针对弹道导弹高动态、非线性的特点, 引入了基于三阶球面－径向容积准则的非线性容积卡尔曼滤波(CKF)算法。此外, 针对其特点, 研究了发射惯性系下BDS/SINS深组合导航下的自适应容积卡尔曼滤波(ACKF)算法。该算法根据Sage滤波开窗法的思想和渐消的思想, 通过引入多重次优渐消因子到CKF滤波器中, 自适应地在线调整CKF滤波器的观测误差协方差阵, 在提高滤波精度的同时实现对快速变化的状态进行强有力的跟踪。实验结果表明: 多重次优渐消因子的引入使得CKF滤波器可以更多地利用系统的先验信息, ACKF滤波器对快速变化的状态具有更强的跟踪, 系统误差在较短的时间内收敛, 提高了组合导航系统的动态性能。

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.