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by John R. Buck Submitted in partial fulfillment of the requirements for the degree of Master of Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY and the WOODS HOLE OCEANOGRAPHIC INSTITUTION August 1991 This thesis describes the implementation and evaluation of an adaptive time-domain algorithm for signal enhancement from multiple-sensor observations. The algorithm is first derived as a noncausal time-domain algorithm, then converted into a causal, recursive form. A more computationally efficient gradient-based parameter estimation step is also presented. The results of several experiments using synthetic data are shown. These experiments first illustrate that the algorithm works on data meeting all the assumptions made by the algorithm, then provide a basis for comparing the performance of the algorithm against the performance of a noncausal frequency-domain algorithm solving the same problem. Finally, an evaluation is made of the performance of the simpler gradient-based parameter estimation step. Thesis Supervisor: Alan V. Oppenheim Title: Distinguished Professor of Electrical Engineering, MIT Thesis Supervisor: Ehud Weinstein Title: Adjunct Scientist, WHO! Acknowledgments Ultimately, my parents made this work possible. Without their love, patience, and understanding, I would not be where I am to write this. I owe a tremendous amount to Al Oppenheim. Al's insistence on quality and considered work has pushed me to improve beyond what I previously thought were my limits. He has always been able to pat me on the back when I was down, or fire me up when I needed motivating, and as only a good friend can, know which I needed at any given time. I am also deeply indebted to U di Weinstein. U di 's combination of patience and contagious enthusiasm was crucial in rekindling my interest in the research at a time when it was lagging. He has been an inspiring example of a conscientious and dedicated scientist for me. Meir Feder offered his insight and advice on the work here. Meir gave me invaluable help in resurrecting his old programs to allow comparison with the new algorithms discussed in this thesis . He also generously allowed me to tap his expertise and intuitions accumulated during his extensive experience with the EM algorithm. I am grateful to the Woods Hole Oceanographic Institution for the opportunity to perform most of the experiments described in this thesis while spending a summer there. I will always remember my summer in Woods Hole as one of the most relaxing and productive summers I've ever had. I will also remember it as a place where the wind is often strong. The Office of Naval Research and the Advanced Research Projects Agency administered by the Office of Naval Research both generously supported me in doing some of the work described in this thesis. To whatever extent this document is written comprehensibly, it is the responsibility of Fr. William J. O'Malley, S.J. and Fr. Lawrence Wroblewski, S.J., men who patiently attempted to teach me to read comprehendingly, think clearly, and write intelligibly. Professor Theo Theoharis encouraged me in developing my writing style. In addition, Mr. Frank Noce and Mr. Thomas Schaeffer instilled in me an appreciation for the beauty of mathematics and the excitement of science, respectively. I have been very fortunate to work in the Digital Signal Processing Group at MIT. I have learned from all of my fellow group members, Paul Beckman, Dan Cobra, Steve Isabelle, Jim Njeru, Mike Richard, Stephen Scherock and Kambiz Zangi. However, I have gained the most in conversation and in teaching with Andy Singer, Jim Preisig and Greg Warnell. Over the last two years, they have generously given me advice, assistance, inspiration, and laughter. I have been truly blessed to have companions such as these. I also wish to thank Deborah Gage, Giovanni Alberti and Giampiero Sciutto, who have all played Virgil to my Dante at many points in my wanderings through the infernal bureaucratic and technical labyrinth of MIT. A number of people were not directly responsible for the technical work here, but helped keep me sane while doing it. Most prominent among them are my housemates, Brecht, Doug, Hilary, Heather, Kirk, Kevin and Mike. Several other people, Dan, Linda, Mel, Suniti and Theo, were also willing ears and arms when I needed them. These people are all indelibly intertwined in my memories of graduate school and this work, and without their understanding and care, I am skeptical I could have ever finished this. Finally, and most importantly, as always, Ad Majorem Dei Gloriam.

Implementation and evaluation of a dual-sensor time-adaptive EM algorithm for signal enhancement