A Perturbation Analysis on the Performance of TOA and TDOA Localization in Mixed LOS/NLOS Environments

In cellular communication systems where non-line-of-sight (NLOS) channels are dominant as compared to line-of-sight (LOS) channels, a time difference of arrival (TDOA) localization method can outperform a time of arrival (TOA) localization method, although the TDOA method loses one degree of freedom in the number of usable range estimates when selecting a range estimate as the reference and doubles the variance of range sampling error when subtracting the reference range estimate. In this paper, we first show the computer simulation result on the localization performance of conventional TOA and TDOA methods in mixed LOS/NLOS environments, and then validate it by theoretical analysis. Here, we analyze the root mean square localization error by decomposing it into two factors; for one factor, which is the contribution from range sampling error, we evaluate it by the Cramer-Rao lower-bound, whereas for the other factor, which is the contribution from positively biased NLOS range error, we analyze it by perturbation method. We show that the theoretical result can well explain the localization performance by computer simulation for both the TOA and TDOA methods, and furthermore, we derive a simple condition among the number of cells, the average and variance of NLOS range error distribution which can correctly predict whether the TDOA method outperforms the TOA method or not for the case of all NLOS channels.