In this work, we deal with the problem of estimation of the time-varying coefficients of a linear system, where the input and output are locally stationary processes. In our approach, we propose two types of estimators, kernel and wavelet estimators. They are time-domain estimators in the sense that they involve Yule-Walker type equations and ordinary least squares method. We provide some simulation results and briefly discuss the (asymptotic) statistical properties of the estimators.