A regularization approach to state estimation using observers

State estimation is an inverse problem, since causes are determined for observed effects. Inverse problems axe generally ill-posed. Essentially, their solution is not unique and/or unstable with respect to perturbation in the data. They axe therefore difficult to solve. To cope with the non-uniqueness and stability problems, regularization methods have been developed in the mathematical literature on inverse problems. In this work linear state estimation, which has been traditionally solved by optimal filters or observers, is reconsidered from the viewpoint of the theory of inverse problems.