Observation problems are restricted here to problems of estimation of state variables (or more generally, internal variables) from two sources of information: online measurements of some variables and the dynamic model relating the quantities to be estimated and the measurements. In the control theory engineering literature the tremendous success of the Kalman filter has left little room to numerical analysis approaches to observation problems. This work is a contribution to the building of a tunnel between numerical analysis and control theory literature on observation problems. The first brick is the statement that state estimation is an ill-posed inverse problem. In the present communication attention is focused on linear systems (with constant or non constant coefficients) for which popular asymptotic estimators (Luenberger observer and Kalman observer) are shown to be regularizations of the ill-posed estimation problem.