The aim of this work is to develop a model-based methodology for monitoring lateral track irregularities based on the use of inertial sensors mounted on an in-service train. To this end, a gyroscope is used to measure the wheelset yaw angular velocity and two accelerometers are used to measure lateral acceleration of the wheelset and the bogie frame. Using a highly simplified linear bogie model that is able to capture the most relevant dynamic behaviour allows for the set-up of a very efficient Kalman-based monitoring strategy. The behaviour of the designed filter is assessed through the use of a detailed multibody model of an in-service vehicle running on a straight track with realistic irregularities. The model output is used to generate virtual measurements that are subsequently used to run the filter and validate the proposed estimator. In addition, the equivalent parameters of the simplified model are identified based on these simulations. In order to prove the robustness of the proposed technique, a systematic parametric analysis has been performed. The results obtained with the proposed method are promising, showing high accuracy and robustness for monitoring lateral alignment on straight tracks, with a very low computational cost.