Characterization of non-line-of-sight (NLOS) bias via analysis of clutter topology

Abstract

Clutter-prone environments are challenging for range-based localization, where distances between anchors and the unlocalised node are estimated using wireless technologies like radio, ultrasound, etc. This is so due to the incidence of Non-Line-Of-Sight (NLOS) distance measurements as the direct path between the two is occluded by the presence of clutter.Thus NLOS distances, having large positive biases, can severely degrade localization accuracy. Till date, NLOS error has been modelled as various distributions including uniform, Gaussian, Poisson and exponential. In this paper, we show that clutter topology itself plays a vital role in the characterization of NLOS bias. We enumerate a feature-set for clutter topologies, including features that can be practically deduced without complete knowl edge of the clutter topology. We then analyze the significance of these features, both individually and in combination with each other, in the estimation of the NLOS rate as well as the NLOS bias distribution for arbitrary clutter topologies. We show that we can obtain the NLOS rate with an error of only 0.03 for a given clutter topology using only those clutter topology features that can be practically realized in a real deployment. We show that estimating the NLOS bias distribution is more challenging which give a small number of poor estimations. I. I NT RODUCTIONLocation awareness has become an integral part of the modern lifestyle. For example, GPS enabled smartphone and GPS receivers enable us to navigate to our destination or provide us information pertinent to our current location. Fleet managers are able to locate and monitor cargo moving in transit. Office and home areas are instrumented to furnish information relating to the time and area we are currently at. Most location services function with the help of anchors, nodes aware of their own positions, and distances measured to them. When there are obstacles in the environment, the accuracy of these measured distances, and thus the estimated position, suffers significantly. This degradation is caused by the existence of Non-Line-of-Sight (NLOS) distances which have large positive biases.Until now, a large body of research has been conducted to address this issue. Some techniques [1], [2] try to detect and separate these erroneous distances from the position estimation process, while others [3], [4], [5], [6] incorporate these distances in a way that mitigates their negative influence on the location accuracy. NLOS bias is hard to model accurately as it is shown to depend on the (arbitrary) underlying topology/arrangement of 978-1-4673-0387-3/12/$31.00 ©20 12 IEEE 1247 the obstacles in the environment [7], [8], [9], [10], [11], [12]. For this reason, it is typically assumed to be uniform [6], [5], [13], [1], Gaussian [14] or exponential [1], [15], [4] for the sake of convenience. Jourdan et al. [12] mention the use of empirically derived NLOS bias distributions in calculating the PEB error bound for localization in a cluttered environment.This paper addresses the p...

Robust Target Localization Based on Squared Range Iterative Reweighted Least Squares

“…Specifically, using Theorem 1 and the definitions of A, W (k) , and D, we can easily verify that (13) holds for the proposed optimization problem in (11). Thus, the optimization problem (11) has a global minimizer for all the iterations. Also by using Theorem 2, y (k) is an optimal solution of (11) if and only if there exists λ ∈ R such that:…”

“…Thus, the probability β denotes the ratio of outlier measurements to all the measurements, also known as the contamination ratio. The outlier error distribution, H(v), is commonly modeled with a Uniform distribution [11,12], a shifted Gaussian distribution [9,13,14], a Rayleigh distribution [14], or an exponential distribution [15]. However, it is worthwhile to mention that our proposed method does not rely on the distribution of H(v).…”

“…. , R. Note that in (11), a quadratic objective function is being minimized subject to a quadratic equality constraint. This special class of optimization problems is called Generalized Trust Region Subproblem (GTRS) [10].…”

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“…For this range measurement setup, we derive a distribution for the path length of the first-arriving NLOS signal under first-order reflections. 1 In achieving this goal, the paper makes the following contributions:…”

“…Thus, in addition to noise, a positive bias term needs to be accounted for in the measurement. The approach to dealing with this term has been the subject of much research over the years in the localization literature [1,Sec. VII], [2].…”