A Rotational Inertial Navigation System (RINS) redundant configuration is commonly adopted in high-accuracy marine navigation. Single-axis RINS and dual-axis RINS redundant configurations are good choices with single-axis RINS being a hot backup system, and are trade-offs between position accuracy, reliability as well as cost. However, lack of information fusion between systems is common. Therefore, a novel navigation information fusion method based on an augmented error state Kalman filter is proposed for a RINS redundant configuration. The azimuth gyro drift of a single-axis RINS whose influence cannot be averaged out by single-axis rotation can be estimated, whereby the deterministic position error can be predicted and compensated. Hence, the position accuracy in the event of dual-axis RINS failure can be guaranteed by improving the performance of a single-axis RINS. In addition, an online performance evaluation method is proposed to select the better performance dual-axis RINS as master RINS in a triple RINS configuration, including two sets of dual-axis RINS and a single-axis RINS, which is used in some particularly high reliability applications. Semi-physical simulations and experiments show the proposed method works well.