Autonomous Underwater Vehicle (AUV) navigation and localization in the complex and changeable marine environment is crucial and challenging. The inaccurate noise covariance matrix may result in significant prediction errors or even filtering divergence for traditional navigation algorithms. Meanwhile, the outliers in sensor observations also have a substantial adverse effect on the AUV positioning accuracy. Therefore, in this paper, we propose an Improved Interacting Multiple Model-Unscented Kalman Filter (IIMM-UKF) with both adaptivity and robustness for AUV navigation. Firstly, the Variational Bayesian (VB) based UKF algorithm is proposed as adaptive sub-models of IIMM to estimate the time-varying measurement noise covariance adaptively. Secondly, an outliers detector sub-model is proposed to enhance the robustness of IIMM. Gaussian Process Regression (GPR) is used to regress state pseudo values for each sub-model as estimations of the filtering process when the outliers are detected by the residual χ2 detector. Multiple models work in parallel to achieve high-precision and robust AUV navigation. The performance of the IIMM-UKF algorithm has been evaluated on AUV with simulation and actual experimental data. In sea trials, the average AUV navigation accuracy of the IIMM-UKF is improved by 61.02% compared to EKF, 43.44% compared to UKF, and 35.54% compared to the IMM-UKF.