Analysis of hyperbolic and circular positioning algorithms using stationary signal-strength-difference measurements in wireless communications

Referring received signal strength (RSS) to a signal propagation model to find user location is one of the most promising strategies in wireless communications. This paper develops a simple method based on relative signal-strength measurements, that is, the differences in stationary signal strength measured at the user location from multiple base transceiver stations (BTSs). The stationary signal strength is the averaged RSS and also is a stationary Gaussian process. In using this method, it is vitally important to confirm that some uncertain propagation parameters can be canceled out while a signal propagation model is merged into our method for locating users. In this way, the differences in stationary signal strength lead to two solutions: One is the distance difference between pairs of BTSs, and the other is the distances from the user location to the multiple BTSs. Consequently, the hyperbolic positioning algorithm due to the distance-difference solution and the circular positioning algorithm due to the distances solution can be presented, respectively. Afterward, some experimental results were drawn from a field trial in a real propagation environment. Results show that the hyperbolic and circular positioning algorithms can locate the user to within about 350 and 300 m in 67 percentile, respectively. Compared with the numerical result reported in the literature on existing methods based on RSS only, our method is superior. Despite the result not meeting Federal Communications Commission (FCC) requirements, this method proved to be sufficiently simple and efficient in terms of the computation at burden and network signaling load.