In-motion initial alignment method using Cayley–Kalman filter on special orthogonal group

Abstract

Aiming at the in-motion initial alignment problem of strapdown inertial navigation system (SINS), this paper proposed a precise direct in-motion alignment method based on attitude matrix representation and Cayley–Kalman filter on the special orthogonal group. There are two innovations in this paper. First, as an element of the special orthogonal group $\mathit{S}\mathit{O}\left(\mathbf{3}\right)$ , the error attitude matrix is used to construct an in-motion alignment model, and it is transformed into the vector space to represent the attitude error state. The error matrix was used as a state to decrease the influence of the state-dependent problem. Second, this method uses the Cayley transform to replace the Taylor expansion to derive the update equation, which is a no approximation mapping relation to assure accuracy when deriving the filtering algorithm. Simulation and experimental results demonstrate the proposed alignment method has advantages over the existing methods in alignment accuracy and alignment time and performs well in the in-motion alignment process of SINS.