Observation Uncertainty in Gaussian Sensor Networks

Abstract : The term "sensor network" encompasses a wide range of engineering systems with dramatically different characteristics. We consider a specific class of sensor networks whose objective is to reconstruct a source at a central terminal. Our objective in this thesis is to quantify the asymptotic error in reconstructing the source as the number of data sources, sensors, and model complexity increases. We consider three types of estimation systems - unconstrained estimators for vector Gaussian sources that are allowed direct access to the sensor observations, estimators for discrete sources that receive information via rate constrained links from the sensors, and estimators for scalar Gaussians whose input is the output of a multiple-access channel. We first establish bounds on the optimal estimator performance of these networks using a centralized estimator with access to all of the sensor observations. We assume the observations are noisy linear functions of the source and are thus specified by a matrix. Because the asymptotic error depends only on the spectral properties of this matrix, we can use tools from matrix analysis to give bounds on the spectrum and error in terms of the entries of the matrix for a number of different scenarios. Finally, we look at the case where the matrix is partially unknown. In some cases we can estimate the matrix directly from the data and in others we must minimize the worst mismatch distortion.