Considering that the cubature Kalman filter (CKF) has low accuracy and poor robustness in the application of SINS initial alignment, a ruduced multiple fading factors strong tracking CKF (RMSTCKF) is presented, the algorithm scheme is given and the suboptimal solution of Multiple fading factors (MFF) is derived. MFF can improve tracking capability in each state according to the uncertainty in different states, which has stronger adaptivity and robustness. RMSTCKF is applied in large azimuth misalignment angle error equation, which is described by EPEA, the simulation is carried out under two condition, including the state of mismatching system noise and the state of disturbed base. Compared with RSTCKF and RCKF, the simulation results of RMSTCKF show that RMSTCKF is obviously superior to RSTCKF and RCKF in filtering precision and rate of convergence, and has stronger practical values.