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　(3)　]　representation　and　the　optimal　attitude　estimation　alignment　idea.　In　this　method,　the　SO(3)　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　O　(3)　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.　©　1963-2012　IEEE.