Road roughness significantly affects vehicle vibrations and ride quality. We introduce a Kalman filter (KF)-based method for estimating road roughness in terms of the international roughness index (IRI) by fusing inertial and speed measurements, offering a cost-effective solution for pavement monitoring. The method involves system identification on a physical vehicle to estimate realistic model parameters, followed by KF-based reconstruction of the longitudinal road profile to compute IRI values. It explores IRI estimation using vertical and lateral vibrations, the latter more common in modern vehicles. Validation on 230 km of real-world data shows promising results, with IRI estimation errors ranging from 1% to 10% of the reference values. However, accuracy deteriorates significantly when using only lateral vibrations, highlighting their limitations. These findings demonstrate the potential of KF-based estimation for efficient road roughness monitoring.