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The rotary INS (inertial navigation system) has been applied to compensate the navigation errors of the MEMS (micro-electro-mechanical-systems) INS recently. In such system, the PVA (position, velocity, and attitude) errors can be compensated through IMU (inertial measurement unit) carouseling. However, the navigation errors are only partially compensated due to the intrinsic property of the inertial system and the randomness of the IMU errors. In this paper, we present an integrated rotary MEMS INS/GNSS (global navigation satellite systems) system based on the ANN (artificial neural networks) technique. The ANFIS (adaptive neuro-fuzzy inference system) is applied to eliminate the residual PV (position and velocity) errors of the rotary MEMS INS during GNSS outages. A cascaded velocity-position structure is designed to recognize the pattern of the rotary MEMS INS PV errors and to reduce them of the rotary inertial system in standalone mode. The road tests are conducted with artificial GNSS outages to evaluate the ability of the integrated system to predict the PV errors. Compared to the position errors of the integrated rotary INS/GNSS system based on an EKF (extended Kalman filtering), they are reduced by 79.98% in the proposed system. [ABSTRACT FROM AUTHOR]