To ensure the reliability and safety of the long-endurance navigation, two or more rotational inertial navigation systems (RINSs) are usually equipped on ships. Through the redundant configuration, fault detection and diagnosis (FDD) can be realized. In this paper, a collaborative FDD method applied to dual homogeneous single-axis RINSs is proposed. The method utilizes geometric constraint observation to construct a detection filter, processes the filtering outputs through the modified Bayesian algorithm, and incorporates a fault confirmation stage to achieve fault diagnosis with stronger robustness. Besides, an azimuth gyro drift variation estimation method using least-squares is further proposed by exploiting the difference in Schuler oscillation mode resulting from an azimuth gyro fault as opposed to the fault-free state when the system is damped by the log. The efficiency and reliability are demonstrated through comparative and repeated experiments. According to the results based on repeated experiments, the proposed method achieves a comprehensive correct diagnosis rate of over 99% across various fault scenarios. When relatively significant faults occur, the average diagnosis time for horizontal gyros, horizontal accelerometers, and azimuth gyros is 0.4569h, 0.2686h, and 1.2204h respectively. In the case of more subtle faults, although the average diagnosis time is extended to 0.5920h, 0.2991h, and 1.9641h, the effectiveness of the method is still well demonstrated.