Document Type


Date of Award

Spring 5-31-1982

Degree Name

Doctor of Engineering Science in Electrical Engineering


Electrical Engineering

First Advisor

Stanley S. Reisman

Second Advisor

Joseph J. Padalino

Third Advisor

Marshall Chuan Yung Kuo

Fourth Advisor

Walter M. Gilbert


A method has been developed for solving practical problems which can be expressed in terms of physical geometry. These problems often involve combining directional information observed by remotely located sensors reported in their own respective local coordinate systems. To transform this information into a common coordinate system, the attitude of the sensors must be measured with respect to this common coordinate system.

Physical geometry is a generalization of mathematical -geometry where objects define the endpoints of figures composed of ensembles of lines. A probabilistic approach has been taken which is based on the fundamental assumption that the objects can be partitioned (for analytical purposes) into volume elements which are very small compared to the distance between objects. This allows the set of directions to the partitioned object to be represented by an ensemble of lines. Each observable volume element is characterized by its normalized contrast which is proportional to the probability that the object lies in the direction specified by the line to that volume element. Thus, the direction to the object can be expressed in terms of a probabilistic vector.

A technique has been developed to measure the attitude of a remotely located sensor based upon both sensors measuring the same set of two physical vectors. These measurements are reported in terms of probabilistic vectors and used to compute a probabilistic matrix which defines the attitude of the remote sensor. This probabilistic matrix can then be used to transform any vector measured by one sensor into its corresponding description in the other sensor's own local coordinate system. This allows directonal information to be combined and thus physical geometry problems to be solved.

The engineering considerations of implementing a Remote Attitude Measurement, ReAtMent, system are presented including the development of an error budget necessary to insure that the ReAtMent system performs to the required accuracy.

An experimental section is presented which illustrates the concepts developed by using an electrooptical sensor to measure three physical vectors in several orientations. Two of these measured probabilistic vectors are used to compute a probabilistic attitude matrix. This matrix then operates on the remaining physical vector as reported in the reference orientation of the sensor to predict the probabilistic vector which would describe the same physical vector in the current orientation. The predicted and actually observed vectors are then compared to give a measure of the accuracy of the technique. Many of the concepts developed in this dissertation were thus validated experimentally.

As the study of ReAtMent is in its infancy, the present work should be used as a springboard for further research. Topics that may be of interest for future studies are suggested.



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