Adaptive quantization and distributed estimation in sensor networks

The purpose of this dissertation is to examine the problem of quantization and distributed estimation in wireless sensor networks (WSN) over noisy channels. Specifically each sensor in the sensor network senses a random signal parameterized by an unknown deterministic parameter. WSN are characterized by power and bandwidth constraints. Due to bandwidth and power constraints, each sensor quantizes its local observation into one bit of information and transmits this bit to a fusion center over noisy channel links. The fusion center has to estimate the unknown parameter based on the bits it receives from the sensors in the WSN. In this dissertation we propose an adaptive quantization (AQ) scheme for distributed estimation in WSN with noisy channel links. The channel links are modeled as binary erasure channels or binary symmetric channels. A computationally efficient Maximum Likelihood estimator, which factors in the problem of bit erasures/bit errors, is formulated. A naive implementation of the ML estimator involves a likelihood function with exponential computational complexity as compared to the proposed estimator, which has a likelihood function with quadratic computational complexity. The performance of the proposed quantization schemes and estimator are validated by mathematical analysis and computer simulation. The Cramer-Rao bound is developed as a benchmark for the considered distributed estimation problem. Simulation results are shown for the AQ quantization scheme and estimators over binary erasure channels and binary symmetric channels.;In the latter part of the dissertation, non-parametric estimators that do not make any assumptions with reference to the sensor noise model or channel noise model are developed. Since non-parametric estimators are data driven and agnostic to any model, they do not suffer from the risk of performance degradation due to model mismatch. In general, the proposed non-parametric estimators are computationally efficient in comparison to the parametric maximum likelihood estimators. Additionally some of the proposed nonparametric estimators are robust to errors induced by the sensor observation noise and the noisy channel links. Numerical simulations are shown to illustrate the performance of the proposed non-parametric estimators over noisy channel links.