This paper develops a state space framework for the statistical analysis of a class of locally stationary processes. The proposed Kalman filter approach provides a numerically efficient methodology for estimating and predicting locally stationary models and allows for the handling of missing values. It provides both exact and approximate maximum likelihood estimates. Furthermore, as suggested by the Monte Carlo simulations reported in this work, the performance of the proposed methodology is very good, even for relatively small sample sizes. Copyright © 2011 John Wiley & Sons, Ltd.