Two Nodes for Positioning System

Abstract

Localization is an essential matter in monitoring and controlling a moving target. The localization could be distributed indoors and outdoors for three or more dimensions based on the required applications. For two-dimensional positioning, mathe-matically, at least three anchor nodes with known positions to locate a target are needed. The first two anchor nodes are utilized to compute the mobile position but with its ambiguous position. Then, the third node is used to eliminate the ambiguous position. This work presents an algorithm to eliminate the ambiguous position without using the third node by creating a criterion to select the correct position. The developed approach could be implemented in indoor or outdoor environments with specific constraints to eliminate the ambiguous position. With these constraints, the target position should be obtained in a perfect situation. The proposed approach is proven mathematically and evaluated using simulation experiments by MatLab and actual experiments using Ultra Wide Band (UWB) technology in the line-of-sight and non-line-of-sight conditions. The average accuracy of this approach in simulation and actual experiments is about 0.2721 $m$ 2 and 0.7630 $m$ 2 of mean square error (MSE), respectively,