In this study, a nonlinear mathematical model for an unmanned underwater survey vehicle (SAGA) is obtained. The structure of the mathematical model of the vehicle comes from a Newton-Euler formulation. The yaw motion is realized by a suitable combination of right and left thrusters. The navigation problem is solved by using the inertial navigation system and vision-based measurements together. These are integrated to more accurately obtain navigation data for the vehicle. In addition, the magnetic compass is used to support the attitude information of the vehicle. A pool experimental set-up is designed to test the navigation system. Performance of the resultant navigation system can be analysed by creating suitable system state, measurement and noise models. The navigational data for the vehicle has been improved using a Kalman filter. The mathematical model of the vehicle includes some unknown parameters such as added mass and damping coefficients. It is not possible to determine all the parameter values as their effects on the state of the system are usually negligible. On the other hand, most of the important' parameters are obtained based on a system identification study of the vehicle using this estimated navigational data for coupled motion. This study is performed in a MATLAB/Simulink environment.