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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.