Numerical study of source localization with non-line-of-sight effects based on time difference of arrival 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 device, based on the time differences in the signals that are received at different receivers. In this investigation the method is studied for two-dimensional (2-D) problems for simplicity, using a vertical 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. However, the accuracy can be influenced significantly by non-line-of-sight effects when multiple walls, realistic ground effects, and scattering objects are added to the propagation route. A more accurate result can be obtained by using a modified method discussed here, which incorporates a transfer function that relates the field at a given receiver to the dipole source amplitude as a function of frequency. A “processed signal” is calculated at each receiver by de-embedding the transfer function from the received signals and multiplying back by a free-space propagation term for each frequency in the signal spectrum, thus removing the effects of the environment and calibrating the channel back to free space. Since the transfer function is different at each possible source position, an iterative method is proposed to do the localization.