Abstract: Based on classical Kalman filter and Mendel's input white noise estimators,using the projection theory,this paper presents the new optimal fixed lag Kalman smoothers with white noise estimators,and gives new algorithms for the smoother gain matrix and the variance matrix of the smoothing error.They avoid the inverses of the variance matrices of the filtering and prediction errors,so that the computational burden is reduced.The corresponding steady state suboptimal fixed lag Kalman smoothers are also presented,which have the asymptotic stability.A simulation example shows the effectiveness of the proposed results.