In order to track the ballistic re-entry target, a square root quadrature Kalman filter (SRQKF) is presented to
estimate the target state. The proposed algorithm is the square root implementation of the quadrature Kalman filter (QKF). The square root quadrature Kalman filter propagates the mean and the square root of the covariance, which guarantees the symmetry and positive semi-definiteness of the covariance matrix, improves numerical stability and numerical accuracy, but at the expense of increased computational complexity. The simulation experiments show that, the estimation accuracy of the new algorithm outperforms that of the QKF and the extended Kalman fitering algorithms, and the method is an effective nonlinear filtering method.