Abstract: Using the modern time series analysis method, based on the autoregressive moving average (ARMA)innovation model and white noise estimators, this paper resents two new fixed-point Kalman smoothers and two new forward fixed-interval Kalman smoothers for linear discrete time-invariant stochastic systems. Their advantages are that the solution of the Riccati equation is avoided, and that the algorithms are simple and can be implemented on line. The optimal initial estimate formulas are given in order to ensure the optimality of the proposed smoothers. A simulation example shows their usefulness.