[en] The shipboard redundant rotational inertial navigation system (RINS) configuration, including a dual-axis RINS and a single-axis RINS, can satisfy the demand of marine INSs of especially high reliability as well as achieving trade-off between position accuracy and cost. Generally, the dual-axis RINS is the master INS, and the single-axis RINS is the hot backup INS for high reliability purposes. An integrity monitoring system performs a fault detection function to ensure sailing safety. However, improving the accuracy of the backup INS in case of master INS failure has not been given enough attention. Without the aid of any external information, a systematic bias collaborative measurement method based on an augmented Kalman filter is proposed for the redundant RINSs. Estimates of inertial sensor biases can be used by the built-in integrity monitoring system to monitor the RINS running condition. On the other hand, a position error prediction model is designed for the single-axis RINS to estimate the systematic error caused by its azimuth gyro bias. After position error compensation, the position information provided by the single-axis RINS still remains highly accurate, even if the integrity monitoring system detects a dual-axis RINS fault. Moreover, use of a grid frame as a navigation frame makes the proposed method applicable in any area, including the polar regions. Semi-physical simulation and experiments including sea trials verify the validity of the method. (paper)