The Euler Angle Error Model Based on Attitude Error of Body Frame in ECEF Frame

The virtual spherical vector position model (VSVPM) is widely used in global navigation. Strapdown inertial navigation system/doppler velocity log (SINS/DVL) is a commonly used underwater navigation method. In order to improve the performance of SINS/DVL under this framework, this article proposes the Euler error model based on the attitude error of body frame. First, the rotational difference between the calculated frame and the ideal frame is defined as the attitude error. Then, based on matrix operation rules, the corresponding differential equations of attitude, velocity, and position errors are derived, and according to the rules of linear approximation, a linear state-space model based on the attitude error of body frame is obtained, and the corresponding measurement equations and feedback corrections of SINS/DVL are provided. Finally, the effectiveness of the proposed model is validated through simulation and field test. The results show that, in case of large misalignment angles, the proposed model exhibits superior attitude convergence velocity and accuracy compared to traditional error models, with a reduction of at least 92.79%. This work also provides a reasonable explanation for which attitude error representation is more accurate.