This thesis deals with three methods for integrating measurements from different sensors for an underwater vehicle. The sensors that were used are inertial measurement unit (IMU), Doppler velocity log (DVL), Hydro- acoustic position reference system (HPR) and tilt and heading measurements. The external measurements (DVL, HPR and attitude) are used to aid the inertial navigation system (INS) which uses the measurements from the IMU to calculate position, velocity and attitude. The different methods presented are extended Kalman filter (EKF), unscented Kalman filter (UKF) and a nonlinear observer. The two Kalman filters were implemented as indirect filters, while the nonlinear observer was implemented as a direct filter. The main difference between the EKF and UKF is that UKF does not make any linarizations such that it captures the covariance of the system more accurate than EKF. To compare the different approaches a navigation system was implemented using Matlab and simulations were carried out to test accuracy and robustness. The nonlinear observer has the most accurate position estimate when all measurements are available. It performed slightly better than UKF which again was more accurate than EKF. A greater difference was seen between UKF and EKF when the noise characteristics in the filters were wrong. For velocity and attitude all estimates were unbiased, but the nonlinear observer produced estimates with far more noise than what the Kalman filters did. All filters handled losing the HPR well. The nonlinear observer did not manage to limit the error in the case of DVL loss as opposed to both Kalman filter which have limited error. They performed with the same grade of degradation of the estimates during the loss. When the measurement returned both Kalman filters immediately regained accuracy but the nonlinear observer did not manage to recover. When losing the IMU measurements both Kalman filters had problems estimating changes in the attitude which again led to error in the position estimate. The position error is however much larger in EKF than UKF. The nonlinear observer has a structure with a separate attitude observer and therefore had a much better attitude estimate during the loss. From these results UKF is considered the best choice for implementation in a real system. It performs accurate estimates during noisy conditions, and suffers only from limited degradation when measurements are lost, both external and inertial.