LMS finite memory estimators for discrete-time state space models

In this paper, a least-mean-squares (LMS) finite memory (FM) estimator for a stochastic discrete-time state space model is obtained by taking the conditional expectation of the estimated state given a finite number of inputs and outputs measured on the recent finite horizon. Any a priori state information is not involved and any arbitrary constraints are not imposed. For a general discrete-time state space model with both system and measurement noises, the LMS FM estimator is represented in a closed-form. It turns out that the proposed LMS FM estimator has the unbiased property and the linear structure with respect to inputs and outputs on the recent finite horizon.