3,697 research outputs found
A Statistically Modelling Method for Performance Limits in Sensor Localization
In this paper, we study performance limits of sensor localization from a
novel perspective. Specifically, we consider the Cramer-Rao Lower Bound (CRLB)
in single-hop sensor localization using measurements from received signal
strength (RSS), time of arrival (TOA) and bearing, respectively, but
differently from the existing work, we statistically analyze the trace of the
associated CRLB matrix (i.e. as a scalar metric for performance limits of
sensor localization) by assuming anchor locations are random. By the Central
Limit Theorems for -statistics, we show that as the number of the anchors
increases, this scalar metric is asymptotically normal in the RSS/bearing case,
and converges to a random variable which is an affine transformation of a
chi-square random variable of degree 2 in the TOA case. Moreover, we provide
formulas quantitatively describing the relationship among the mean and standard
deviation of the scalar metric, the number of the anchors, the parameters of
communication channels, the noise statistics in measurements and the spatial
distribution of the anchors. These formulas, though asymptotic in the number of
the anchors, in many cases turn out to be remarkably accurate in predicting
performance limits, even if the number is small. Simulations are carried out to
confirm our results
Fundamental Limits of Wideband Localization - Part II: Cooperative Networks
The availability of positional information is of great importance in many
commercial, governmental, and military applications. Localization is commonly
accomplished through the use of radio communication between mobile devices
(agents) and fixed infrastructure (anchors). However, precise determination of
agent positions is a challenging task, especially in harsh environments due to
radio blockage or limited anchor deployment. In these situations, cooperation
among agents can significantly improve localization accuracy and reduce
localization outage probabilities. A general framework of analyzing the
fundamental limits of wideband localization has been developed in Part I of the
paper. Here, we build on this framework and establish the fundamental limits of
wideband cooperative location-aware networks. Our analysis is based on the
waveforms received at the nodes, in conjunction with Fisher information
inequality. We provide a geometrical interpretation of equivalent Fisher
information for cooperative networks. This approach allows us to succinctly
derive fundamental performance limits and their scaling behaviors, and to treat
anchors and agents in a unified way from the perspective of localization
accuracy. Our results yield important insights into how and when cooperation is
beneficial.Comment: To appear in IEEE Transactions on Information Theor
Cramer-Rao Bounds for Joint RSS/DoA-Based Primary-User Localization in Cognitive Radio Networks
Knowledge about the location of licensed primary-users (PU) could enable
several key features in cognitive radio (CR) networks including improved
spatio-temporal sensing, intelligent location-aware routing, as well as aiding
spectrum policy enforcement. In this paper we consider the achievable accuracy
of PU localization algorithms that jointly utilize received-signal-strength
(RSS) and direction-of-arrival (DoA) measurements by evaluating the Cramer-Rao
Bound (CRB). Previous works evaluate the CRB for RSS-only and DoA-only
localization algorithms separately and assume DoA estimation error variance is
a fixed constant or rather independent of RSS. We derive the CRB for joint
RSS/DoA-based PU localization algorithms based on the mathematical model of DoA
estimation error variance as a function of RSS, for a given CR placement. The
bound is compared with practical localization algorithms and the impact of
several key parameters, such as number of nodes, number of antennas and
samples, channel shadowing variance and correlation distance, on the achievable
accuracy are thoroughly analyzed and discussed. We also derive the closed-form
asymptotic CRB for uniform random CR placement, and perform theoretical and
numerical studies on the required number of CRs such that the asymptotic CRB
tightly approximates the numerical integration of the CRB for a given
placement.Comment: 20 pages, 11 figures, 1 table, submitted to IEEE Transactions on
Wireless Communication
Benchmarking of localization solutions : guidelines for the selection of evaluation points
Indoor localization solutions are key enablers for next-generation indoor navigation and track and tracing solutions. As a result, an increasing number of different localization algorithms have been proposed and evaluated in scientific literature. However, many of these publications do not accurately substantiate the used evaluation methods. In particular, many authors utilize a different number of evaluation points, but they do not (i) analyze if the number of used evaluation points is sufficient to accurately evaluate the performance of their solutions and (ii) report on the uncertainty of the published results. To remedy this, this paper evaluates the influence of the selection of evaluation points. Based on statistical parameters such as the standard error of the mean value, an estimator is defined that can be used to quantitatively analyze the impact of the number of used evaluation points on the confidence interval of the mean value of the obtained results. This estimator is used to estimate the uncertainty of the presented accuracy results, and can be used to identify if more evaluations are required. To validate the proposed estimator, two different localization algorithms are evaluated in different testbeds and using different types of technology, showing that the number of required evaluation points does indeed vary significantly depending on the evaluated solution. (C) 2017 Elsevier B.V. All rights reserved
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