Errors in automatic location identification using timing advance

Automatic location identification (ALI) techniques using timing advance (TA) are under active discussion for some TDMA cellular technologies. This technique measures distance from each receiving base station in terms of the amount that the timing of the mobile has to be advanced in order to properly fit into the correct time slot. TA is used as an approximation for TOA (time of arrival-the transit time from mobile station to base station) which allows one to draw circular contours around each receiving antenna; the location of the mobile is at the best intersection of all those contours in the least-squares sense. We analyze the statistical errors from the use of TA as an estimator for TOA and apply the results to example ALI problems. The equipment uses a process whereby a measurement of TOA is made with some intrinsic error and then a broad TA time slot is assigned; the user may not have access to the original TOA measurement. In estimating the errors it is critical to recognize that there is a non-negligible probability that the TOA measurement error is large enough that the wrong TA time slot (i.e., it does not bracket the true value of TOA) may be assigned. Given that the user only knows the time slot, the problem is to find an estimator and its error for the actual TOA.