In this study, a nonlinear mathematical model for an unmanned underwater survey vehicle is obtained. The inertial navigation system and vision-based measurement systems are modelled. The magnetic compass, depth sensor and pitot tube are used in order to support vehicle's attitude, velocity and depth information. The state errors are estimated with error state estimation algorithm from the noisy measurement data. The navigational data of the vehicle can be obtained accurately using the extended Kalman filter. Then, some parameters which are vaguely known in the mathematical model of the vehicle have been estimated by a system identification study. All of this study is performed in Matlab/Simulink.