Localization of a wireless device using the time-of-arrivals (TOAs) from different base stations has been studied extensively in the literature. Numerous localization algorithms with different accuracies, computational complexities, a-priori knowledge requirements, and different levels of robustness against non-line-of-sight (NLOS) bias effects also have been reported. However, to our best knowledge, a detailed unified survey of different localization and NLOS mitigation algorithms is not available in the literature. This paper aims to give a comprehensive review of these different TOA-based localization algorithms and their technical challenges, and to point out possible future research directions. Firstly, fundamental lower bounds and some practical estimators that achieve close to these bounds are summarized for line-of-sight (LOS) scenarios. Then, after giving the fundamental lower bounds for NLOS systems, different NLOS mitigation techniques are classified and summarized. Simulation results are also provided in order to compare the performance of various techniques. Finally, a table that summarizes the key characteristics of the investigated techniques is provided to conclude the paper.

A Survey on TOA Based Wireless Localization and NLOS Mitigation Techniques

We consider least squares (LS) approaches for locating a radiating source from range measurements (which we call R-LS) or from range-difference measurements (RD-LS) collected using an array of passive sensors. We also consider LS approaches based on squared range observations (SR-LS) and based on squared range-difference measurements (SRD-LS). Despite the fact that the resulting optimization problems are nonconvex, we provide exact solution procedures for efficiently computing the SR-LS and SRD-LS estimates. Numerical simulations suggest that the exact SR-LS and SRD-LS estimates outperform existing approximations of the SR-LS and SRD-LS solutions as well as approximations of the R-LS and RD-LS solutions which are based on a semidefinite relaxation.

Exact and Approximate Solutions of Source Localization Problems

Three or more base stations (BS) making time-of-arrival measurements of a signal from a mobile station (MS) can locate the MS. However, when some of the measurements are from non-line-of-sight (NLOS) paths, the location errors can be very large. This paper proposes a residual test (RT) that can simultaneously determine the number of line-of-sight (LOS) BS and identify them. Then, localization can proceed with only those LOS BS. The RT works on the principle that when all measurements are LOS, the normalized residuals have a central Chi-Square distribution, versus a noncentral distribution when there is NLOS. The residuals are the squared differences between the estimates and the true position. Normalization by their variances gives a unity variance to the resultant random variables. In simulation studies, for the chosen geometry and NLOS and measurement noise errors, the RT can determine the correct number of LOS-BS over 90% of the time. For four or more BS, where there are at least three LOS-BS, the estimator has variances that are near the Cramer--Rao lower bound.

/pdf/time-of-arrival-based-localization-under-nlos-conditions-1in84jlxfl.pdf

Time-of-arrival based localization under NLOS conditions

Non-line-of-sight (NLOS) identification and mitigation carry significant importance in wireless localization systems. In this paper, we propose a novel NLOS identification technique based on the multipath channel statistics such as the kurtosis, the mean excess delay spread, and the root-mean-square delay spread. In particular, the IEEE 802.15.4a ultrawideband channel models are used as examples and the above statistics are found to be well modeled by log-normal random variables. Subsequently, a joint likelihood ratio test is developed for line-of-sight (LOS) or NLOS identification. Three different weighted least-squares (WLSs) localization techniques that exploit the statistics of multipath components (MPCs) are analyzed. The basic idea behind the proposed WLS approaches is that smaller weights are given to the measurements which are likely to be biased (based on the MPC information), as opposed to variance-based WLS techniques in the literature. Accuracy gains with respect to the conventional least-squares algorithm are demonstrated via Monte-Carlo simulations and verified by theoretical derivations.

/pdf/nlos-identification-and-weighted-least-squares-localization-1qutgel1kz.pdf

NLOS identification and weighted least-squares localization for UWB systems using multipath channel statistics

Localization of objects is fast becoming a major aspect of wireless technologies, with applications in logistics, surveillance, and emergency response. Time-of-arrival (TOA) localization is ideally suited for high-precision localization of objects in particular in indoor environments, where GPS is not available. This paper considers the case where one transmitter and multiple, distributed, receivers are used to estimate the location of a passive (reflecting) object. It furthermore focuses on the situation when the transmitter and receivers can be synchronized, so that TOA (as opposed to time-difference-of-arrival (TDOA)) information can be used. We propose a novel, Two-Step estimation (TSE) algorithm for the localization of the object. We then derive the Cramer-Rao Lower Bound (CRLB) for TOA and show that it is an order of magnitude lower than the CRLB of TDOA in typical setups. The TSE algorithm achieves the CRLB when the TOA measurements are subject to small Gaussian-distributed errors, which is verified by analytical and simulation results. Moreover, practical measurement results show that the estimation error variance of TSE can be 33 dB lower than that of TDOA based algorithms.

Accurate Passive Location Estimation Using TOA Measurements

Sensors at separate locations measuring either the time difference of arrival (TDOA) or time of arrival (TOA) of the signal from an emitter can determine its position as the intersection of hyperbolae for TDOA and of circles for TOA. Because of measurement noise, the nonlinear localization equations become inconsistent; and the hyperbolae or circles no longer intersect at a single point. It is now necessary to find an emitter position estimate that minimizes its deviations from the true position. Methods that first linearize the equations and then perform gradient searches for the minimum suffer from initial condition sensitivity and convergence difficulty. Starting from the maximum likelihood (ML) function, this paper derives a closed-form approximate solution to the ML equations. When there are three sensors on a straight line, it also gives an exact ML estimate. Simulation experiments have demonstrated that these algorithms are near optimal, attaining the theoretical lower bound for different geometries, and are superior to two other closed form linear estimators.

H. Yau Chin Hang

Papers

Exact and approximate maximum likelihood localization algorithms