Abstract

The time of arrival (TOA) trilateration is one of the representative location detection technologies (LDT) that determines the true location of a mobile station (MS) using a unique intersection point of three circles based on three radii corresponding to distances between MS and base stations (BSs) and center coordinates of BSs. Since the distance between MS and BS is estimated by using the number of time delays, three circles based on the estimated radii are generally increased and they may not meet at a single point, resulting in the location estimation error. In order to compensate this estimation error and to improve estimation performance, we present two advanced TOA trilateration localization algorithms with detail mathematical expressions. The considered algorithms are the shortest distance algorithm, which calculates an average of three interior intersection points among an entire six intersection points from three intersecting circles, and the line intersection algorithm, which calculates an intersection point of three lines connecting two intersection points of two circles among the three circles, as the estimated location of the MS. In this paper, we present both algorithms with detailed mathematical expressions. The computer simulation results are provided to compare the location estimation performance of both algorithms. In addition, in this paper, mathematical analysis is provided to indicate the relation between the line intersection algorithm and the shortest distance algorithm. In this analysis, we verify that line equations based on the intersection points obtained from the shortest distance algorithm are identical to those obtained from the line intersection algorithm.

Highlights

  • The location detection technique of mobile stations (MSs) is of great importance in the development of the modern wireless cellular communication system

  • We observe that Mean square error (MSE) for estimating the distances between MS and base stations (BSs) are decreased as the sampling rate is increased

  • Between three algorithms, we enlarge the plot in the sampling rate range from 109 Hz to

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Summary

Introduction

The location detection technique of mobile stations (MSs) is of great importance in the development of the modern wireless cellular communication system. Many researchers around the world are working on achieving MS location accuracy at low cost, with precision, reliability, and reusability in its components [1,2]. In the wireless communication system, the accurate location detection of the MS has gained considerable interest, since the U.S Federal Communications Commission (FCC) made the rule to cellular providers to generate precise locations of the MS for enhanced 911 (E-911) services. The mandated rule specified that for a minimum of 95%. Of emergency calls, in a network-based system, a resolution of 300 m should be achieved, and in a handset-based system, the resolution should be 150 m.

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