We give some results on the convergence of the Kalman filter (KF) when used as an observer for linear time-varying systems. Based on the block-input/block-output state model, we prove that the state observer given in Kamen (1993) is equivalent to the KF algorithm. One of the main features, however, is that no assumption on the invertibility of the state matrix is needed and the computational requirements are reduced. Furthermore, the obtained result can be extended by duality to resolve the state feedback control problem.