Based on the Kalman filter and projection theory,the new optimal fixed-point,fixed-interval and fixed-lag Kalman smoothers are presented for systems with correlated noises having non- zero means.They avoid to calculate the inverse of the estimation error variance matrices,and have the generality.The classical results for systems with uncorrelated noises having zero means are extended and modified.The corresponding steady-state Kalman smoothers and pole- assignment Kalman smoothers are also presented,and their local or global asymptotic stability is proved.