In this paper, a methodology for estimating a regression model with locally stationary errors is proposed. In particular, we consider models that have two features: time-varying trends and errors belonging to a class of locally stationary processes. The proposed procedure provides an efficient methodology for estimating, predicting and handling missing values for non-stationary processes. We consider a truncated infinite-dimensional state space representation and, with the Kalman filter algorithm we estimate the parameters of the model. As suggested by the Monte Carlo simulation studies, the performance of the Kalman filter approach is very good, even with small sample sizes. Finally, the proposed methodology is used in two real life applications. (C) 2013 Elsevier B.V. All rights reserved.