Date of Graduation

2012

Document Type

Thesis

Degree Type

MS

Committee Chair

Daryl S. Reynolds

Abstract

The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood (ML) estimation problem. Spatially sparse sensor observations are distorted by additive white Gaussian noise. These observations are then communicated over parallel additive white Gaussian channels to the fusion center (FC) for a joint estimation. This work studies cases of both analog and digital channels. In the case of the analog channel, each sensor transmits its observation without any prior processing. A Newton’s method is used to iteratively solve for ML estimates of unknown parameters of the field. In the case of the digital channel, each sensor quantizes its observation to M levels and transmits the quantized data to the FC. An iterative expectation-maximization (EM) algorithm to estimate the unknown parameters is formulated, and its linearized version is adopted for numerical analysis. Numerical examples are provided for both cases of the channels. The unknown field is modeled as a Gaussian bell. Dependence of the integrated mean-square error (IMSE) between the true field and the estimated field on the number of sensors in the network and the SNR in observation and transmission channels is analyzed for both kinds of channels. In the case of the digital channel, we also evaluate the dependence of the IMSE on the number of quantization levels. In addition, we assume that the physical field is generated by an object with the location unknown to the FC. We numerically analyze the dependence of the mean-square error (MSE) between the true object location and the estimated object location. The effect of the number of sensors, SNRs, and the number of quantization levels is evaluated. Robustness of the EM algorithm with respect to convergence of the algorithm to the true parameter values is expressed in terms of Probability of Outliers.

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