Two-Frame Group Error Model for SINS/DVL Integration: Analysis and Comparison

This article investigates a two-frame group representation method for the strapdown inertial navigation system (SINS) aided by the Doppler velocity log (DVL). The SINS-calculated attitude, velocity, position, DVL dead-reckoning position, and sensor biases are formulated as the elements of two-frame group. Also, according to two definitions of group error, the corresponding two-frame group right error (TFGRSE) model and two-frame group left error (TFGLSE) model are in detail derived. In addition, the Earth rotation and Coriolis effect are also taken into account in the proposed model, which has been ignored in the previous two-frame group method. Compared with the existing Lie group model, the proposed model is more suitable for high-precision inertial-based integration under large misalignments because the sensor biases in the state transition matrix facilitate faster convergence. Furthermore, both the DVL body velocity and the DVL dead-reckoning position are used as measurements for SINS/DVL integration. Due to the DVL velocity approximation in right-invariant observations, dead-reckoning positions are more accurate for left-invariant observations. Therefore, TFGLSE proves to be more applicable than TFGRSE for SINS/DVL integration. Finally, the effectiveness and superiority of the proposed model in this article are demonstrated through ship experiments. The experimental results demonstrate that the proposed model achieves higher accuracy estimation, faster convergence speed (CS), and smaller position errors compared to existing models, particularly in cases with extremely large initial misalignments.