Aiming at the highly dynamic and nonlinear characteristics of ballistic missiles,this paper introduces a nonlinear Cubature Kalman Filter (CKF) algorithm based on the third-order spherical-radial cubature rule.In addition,according to its characteristics,the Adaptive Cubature Kalman Filter (ACKF) algorithm for BDS/SINS deeply integrated navigation under the launch inertial system is studied.The algorithm is based on the idea of the Sage filter windowing method and the evanescent idea.By introducing multiple suboptimal fading factors into the CKF filter,the covariance matrix of observation error of the CKF filter can be adaptively adjusted online,and the fast-changing state can be effectively tracked while improving the filtering accuracy.Simulation results show that:Through the introduction of multiple suboptimal fading factors,the CKF filter can make better use of the systems prior information and make a stronger tracking of rapidly changing conditions;and the systematic errors can converge in a short period of time.Thus the dynamic performance of the integrated navigation system is improved greatly.