FUNDAMENTAL LIMITS IN WIRELESS LOCALIZATION ALGORITHMS

FUNDAMENTAL LIMITS IN WIRELESS LOCALIZATION ALGORITHMS

By Jun Chen

Advisor: Dr. Ali Abedi

An Abstract of the Thesis Presented

in Partial Fulfillment of the Requirements for the

Degree of Master of Science

(in Electrical Engineering)

August, 2010

Localization is a process of determining the position of an object. Localization techniques such as received signal strength (RSS), time of arrival (TOA) and angle of arrival (AOA) are widely used in wireless communications. The received signal strength refers to the magnitude of the electric field in a received radio signal. The distance between transmitter and receiver can be estimated by measuring the received signal power at the receiver. Time of arrival means the travel time of a radio signal from a single transmitter to a receiver. By the relation between the light speed and the carrier frequency of a signal the time is a measure for the distance between transmitter and receiver.  Angle of arrival is a method for determining the direction of propagation of a radio-frequency wave incident on an antenna array. In wireless localization, the position of a transmitter (object) can be determined by using the distance between transmitter and receiver or the direction of the incoming signals at the receiver.  The purpose of this thesis is to explore fundamental limits of the precise position estimation in a practical noise environment.

In this thesis, the mathematical modeling of localization is set up in two cases: (i) passive wireless sensor networks (PWSNs) and (ii) active wireless systems. Passive wireless sensor is a device that harvests the electromagnetic (EM) energy so as to emit or reflect sensory information to the receiver, while an active wireless device typically operates using an external power source. The modeling presents a framework of hybrid models based on multilateral radio localization techniques that use RSS, TOA and AOA measurements. The accuracy of localization is analyzed based on mathematical methods and advanced signal processing such as the Cramer-Rao lower bound (CRLB), the Taylor-series approximation and the multi-step least square estimator. Explicit formulas that provide the link among RSS, TOA or AOA methods are analytically explained. Furthermore, wireless propagation models are presented to simulate realistic and noisy wireless propagation channels including indoor propagation, building penetration, hilly terrain, rural area, urban areas and ultra-wideband (UWB) channels. 

   It is demonstrated that hybrid models provide much higher location accuracy than individual localization techniques. Numerical simulations show that the positioning accuracy within a centimeter could be achieved using the proposed algorithm in passive wireless sensor networks.

Keywords:  localization, received signal strength, time of arrival, angle of arrival, passive wireless sensor networks, Cramer-Rao lower bound, Taylor-series approximation, multi-step least square estimator, wireless propagation models.