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.　©　2001-2012　IEEE.