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A TOA-BASED LOCATION ALGORITHM FOR NLOS ENVIRONMENTS USING QUADRATIC PROGRAMMING Kai Yang, Jianping An, Xiangyuan Bu, and Yao Lu Department of Electronic Engineering Beijing Institute of Technology, Beijing 100081, China Email: { yangk, an, bxy, luyao1 } @bit.edu.cn ABSTRACT Location of a source is of considerable interest in wireless sensor networks. A novel algorithm for source location by utilizing the time-of-arrival (TOA) measurements of a signal received at spatially separated sensors under non-line-of-sight (NLOS) environments is proposed. The algorithm is based on quadratic programming, which is a special type of mathemat- ical optimization problem. Comparisons of performance with other algorithms are made, and Monte Carlo simulations are performed. Simulation results show that the proposed algo- rithm gives better results. Index Terms —non-line-of-sight (NLOS), time-of-arrival (TOA), quadratic programming 1. INTRODUCTION With the emergence of location based applications, determin- ing the location of a source from its emissions is becoming increasingly important [1, 2]. There are several fundamental approaches for implementing a radio location system includ- ing those based on time-of-arrival (TOA), time-difference-of- arrival (TDOA), received signal strength (RSS) and angle-of- arrival (AOA) [3]. The assumption in applying the traditional location ap- proaches is that there is a line-of-sight (LOS) path between the source and each fixed sensor [4–6]. Foy [4] used the Tay- lor series technique to correct an initial estimate iteratively. Chan and Ho [5] proposed to use a two-stage weighted least- squares (WLS) to solve for the source location, while Cheung et al. [6] proposed to use constrained weighted least-squares (CWLS) to solve for the source location by using the tech- nique of Lagrange multipliers to minimize a Lagrangian. Unfortunately, in most terrestrial wireless signal propaga- tion environments, especially in urban/indoor environments, the direct path from the source to a fixed sensor may be block- ed by buildings or other obstacles, which means that the LOS condition may not be available. In such scenario, the signal measurement includes an error due to the extra path length traveled because of reflection or diffraction, which is known as non-line-of-sight (NLOS) error [7]. In an NLOS environ- ment, directly applying the LOS algorithms will result in er- roneous location estimation [8]. Hence, it is necessary to de- velop the location algorithms which are robust to NLOS ef- fects. In this paper, we focus on source location using the TOA information. For a TOA-based location system, the delay of the first arriving signal path is considerably larger than the true TOA due to signal propagation around obstacles such as buildings in NLOS environments [9]. Wylie and Holtzman [7] pro- posed a simple LOS TOA reconstruction algorithm to reduce the location estimation error due to NLOS propagation. The algorithm requires a prior knowledge of NLOS error statis- tics and cannot be expected to locate the source effectively in pure NLOS conditions. Yu and Guo [10] proposed a Taylor-
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