Date of Award

Fall 2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Electrical Engineering - (Ph.D.)

Department

Electrical and Computer Engineering

First Advisor

Alexander Haimovich

Second Advisor

Yeheskel Bar-Ness

Third Advisor

Ali Abdi

Fourth Advisor

Osvaldo Simeone

Fifth Advisor

Hana Godrich

Abstract

Accurate localization of a signal source, based on the signals collected by a number of receiving sensors deployed in the source surrounding area is a problem of interest in various fields. This dissertation aims at exploring different techniques to improve the localization accuracy of non-cooperative sources, i.e., sources for which the specific transmitted symbols and the time of the transmitted signal are unknown to the receiving sensors. With the localization of non-cooperative sources, time difference of arrival (TDOA) of the signals received at pairs of sensors is typically employed.

A two-stage localization method in multipath environments is proposed. During the first stage, TDOA of the signals received at pairs of sensors is estimated. In the second stage, the actual location is computed from the TDOA estimates. This later stage is referred to as hyperbolic localization and it generally involves a non-convex optimization. For the first stage, a TDOA estimation method that exploits the sparsity of multipath channels is proposed. This is formulated as an f1-regularization problem, where the f1-norm is used as channel sparsity constraint. For the second stage, three methods are proposed to offer high accuracy at different computational costs. The first method takes a semi-definite relaxation (SDR) approach to relax the hyperbolic localization to a convex optimization. The second method follows a linearized formulation of the problem and seeks a biased estimate of improved accuracy. A third method is proposed to exploit the source sparsity. With this, the hyperbolic localization is formulated as an an f1-regularization problem, where the f1-norm is used as source sparsity constraint. The proposed methods compare favorably to other existing methods, each of them having its own advantages. The SDR method has the advantage of simplicity and low computational cost. The second method may perform better than the SDR approach in some situations, but at the price of higher computational cost. The l1-regularization may outperform the first two methods, but is sensitive to the choice of a regularization parameter. The proposed two-stage localization approach is shown to deliver higher accuracy and robustness to noise, compared to existing TDOA localization methods.

A single-stage source localization method is explored. The approach is coherent in the sense that, in addition to the TDOA information, it utilizes the relative carrier phases of the received signals among pairs of sensors. A location estimator is constructed based on a maximum likelihood metric. The potential of accuracy improvement by the coherent approach is shown through the Cramer Rao lower bound (CRB). However, the technique has to contend with high peak sidelobes in the localization metric, especially at low signal-to-noise ratio (SNR). Employing a small antenna array at each sensor is shown to lower the sidelobes level in the localization metric.

Finally, the performance of time delay and amplitude estimation from samples of the received signal taken at rates lower than the conventional Nyquist rate is evaluated. To this end, a CRB is developed and its variation with system parameters is analyzed. It is shown that while with noiseless low rate sampling there is no estimation accuracy loss compared to Nyquist sampling, in the presence of additive noise the performance degrades significantly. However, increasing the low sampling rate by a small factor leads to significant performance improvement, especially for time delay estimation.

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