The Effects of Noise on Measurements

It is the objective of this thesis to explore some of the problems associated with a distributed system driven by noise. Three main areas are investigated. First, the correlation of two sensors placed along a stochastically driven distributed system is considered and an expression relating correlation coefficient, sensor spacing and sensor position is found. Second, the noise bandwidth of a distributed system is examined. Finally, state estimation using the Kalman-Bucy filter and finite-dimensional approximations to the state-equation of a distributed system is explored. The effects of filter order (modeling accuracy) and multiple sensors are considered, and a lower bound on estimation accuracy is found for the single sensor case. A one-dimensional diffusion equation with two different sets of boundary conditions is used for the distributed parameter system. THESIS SUPERVISOR: Leonard A. Gould TITLE: Professor of Electrical Engineering -3ACKNOWLEDGEMENTS The author wishes to thank his thesis advisor, Professor Leonard A. Gould, for his suggesting and supervising this problem. His comments and criticisms throughout this work were most useful. Thanks are also due to the author's colleagues at the Electronic Systems Laboratory. In particular, discussions with Dr. Gervasio Prado and Dr. John Fay were most fruitful, and the computer program donated by Mr. Michael Warren was invaluable. The author is also grateful to the E. S. L. Drafting Department for their reproduction of the many figures in this work. Finally, the author wishes to thank Mrs. Rita Baughman for her patience in typing this manuscript. This thesis was sponsored in part by the National Science Foundation grant NSF 72917. -'4TABLE OF CONTENTS page CHAPTER