To address the fault diagnosis challenges faced by inertial navigation systems on long-endurance naval vessels in underwater or other global navigation satellite system-denied environments, an autonomous online FDD(fault detection and diagnosis) algorithm for DRINSs(dual-axis rotational inertial navigation systems) in redundant configuration was proposed. The joint state equation was constructed based on the error states of two sets of DRINSs as the system state, and the residual-normalized strong tracking filter could be established based on geometric constraint observation between the two. Furthermore, the asynchronous rotation strategy for two sets of inertial navigation systems was designed. The gyro drifts and accelerometer biases of both systems were proved to be observable and they could be estimated separately. The modified Bayes FDD algorithm was constructed based on the estimation results of the error states. The fault confirmation stage was designed to improve the robustness of the algorithm. The experimental results demonstrate that the proposed algorithm can achieve the autonomous online diagnosis of inertial sensor faults, and the correct diagnosis rate is greater than 99%, which can effectively guarantee the reliability of navigation information for inertial navigation systems on long-endurance naval vessels.