Constrained Least Squares Algorithm for TOA-Based Mobile Location under NLOS Environments

Abstract

This paper presents a mobile station (MS) location method using constrained least-squares (CLS) estimation in the non-line-sight (NLOS) conditions. Three or more time-of-arrival (TOA) measurements of a signal traveling between a MS and base stations (BSs) are necessary for its localization. However, when some of the measurements are from NLOS paths, the location errors can be very large. We propose a method that mitigates possible large TOA error measurements caused by NLOS. This method does not depend on a particular distribution of the NLOS error. Simulation results show that the location accuracy is significantly improved over traditional algorithms, even under highly NLOS conditions. geometrical approach, the geometric relationship between the mobile device and its reference is exploited to establish the Euclidean distance between them and to identify the physical location of the device. In this paper, we propose a novel least-square (LS) approach combining with geometrical relationship. It firstly adjusts the NLOS-corrupted range measurements to approach their LOS values, and then minimizes a constrained least- squares function incorporating the known relation between the intermediate variable and the position coordinate, based on the technique of Lagrange multipliers. This algorithm does not require the distinction between NLOS and LOS BSs (6), and the knowledge of the statistics of measurement noise and NLOS errors. Our approach also has the advantage of requiring no modifications to the subscriber equipment. The location estimation can be performed at either the MS if it has the functionality or at special location units in the network. The remainder of this paper is organized as follows. The proposed algorithm is outlined in Section II and the simulation results and performance analysis are discussed in Section III. Finally, conclusions are drawn in Section IV.