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To address the initial self-alignment problem of strapdown inertial navigation system under marine mooring conditions, a rapid initial self-alignment method based on the constraint matrix Kalman filter (CMKF) is proposed in this paper. The novelties of this method are two-fold. First, based on the Lie group differential equation, a one-step direct self-alignment model without coarse alignment process is designed directly based on a special orthogonal group of rigid-body rotations. In addition, to improve the alignment accuracy, the sensor biases are augmented into the state matrix to be estimated and compensated during the alignment process. Second, because the state of the proposed model is a matrix containing a special orthogonal group, a CMKF is developed to ensure the estimated accuracy. And a Lagrange function is designed in the CMKF to maintain the orthogonality of the special orthogonal group during the filtering process. 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 under marine mooring conditions.

The in-motion alignment of the strapdown inertial navigation system (SINS) is still a challenging problem due to the complex environmental changes that occur during carrier movement. This article proposes a novel initial alignment method by integrating the advantages of the Special Orthogonal Group of order 3 [ $SO\left ({{3} }\right)$ ] representation and the optimal attitude estimation alignment idea. In this method, the ${SO}\left ({{3} }\right)$ is used to represent the initial attitude matrix, and the optimal attitude estimation alignment model is established by analyzing the influence of the sensor error during the calculation process. Next, state-dependent extended Kalman filter is investigated by mapping the $SO\left ({{3} }\right)$ equations to the Lie algebra space, and the Lagrange formula is used to separate the state-dependent errors in the Lie algebraic filtering equation. The simulation and experimental results indicate that the proposed initial alignment method can achieve better alignment accuracy and shorter alignment time than existing methods and can fulfill the in-motion alignment tasks for SINSs in various environments.