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Navigation technology is one of the most important challenges in the applications of autonomous underwater vehicles (AUVs) which navigate in the complex undersea environment. The ability of localizing a robot and accurately mapping its surroundings simultaneously, namely the simultaneous localization and mapping (SLAM) problem, is a key prerequisite of truly autonomous robots. In this paper, a modified-FastSLAM algorithm is proposed and used in the navigation for our <em>C-Ranger</em> research platform, an open-frame AUV. A mechanical scanning imaging sonar is chosen as the active sensor for the AUV. The modified-FastSLAM implements the update relying on the on-board sensors of <em>C-Ranger</em>. On the other hand, the algorithm employs the data association which combines the single particle maximum likelihood method with modified <em>negative evidence</em> method, and uses the rank-based resampling to overcome the particle depletion problem. In order to verify the feasibility of the proposed methods, both simulation experiments and sea trials for <em>C-Ranger</em> are conducted. The experimental results show the modified-FastSLAM employed for the navigation of the <em>C-Ranger</em> AUV is much more effective and accurate compared with the traditional methods.