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In order to solve the coarse alignment problem of the strapdown inertial navigation system on a rocking base, a fast coarse alignment method using the Special Orthogonal Group optimization has been proposed in this paper. In this method, based on the alignment idea of tracing gravitational apparent motion in inertial frame, the model of coarse alignment on a rocking base has been established using the Special Orthogonal Group directly. A new attitude error function has been proposed on the basis of the cosines between the measurement vector and predictive vector to describe the error between the estimated attitude and the true one. In order to directly reflect the change in the attitude error in the new innovation term and enable the attitude error to converge to zero as fast as possible, the gradient of the new attitude error function has been selected as the new innovation term to compensate for the attitude in the estimation process. Finally, the stability of the proposed optimization estimation method has been proved by employing the Lyapunov stability theory. Simulation and experiment results show that the method presented in this paper exhibits good performance in terms of alignment accuracy and time and can be applied to coarse alignment under a rocking base under different environments.

Aimed at the alignment problem of strapdown inertial navigation system (SINS) on the swing base, a novel coarse alignment method using special orthogonal group optimal estimation is proposed. There are two main contributions in this paper. First, based on the Lie group differential equation, the rotation matrix is updated directly by using error Lie algebra, which avoids the non-convexity of traditional methods and the need for non-collinear vector observation. Second is that a novel optimal estimation method is developed by using the exact error Lie algebra, which is calculated based on the physical definition of Lie algebra, as the innovation term to compensate the initial special orthogonal group in the estimation process. The asymptotic convergence of the proposed optimal estimation method is proved by Lyapunov's second law. The simulation and experimental results demonstrate that the proposed method exhibits better performance than existing methods in alignment accuracy and time, which can achieve the self-alignment of SINS on the swing base.