Improvement in estimation of time of arrival (TOA) from timing advance (TA)

Wireless systems reporting TOA (time of arrival), the propagation time from the mobile station (MS) to the base station (BS), may use this information to assist with automatic location identification (ALI). The TA (timing advance), used in TDMA systems, may be used as an approximation for TOA. The MS/BS system measures TOA with a certain raw measurement error. The TA is assigned from this to one of a finite set of discrete values, resulting in a multinomial distribution of results. We assume that the user does not have access to the original TOA measurement and must attempt to reverse the process and estimate the TOA from the TA. The resultant error in the estimated TOA might be large if, by random error, the wrong TA bin has been selected. A simple solution to improve the accuracy of the TOA information thus obtained from the system is to take an average of two or more consecutive TA values. Paradoxically, the mean square error of this average is best at a value of the raw TOA measurement error that is not too small. This is a consequence of the fact that we cannot construct an estimator that is consistent in the statistical sense due to the finite TA bin size. We must also take into account the effects of the RF path and the possible motion of the mobile. We discuss the solution for any system with TA information. We also discuss the significance of multipath and its impact on the estimation of TOA. Simulations for the particular case of GSM are used to illustrate the results.