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

A new class of discrete-time optimal linear estimators is introduced that m inimizes a minimum variance criterion but where the structure is prespecifi ed 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 estima tor 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 s uccessful structure used in control systems, that is. to propose a proporti onal, integral, derivative structure for the observer gain calculation. The resulting estimator can be of much lower order than a Kalman or Wiener est imator, and it minimizes the estimation error variance subject to the const raint referred to above.