach to the estimation of the linearly varying frequency based on iterative filtering yielding simple linear regression model with a scalar parameter. Illustrative numerical simulations support the theoretical results. We also present a comparison with other known methods.