Title

Detection and location estimation of a random signal source using sensor networks

Date of Award

2010

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Pramod K. Varshney

Keywords

Location estimation, Sensor networks, Source localization

Subject Categories

Electrical and Computer Engineering

Abstract

In this dissertation, the problem of detection and localization of a random signal source is considered using a network of sensors. The measurements received at individual sensors are characterized by a probability density (or mass) function. Formulating the detection problem as a binary hypothesis testing problem, the design of a distributed detection system for detecting the presence of a random signal source is considered. Both cases of known and unknown signal parameters are considered. Design of optimal fusion and local sensor rules are first discussed under the assumption that sensor observations are conditionally independent over space as well as time.

However, while observing a source of random signal, the sensor measurements may exhibit significant spatial dependence, which should be incorporated to enhance performance of the signal processing system. This dissertation investigates the usage of copula theory to model the joint statistics of sensor observations. Using copula theory, approximate joint probability distribution functions can be constructed using the knowledge of marginal distribution functions by employing copula functions that have emerged as powerful tools for modeling dependence. Moreover, using copula functions, non-linear dependence can be modeled. This is in contrast to Pearson's correlation coefficient, which can characterize only linear dependence. The problem of distributed detection using dependent sensor observations is considered and a copula based solution is discussed. The accuracy of parameter estimation may also get affected by ignoring dependence between sensor observations. The design of a copula based location estimator is also discussed in this dissertation. Using simulated data, the copula based systems for detection and location estimation are shown to result in superior performance as compared to the assumptions of conditional independence or linear dependence of sensor observations. A number of copula functions exist and using an incorrect copula function can lead to model mismatch that may result in performance degradation. Methods for selecting the most suitable copula function from a finite set of copulas are also discussed. The results obtained emphasize the importance of copula selection.

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