The position-control systems for dynamically positioned vessels include wave filters to remove the wave motion signals. These ensure that the sytem only responds to low-frequency forces that would cause the vessel to move off-station. Several filters have been proposed and used in this role, and in the following discussion the Kalman filter is considered. The Kalman filter depends upon the model of the vessel, and the development of such a model is described. Simulation results are given to illustrate the performance of the filter and the performance of the combined Kalman filter and optimal state-feedfack control system.