Redundant inertial measurement units (RIMUs) are more reliable than normal IMUs, but they are suffering from the calibration of non-orthogonal gyroscopes and accelerometers. In this paper, aiming at the problem of relying on the orthogonal axis IMU information and error term coupling in the online calibration of RIMUs, a method based on the multi-stage EKF algorism is proposed. In this method, the calibration model of the inertial system is established, which does not depend on the orthogonality with the inclined axis inertial system, meanwhile, the attitude, velocity, and position information is taken as the measurement, and a filtering model is established based on the EKF method. Based on this model, the observability of the calibration method is proved, and the window and threshold for secondary filtering are set to reduce the coupling effect of scale factor error and installation error. The digital simulation indicates that the proposed method can provide high-precision online calibration results for the inclined axis scale factor error and installation error of RIMUs, and the calibration error is below 10%.