Strapdown inertial navigation system (SINS) estimates the position, velocity, and orientation of the vehicle and consists of an inertial measurement unit composed of three orthogonal accelerometers and three orthogonal gyros. Navigation in the SINS is done based on dead-reckoning principle, the gyros signals are used to find the attitude of the vehicle, subsequently knowing the attitude and the accelerometers signals, acceleration values in the navigation coordinates are calculated. Finally the acceleration signals are integrated to estimate the velocity and double integrated to find the position of the vehicle. Due to different imperfections in accelerometers and gyros’ signals due to the noise and bias instability, and the consecutive integration of the acceleration signals, estimation error increases with time and it is acceptable only for short times. In order to reduce the error, auxiliary sensors together with inertial sensors are utilized. In underwater navigation, it is common to use the auxiliary sensors such as Doppler Velocity Log (DVL), gyrocompass or magnetic compass, depth meter, global positioning system (GPS) and acoustic positioning system (APS) for reducing the position error. Unfortunately, the GPS signals are not receivable underwater and the INS/GPS integrated systems for underwater navigation are limited to shallow-water applications where the vehicle must come to the surface regularly to correct its position. One alternative solution for navigation of underwater vehicles is to make use of APS, which estimates absolute position of the vehicle, but it requires additional traonders to be either installed at sea floor or mounted to a surface vessel. Since in this approach, vehicle must be placed within the coverage area of traonders, its operation range is restricted. In addition, the position calibration of the traonders is difficult and is a time-consuming task. The auxiliary sensors utilized in this thesis consist of DVL, magnetic compass and depth meter. Using these sensors, unlike GPS and APS auxiliary systems, keeps the navigation system independent from external sources. In order to combine the data estimated by SINS with the data measured by auxiliary sensors, data fusion methods based on kalman filtering is used. The extended kalman filter (EKF) has been used widely in integrated navigation systems. Since this filter uses only the first order terms of the Taylor series expansions of the nonlinear functions, thus it is not appropriate for severely nonlinear systems. To remove this drawback, the unscented Kalman filter (UKF) has been proposed. In this filter, it is not required to linearize system dynamic and measurement model through calculating the Jacobian matrix. Error State Kalman Filter (ESKF) is another data fusion method in which the state space model is expressed based on a linearized system model. In this thesis, a complete navigation simulator for underwater vehicles consisting of a path designer, signal simulator and different Kalman filters is designed. The inertial sensors imperfection parameters and their effect on the estimated position are investigated. In order to verify the navigation simulator, EKF, UKF and ESKF data fusion methods are compared for under-water navigation using simulated data and real measurements. Finally the accuracy of different methods of data fusion is studied for different paths and maneuvers. Keywords: Inertial navigation system, Integrated navigation system, EKF, UKF, ESKF