Non-line-of-sight Bias Research Articles

A Robust Bisection-Based Estimator for TOA-Based Target Localization in NLOS Environments

This letter addresses the problem of target localization in harsh indoor environments based on range measurements. To mitigate the non-line-of-sight (NLOS) bias, we propose a novel robust estimator by transforming the localization problem into a generalized trust region sub-problem framework. Although still non-convex in general, this class of problems can be readily solved exactly by means of bisection procedure. The new approach does not require to make any assumptions about the statistics of NLOS bias, nor to try to distinguish which links are NLOS and which are not. Unlike the existing algorithms, the computational complexity of the proposed algorithm is linear in the number of reference nodes. Our simulation results corroborate the effectiveness of the new algorithm in terms of NLOS bias mitigation and show that the performance of our estimator is highly competitive with the performance of the state-of-the-art algorithms. In fact, they show that the novel estimator outperforms slightly the existing ones in general, and that it always provides a feasible solution.

A bisection-based approach for exact target localization in NLOS environments

This work addresses the range-based target localization problem in adverse non-line-of-sight (NLOS) environments. We start by deriving the maximum likelihood (ML) estimator from the measurement model, since it is asymptotically efficient. However, this estimator is highly non-convex and difficult to solve directly. Hence, we convert the localization problem into a generalized trust region sub-problem (GTRS) framework. Although still non-convex in general, the derived estimator is strictly decreasing over a readily obtained interval, and thus, can be solved exactly by a bisection procedure. In huge contrast to existing algorithms, which either require the knowledge about the magnitude of the NLOS bias or to a priori distinguish between line-of-sight (LOS) and NLOS links, the new one does not require such prerequisites. Also, the computational complexity of the proposed algorithm is linear in the number of reference nodes, unlike the majority of existing ones. Our simulation results show that the new algorithm possesses a steady NLOS bias mitigation capacity and that it represents an excellent alternative in the sense of the trade off between accuracy and complexity. To be more specific, it not only matches the performance of existing methods (majority of which significantly more computationally complex) but outperforms them in general. Moreover, the performance of the proposed algorithm is validated through real-indoor experimental data.

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

One of the challenging problems in collaborative position localization arises when the distance measurements contain non-line-of-sight (NLOS) biases. Convex optimization has played a major role in modelling such problems and numerical algorithm developments. One of the successful examples is the semi-definite programming (SDP), which translates Euclidean distances into the constraints of positive semidefinite matrices, leading to a large number of constraints in the case of NLOS biases. In this paper, we propose a new convex optimization model that is built upon the concept of Euclidean distance matrix (EDM). The resulting EDM optimization has an advantage that its Lagrangian dual problem is well structured and hence is conducive to algorithm developments. We apply a recently proposed 3-block alternating direction method of multipliers to the dual problem and tested the algorithm on some real as well as simulated data of large scale. In particular, the EDM model significantly outperforms the existing SDP model and several others.

HEVA: cooperative localization using a combined non-parametric belief propagation and variational message passing approach

This paper proposes a novel cooperative localization method for distributed wireless networks in 3-dimensional (3D) global positioning system (GPS) denied environments. The proposed method, which is referred to as hybrid ellipsoidal variational algorithm (HEVA), combines the use of non-parametric belief propagation (NBP) and variational Bayes (VB) to benefit from both the use of the rich information in NBP and compact communication size of a parametric form. InHEVA, two novel filters are also employed. The first one mitigates non-line-of-sight (NLoS) timeof- arrival (ToA) messages, permitting it to work well in high noise environments with NLoS bias while the second one decreases the number of calculations. Simulation results illustrate that HEVA significantly outperforms traditional NBP methods in localization while requires only 50%of their complexity. The superiority of VB over other clustering techniques is also shown.

Least Square Cooperative Localization

Location awareness is becoming essential for emerging wireless applications where most network activities require the location information of network nodes, e.g., routing between nodes in ad-hoc sensor networks, positioning vehicles on the road, or tracking targets in underwater acoustic sensor networks. In particular, cooperation among nodes is highly beneficial for the localization accuracy and coverage in harsh environments. In this paper, we study least square (LS) cooperative localization in the presence of arbitrary non-line-of-sight (NLOS) ranging bias. To develop the network position error bound (PEB), we first derive the Fisher information matrix (FIM) for a general NLOS bias model and show that a Gaussian bias due to NLOS effects is the worst case that produces the extremal FIM, whereas a constant bias or equivalently full line-of-sight is the best situation leading to the largest FIM in a sense of Löwner partial ordering. We then analyze the asymptotic performance, such as uniform convergence, consistency, and efficiency, of LS cooperative localization to quantify the deviations of localization accuracy for LS, squared-range LS, and squared-range weighted LS solutions from the fundamental limit (i.e., Cramér-Rao lower bound) due to their practical tractability. We also propose a simple distributed algorithm for LS cooperative localization by integrating squared-range relaxation into Gaussian variational message passing on the localization network. To account for stochastic natures of node locations and populations, we further characterize the network PEB for Gilbert's disk localization network, where anchors and/or agents are randomly distributed in the network according to point processes.

A Two-Step Optimizing Algorithm for TOA Real-Time Dynamic Localization in NLOS Environment

Non-line-of-sight (NLOS) is one of the main factors that affect the ranging accuracy in wireless localization. This paper proposes a two-step optimizing algorithm for TOA real-time tracking in NLOS environment. Step one, use weighted least-squares (WLS) algorithm, combined with the NLOS identification informations, to mitigate NLOS bias. Step two, utilize Kalman filtering to optimize the localization results. Simulation results show that the proposed two-step algorithm can obtain better localization accuracy, especially when there are serious NLOS obstructions.

Sequential Quadratic Method for GPS NLOS Positioning in Urban Canyon Envi-ronments

In this paper, the problem of GPS non-line-of-sight (NLOS) positioning in urban canyon environment is considered. We propose a new position-determination estimator based on the sequential quadratic programming (SQP) that is able to estimate and eliminate the path-delay error caused by the indirect transmission of the GPS signal. The estimator takes into account the measurement bias resulting from NLOS transmission, and in the mean-time also improves the location accuracy of a satellite positioning system. The present method can effectively eliminate the NLOS delay errors and is also able to improve the location accuracy of a satellite navigation receiver in an urban canyon environment. A Wilcoxon-norm-based regressor is further derived to improve the probability of detection of the NLOS biases. The Wilcoxon regressor is a robust estimator that is well suitable for identifying outliers (in our case, the NLOS biases) during the regression process. In our experimental results, it is demonstrated that the proposed estimator can compute the coordinate of a user location in an accurate fashion after identifying and removing the measurement biases.

Mobile Location with NLOS Identification and Mitigation Based on Modified Kalman Filtering

In order to enhance accuracy and reliability of wireless location in the mixed line-of-sight (LOS) and non-line-of-sight (NLOS) environments, a robust mobile location algorithm is presented to track the position of a mobile node (MN). An extended Kalman filter (EKF) modified in the updating phase is utilized to reduce the NLOS error in rough wireless environments, in which the NLOS bias contained in each measurement range is estimated directly by the constrained optimization method. To identify the change of channel situation between NLOS and LOS, a low complexity identification method based on innovation vectors is proposed. Numerical results illustrate that the location errors of the proposed algorithm are all significantly smaller than those of the iterated NLOS EKF algorithm and the conventional EKF algorithm in different LOS/NLOS conditions. Moreover, this location method does not require any statistical distribution knowledge of the NLOS error. In addition, complexity experiments suggest that this algorithm supports real-time applications.

Characteristics of the NLoS Bias for an Outdoor-to-Indoor Scenario at 2.45 GHz and 5.2 GHz

Time-based localization by terrestrial cellular mobile radio as a complement to global navigation satellite systems has gained significant attention. However, under non-line-of-sight (NLoS) conditions, the performance of positioning receivers is degraded by an additional bias. This NLoS bias is defined as the additional propagation distance between the first detectable path and the geometric line of sight. In this letter, we address the NLoS bias as obtained by a channel measurement campaign at different carrier frequencies in an outdoor-to-indoor scenario. It turns out that the obtained NLoS bias is mainly uncorrelated between different base-station links. Furthermore, the NLoS bias is found to be strongly dependent on the geometry of the scenario. In so-called ”mild” scenarios, we found out that the NLoS bias is small and almost frequency-independent. In scenarios we call ”severe,” the NLoS bias is large and frequency-dependent. Additionally, we present the joint probability distributions of the NLoS bias, the normalized power of the first detectable path, and its angle of arrival for carrier frequencies of 2.45 and 5.2 GHz. Moreover, the decorrelation distance of the NLoS bias for a moving receiver is evaluated.

CHARACTERIZATION AND MITIGATION OF RANGE ESTIMATION ERRORS FOR AN RTT-BASED IEEE 802.11 INDOOR LOCATION SYSTEM

Inaccurate range estimates often restrict indoor position- ing systems, resulting in a more remarkable drawback when using an already-deployed IEEE 802.11 network. This is the case of the time de- lay based location system that this paper deals with. The main causes of these inaccuracies are multipath and non-line-of-sight (NLOS) ef- fects. These efiects can be solved to a large degree by characterizing arrival times and range estimation errors. For this reason, this pa- per analyzes multipath and NLOS efiects involved in the round-trip time (RTT) discrete measuring process, which is conducted before each range estimate. RTT observations obtained in this process for difier- ent real indoor environments provide useful statistical information that allows to make the work extendable to other similar scenarios. More- over, from this statistical information, the nodes in the network can estimate several parameters of the range estimates distribution while performing the location process. These are used to reduce the error caused by multipath components and to predict and correct the NLOS biases produced. In this way, the NLOS error is dynamically estimated and corrected, achieving better results than classical approaches based on static parameters.

NLOS Mitigation Using Linear Programming in Ultrawideband Location-Aware Networks

In this paper, we propose a linear-programming (LP) approach to the problem of nonline-of-sight (NLOS) mitigation in ad hoc ultrawideband wireless networks. The locations of ldquounlocalizedrdquo nodes can be estimated using range or distance estimates from location-aware ldquoanchorrdquo nodes. In the absence of LOS between the unlocalized and anchor nodes, e.g., in indoor networks, the NLOS range estimates can be significantly biased. The direct incorporation of these biased range estimates into practical location estimators, such as the least squares estimator, without the mitigation of these bias errors, can potentially lead to severe degradation in the accuracy of node-location estimates. On the other hand, with certain geometries of anchor nodes, NLOS range estimates can be used to improve the accuracy of location estimation. Furthermore, discarding the biased range estimates may not be a viable option, as the number of range estimates available may be limited. We present a novel NLOS-bias mitigation scheme based on LP, that 1) allows us to incorporate NLOS range information into location estimation, but 2) does not allow NLOS bias errors to degrade node-localization accuracy.

Non-line-of-sight identification in ultra-wideband systems based on received signal statistics

Non-line-of-sight (NLOS) propagation can severely degrade the reliability of communication and localisation accuracy in indoor ultra-wideband (UWB) ‘location-aware’ networks. Link adaptation and NLOS bias mitigation techniques have respectively been proposed to alleviate these effects, but implicitly rely on the ability to accurately distinguish between LOS and NLOS propagation scenarios. A statistical NLOS identification technique based on the hypothesis-testing of received signal parameters in UWB propagation channels is discussed. In contrast to narrowband and wideband signals, UWB signals possess higher temporal resolution and robustness to multipath fading. We show that these characteristics result in differences in the statistics of (a) the time-of-arrival (TOA), (b) the received signal strength (RSS) and (c) the root-mean-squared delay spread (RDS) of the received signals, between LOS and NLOS propagation scenarios, which can be exploited for accurate channel identification. We statistically characterise the ability of TOA, RSS and RDS estimates to distinguish between LOS and NLOS propagation based on an extensive indoor measurement campaign. Our measurement results suggest that the RDS of UWB signals can, even in isolation and without complete statistical information, serve as a robust and computationally efficient indicator of the LOS/NLOS nature of propagation. Finally, we demonstrate the efficacy of the discussed NLOS identification method in a location-tracking application based on indoor UWB measurements.