Distance difference error correction by least square for stationary signal-strength-difference-based hyperbolic location in cellular communications

A proposal for hyperbolic location analysis based on the difference between pairs of received signal strength, called the stationary signal-strength difference (SSSD), has been made. Its location accuracy, in general, is limited because of two impairment factors: One factor is a high level of SSSD measurement error resulting from the shadowing, multiple-access interference, and nonline-of-sight effects; another factor is an error resulting from the estimation of the reference distance between the mobile subscriber and the serving base transceiver station (BTS), called the estimation error. Because of both factors, a larger bias error in the corresponding distance difference is expected, particularly when the SSSD levels are measured using standard handheld devices. This paper studies first the effects of bias error and then proposes an error correction method to decrease the larger bias error initially met. The method is based on the least square algorithm, which is simple, has a low computation burden, and gives noniterative and explicit solutions. Using the calibration data that are collected in a commercial cellular 900 MHz network, we analyze the estimation and SSSD measurement errors and demonstrate the performance merits of the proposed correction method. Field trial results show that our method achieves significant improvement in bias error compensation and, consequently, in location error mitigation. Specifically, for urban and rural environments with a six-BTS case, the mean error of location estimation can be reduced by an average of approximately 27% and 29%, respectively, reaching the lowest (best) values of 205 and 271 m, respectively.