  In this paper we propose a method to estimate the initial state of a linear
dynamical system with noisy observation. The method allows the user to have
estimations in real time, that is, to have a new estimation for each new
observation. Moreover, at each step, the covariance matrix of the error is
known and it is proved that the dynamic of the state estimator error is always
Lyapunov stable. Also, %necessary and sufficient conditions are given to
guarantee asymptotic stability for the error dynamics of an LTI dynamical
system, which is itself an LTV system.
