Comparison Approach of Intersection Distances for Advanced TOA Trilateration

Abstract

The time of arrival trilateration method is one of the representative algorithms for the location detection technology, which estimates the location of mobile station (MS) at a unique intersection point of three circles with radiuses corresponding to distances between MS and base stations (BSs) and centers corresponding to coordinates of BSs. However, there may be serious estimation errors, when they do not meet at a point because the estimated radiuses of them are increased. The solutions for reducing the estimation position error in the main case of meeting three circles with the extended radius have been recently provided as the shortest distance algorithm and the line intersection algorithm. In general, they have good performance for the location estimation, but they may have serious errors in some cases. In this paper, we propose the efficient location estimation algorithm for the specific case of two large circles and one relatively small circle, which is located in the area of two large circles. In this case, there are six intersections in total based on the three extended circles and a small circle has four intersections with two large circles. The proposed approach compares four distances based on four neighboring intersections and selects the shortest one. Finally, it determines the averaged coordinate of two intersections corresponding to the shortest distance, as the location of MS. The location-estimating performance of the proposed algorithm is illustrated by the computer simulation example.