In this paper, an in-motion initial alignment algorithm based on Lie group matrix kalman filter is proposed. According to the Lie group’s properties and the attitude optimization-based initial alignment idea, the attitude matrix is decomposed into three continuous special orthogonal matrices to separate the rotation information and motion information under the in-motion conditions. A linear system model is established based on the differential equation of Lie group, which can replace the traditional quaternion model and avoid the non-uniqueness of unit quaternion representation. Then the Lie Group Matrix Kalman Filter is proposed for estimating the initial inertial matrix directly. And the Simplified Lie Group Matrix Kalman Filter with special process noise is proposed in some specific situations. From the simulation, the alignment accuracy and stability of the two algorithms satisfies the SINS navigation requirements. These two methods have good application prospects for the in-motion initial alignment of SINS.
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