Masters Theses

Raed Hijer

Date of Award

12-1991

Degree Type

Thesis

Degree Name

Master of Science

Major

Electrical Engineering

Major Professor

James C. Hung

Committee Members

Marshall Pace, Don Hinton

Abstract

One of the major problems associated with any control system involving measurements is the observability. This problem can be looked upon either globally or locally. In the global sense, we are interested in exploring the observability characteristics of the system in general i.e., in the whole period of studying the system behavior. On the other hand, in the local sense, we might be interested in studying the observability effect on the system within a short period of time. Generally speaking, local observability concept is more practical in investigating the observability of control systems. This is due to the fact that some of the control systems are partially unobservable. That is, they may be unobservable only within a certain period of time. In this case, it is more practical to examine the local observability characteristics of such systems rather than their global observability characteristics.

A useful measure of the local observability is introduced by the concept of the local observability matrix. This matrix gives an indication of the degree of the system observability at each instant. The conditional number of the local observability matrix can be used as a measure of local observability.

In this study, a Kalman filter which is used in the Terrain-Aided Inertial Navigation System (INS) is considered as an application of the above measure. The standard deviations of the estimated parameters of the system were con- sidered to represent the estimation error of these parameters. It turns out from the simulated results that when the local observability concept was employed in the case of an unobservable or partially observable systems, no substantial improvement in the convergence process of the estimation error was noticed. This is due to the fact that the adaptive concept for updating the system state parameters is embedded in the structure of the Kalman filter. That is, the gain of Kalman filter is automatically reduced whenever the system is unobservable iii at any instant. The simulation results also show that strong observability is as- sociated with low navigation error and weak observability associated with high navigation error.

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