The single-axis rotational inertial system (RINS) can average out the biases of inertial sensor perpendicular to rotation axis. However, these inertial sensor biases will introduce Schuler oscillation and saw-tooth error in the velocity output. Redundant RINS configuration is widely used in the ships and underwater vehicles. However, the information fusion between the redundant systems is ignored. In this paper, a joint error model and a measurement model are constructed for the redundant RINSs, whereby a novel Kalman filter is designed to estimate the inertial sensor biases. The designed Kalman filter does not require external reference information aiding. Based on the estimates of the inertial sensor bias, a velocity error prediction model is designed to predict the velocity error caused by inertial sensor biases. By velocity error output correction, the velocity fluctuation is decreased by 30%. As a typical application, the compensated velocity output from the master RINS is provided for the slave inertial navigation system (INS) to accomplish transfer alignment. Simulation test and experiments are conducted to verify the effectiveness of the proposed method.