The Design of an Optimal Observer for Linear Discrete Time Dynamical Systems.

摘要

This report investigates the idea of utilizing Luenberger's minimal-order observer as an alternate to the Kalman filter for obtaining state estimates in linear discrete time stochastic systems. More specifically, this dissertation presents a solution to the problem of construction as optimal minimal order observer for linear discrete time stochastic systems where optimality is in the mean square sense. The approach taken in this report leads to a completely unified theory for the design of optimal minimal-order observers and is applicable to both time-varying and time-invariant linear systems. To illustrate the theory and application of the observer designs developed in the dissertation, the problem of designing a radar tracking system is considered. Examples are included which illustrate clearly the practicality and usefulness of the proposed optimal observer design technique. Finally, a host of topics for future research is presented in the hope of stimulating further research in the domain of observer theory.