Optimal minimal-order observer-estimators for discrete linear time-varying systems

This paper generalizes and unifies the concepts developed by Kalman and Luenberger pertaining to the design of discrete linear systems which estimate the state of a linear plant on the basis of both noise-free and noisy measurements of the output variables. Classes of minimal-order optimum "observer-estimators" are obtained which yield the conditional mean estimate of the state of the dynamical system. One explicit minimal-order optimal observer-estimator is constructed which generates one version of the conditional mean state estimate.