Kalman filtering techniques applied to the dynamic ship positioning problem
The dynamic ship positioning problem using Kalman filtering techniques is considered. The main components of the system are discussed. The ship dynamics, based on a linearised model, are represented by state equations. These equations involve low and high frequency subsystems. A simplified design procedure for the implementation of a Kalman filter is described based on the linearised equations of motion. The Kalman filter involves a model of the system and is therefore particularly appropriate for separating the low and high frequency motions of the vessel. The filtering problem is one of estimating the low-frequency motions of the vessel so that control can be applied. An optimal feedback control system simulation based on optimal stochastic control theory is used. The optimal control performance criterion weighting matrices Q, R were pre-selected and the optimal feedback gain matrix was computed. This control scheme involves the low-frequency part of the ship model. The Kalman filter has been simulated on a digital computer for different modelled operating conditions. The computer simulation results showing the behaviour and responses of the Kalman filter applied to the dynamic ship positioning problem were investigated. The system dynamics vary as the weather conditions vary and can be classified from a calm sea condition (Beaufort number 5) to the worst condition (Beaufort number 9). Different tests involving systems modelling and filter mismatching have been carried out. Another field in which the robustness of a Kalman filter has been assessed involved a test in which the system observation noise covariance was increased keeping the filter with the usual noise information. Saving in both computation and computer storage requirement were achieved using a form of semi-constant filter gain and reduced-order Kalman filter respectively. System non-linearities have been considered and a non-linear control algorithm was proposed and implemented using an extended Kalman filter. These non-linearities involve the thruster dynamics and the associated low-frequency part of the system model. All data that have been used within this work for system implementation were obtained from two different models ("Wimpey Sealab" and "Star Hercules" vessels). Our system has been employed by GEC Electrical Projects Limited, Rugby, for a new vessel ("Star Hercules") and this has been commissioned and is currently operating successfully off Brazil.