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As the autonomous underwater vehicle (AUV) becomes more popular in various ocean applications, its navigation technique has attracted great attention since it is often crucial that the vehicle position be known precisely. Selection of a practical navigation scheme is a tradeoff between performance, space/power budget and cost. In this study, a low-cost, small-size navigation system for an AUV carrying synthetic aperture sonar (SAS) is presented. An integrated navigation method is also developed based on the extended Kalman filter, in which two novel processes, track-based compass calibration and adaptive beamforming-based SAS micro-navigation, are incorporated. For compass calibration, the heading bias caused by hard iron interferences is estimated through a surface calibration run; for displaced phase centre antenna-based micro-navigation, sway estimation is done by applying adaptive beamforming to the overlapped phase centre array. A number of AUV field tests were implemented and the results demonstrate that a relative navigation error of as low as 0.23% of the travelling distance in circular runs can be achieved using the developed approach.