Numerical study of source localization using the TDOA method

The time difference of arrival (TDOA) positioning method is a classic method that is used to determine the unknown location of a transmitting wireless terminal, based on the time differences in the signals that are received at different receivers. In this research the method is studied for two- dimensional (2-D) problems for simplicity, for an electromagnetic dipole source radiating a carrier wave that is modulated by a baseband signal. By maximizing the cross-correlation between the signals arriving at any two receivers, the TDOA between these two receivers is estimated. In principle, only three receivers are needed for source localization in 2-D problems in the absence of noise, using the TDOA between any two pairs of receivers. The source is then constrained to lie at the intersection of two hyperbolas, arising from these two pair of receivers. Localization in the presence of noise is usually based on minimizing the square error between the measured TDOA between all possible pairs of receivers (multiplied by the speed of light) and the difference in distances between the estimated transmitter location and the corresponding pair of receivers.