Estimation using Quantized Innovations for Wireless Sensor Networks

Acknowledgements I would like to thank Babak Hassibi, my mentor who was always around to give valuable suggestions—for both my project and my academic endeavours, and Ravi Teja Sukhavasi, my brilliant grad-student mentor who kindly took me under his wing and who always took the time to explain and derive important concepts for me. I have learned so much under both of their guidance. Abstract Recent advancements in integrated small scale micro-electromechanical system technology has created cheap, low power-consuming sensors that can be used in wireless sensor networks, an increasingly popular technology because of its potentially diverse applications. However, sensor networks have many constraints, such as limited bandwidth and power, which have inspired a considerable amount of research for the development of energy efficient detection and estimation algorithms using quantized observations. Though optimal estimation algorithms using quantized innovations have been recently developed to tackle this problem, bounds are not available on the error of the resulting optimal filter. Because tight bounds on the estimation error are essential in determining the stabilizability of the corresponding closed loop dynamical system and thus the applicability of a filter to a specific system, this project focuses on developing error bounds from a close study of the filtering algorithms. Initial attempts were unable to show that the estimation error of a system using quantized innovations followed a Ricatti recursion. Thus, a number of different algorithms and coder-estimator pairs were then analyzed to determine performance and to better understand means of proving stabilizability. Our primary goal is to have a better understanding of the evolution of the lower and upper bounds of estimation errors under measurement quantization, so that filters with verifiable performance specifications can be systematically designed for particular dynamical systems.