Multiplictty and martingale approach to infinite dimensional estimation

New results in infinite dimensional state estimation theory are developed here by exploiting two fundamental properties of stochastic processes: the multiplicity and representation of the observation process, and the wide-sense Martingale property in the signal process. The optimal estimate is characterized for the general case when an observation is in an arbitrary finite dimensional form with applications in the special case of additive noise. By considering the signal process as a simple linear transformation of a wide-sense Martingale the new filtering and prediction formulas are obtained.