The fusion of measurements from distributed sensors for dynamic positioning (DP) system based on state estimation algorithms is studied in this thesis in order to increase the accuracy and redundancy of the reference system in DP and a state observer is also designed to estimate of the low frequency vessel motion for the input of DP controller. Different filters such as lowpass filter, notch filter, Kalman filter (KF), extended Kalman filter (EKF), unscented Kalman filter (UKF) and square-root unscented Kalman filter (SRUKF) are introduced and discussed in this thesis. The square-root unscented Kalman filter is proposed for the fusion of measurements, wave filtering and state estimation based on kinematics while the Kalman filter is used as an observer for the estimation of the state vector of a vessel mathematical model for dynamic positioning operation. Thereafter a Matlab/Simulink based marine system simulator containing external environment, vessel model, reference sensors, sensor fusion system, observer and controller is built to test the algorithms of sensor fusion and observer designed in this thesis. The results of the simulation show that the errors of low frequency position and heading prediction are below 0.2m and 0.3 degree respectively which is accurate enough for DP operation. The dead reckoning starts automatically as soon as the reference system fails and the error of the dead reckoning increases gradually overtime. The position error in dead reckoning is about 5m after 1800s in simulation, which means the DP system is still able to estimate the position of the vessel without any position measurements in certain time, avoiding collision caused by the sudden position loss.