The conventional Kalman filter(KF) which uses the current measurement to estimate the current state is a posterior estimation. KF is identified as the optimal estimation in linear models with Gaussian noise. However,the performance of KF with incomplete information may be degraded or diverged. In order to improve the performance of KF, an Amended KF(AKF) is proposed by using more posterior measurements. The principle, derivation and recursive process of AKF are presented. The differences among Kalman smoother, adaptive fading method and AKF are analyzed. The simulation results of target tracking with different covariance of motion model indicate the high precision and robustness of AKF. KF is identified as the optimal estimation in linear models with Gaussian noise. However, the performance of KF with incomplete information may be degraded or diverged The order, derivation and recursive process of AKF are presented. The differences among Kalman smoother, adaptive fading method and AKF are analyzed. The simulation results of target tracking with different covariance of motion model indicate the high precision and robustness of AKF.