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 three-dimensional motion is realized by a suitable combination of right, left and vertical thrusters. The navigation problem is solved by a combination of the inertial navigation system and acoustic-based measurements, which are integrated to obtain more accurate vehicle navigation data. In addition, a magnetic compass and a depth sensor are used to support vehicle attitude and depth information. A pool experimental set-up is designed for the navigation system. The performance of the resultant navigation system can be analysed by creating suitable system state, measurement and noise models. The vehicle navigational data are improved with 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 effect on the state of the system is usually negligible. However, most of the important' parameters are obtained from a system identification study of the vehicle by means of the estimated navigational data for coupled motion. The entire study is performed in a Matlab/Simulink environment.