The effect of base stations configurations on the accuracy of hyperbolic position location in macrocellular and microcellular GSM systems

One method of position location (PL) in cellular systems is based on measuring the time difference of arrival (TDOA) of signal received by three or more base stations. The received signals are cross-correlated to determine the TDOAs and a set of nonlinear equations is obtained and then solved to produce the location estimate. In this paper two algorithms, Taylor-series and Chan are used. They can provide a precise position estimate at reasonable noise levels. The Taylor-series is an iterative method, so it suffers from the convergence problem and is computationally intensive as the least squares (LS) computation is required in each iteration. Chan's method can provide a non-iterative closed form solution with the same accuracy as in the Taylor method and there is no convergence problem. Also the effect of number and arrangement of base stations on the accuracy of the hyperbolic position location based on TDOA techniques is investigated. This is performed for a range of base stations (BSs) (up to 7) and for two different configurations, macrocellular and microcellular environments in ideal and non-ideal arrangements.