In this talk, we will propose an algorithm for recovering the initial state of a linear dynamical system by knowing noisy observations, and we will present its stability analysis. The ideas come from well-known methods in Control Theory which are called Kalman filters. The particularity of the method is that it allows the user to update the last estimation and the covariance of the error when in presence of a new observation. Moreover, it can be applied to non-autonomous dynamical systems and even with noisy dynamics. We will compare with other proposed methods in dynamical sampling and explain why the classical stability analysis for Kalman filters needs a little adjustment to include the dynamical sample problem.