中文摘要：

针对使用扩展卡尔曼算法（extended Kalman filter,EKF）对复杂非线性状态估计时收敛速度慢、估计精度低的问题,提出一种平方根容积滤波算法（square root cubature Kalman filter,SRCKF）。SRCKF使用基于容积原则的数值积分方法直接计算非线性随机函数的均值和方差。该算法实现时只需计算函数值,避免了求导运算,降低了计算复杂度。且该算法传播了状态协方差的平方根,确保了协方差矩阵的对称性和半正定性,改进了数值精度和稳定性。把平方根容积卡尔曼滤波算法（SRCKF）应用到未知弹道系数的再入弹道目标的状态进行估计中。Monte Carlo数值仿真表明,平方根容积滤波算法大大降低了未知弹道系数的再入弹道目标的状态估计误差,提高估计精度,且运行速度较快。

英文摘要：

To solve the slow convergence speed and low estimation accuracy of the extended Kalman filter（EKF） for the complex nonlinear state estimation,the square root cubature Kalman filter（SRCKF） is introduced in the study.In the SRCKF algorithm,the cubature rule based numerical integration method is directly used to calculate the mean and covariance of the nonlinear random function.The algorithm is implemented only using the functional evaluation and is derivative-free so the computational complex is decreased.And the SRCKF propagates the square root of the covariance so that it guarantees the symmetry and positive semi-definiteness of the covariance matrix and improves numerical stability and numerical accuracy.The algorithm is applied to state estimation for reentry ballistic target with unknown ballistic coefficient.The simulation results indicate that the state error in the SRCKF is largely decreased and its estimation accuracy is improved.Moreover,the run speed of SRCKF is faster.