Restricted structure optimal linear pseudo-state filtering for discrete-time systems

A new class of discrete-time optimal linear estimators is introduced that minimizes a minimum variance criterion but where the structure is prespecified to have a relatively simple form. There are three new ideas on which the results depend. The first is the use of the pseudo-state modeling approach, with the estimator represented in an observer form. The second is the use of a restricted structure gain calculation that enables the optimal estimator to be generated but where the gain transfer function is only allowed to be of a prespecified form. The third idea introduced is to borrow a very successful structure used in control systems, that is, to propose a proportional, integral, derivative structure for the observer gain calculation. The resulting estimator can be of much lower order than a Kalman or Wiener estimator, and it minimizes the estimation error variance subject to the constraint referred to above