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-