32,233 research outputs found
Distributed localization of a RF target in NLOS environments
We propose a novel distributed expectation maximization (EM) method for
non-cooperative RF device localization using a wireless sensor network. We
consider the scenario where few or no sensors receive line-of-sight signals
from the target. In the case of non-line-of-sight signals, the signal path
consists of a single reflection between the transmitter and receiver. Each
sensor is able to measure the time difference of arrival of the target's signal
with respect to a reference sensor, as well as the angle of arrival of the
target's signal. We derive a distributed EM algorithm where each node makes use
of its local information to compute summary statistics, and then shares these
statistics with its neighbors to improve its estimate of the target
localization. Since all the measurements need not be centralized at a single
location, the spectrum usage can be significantly reduced. The distributed
algorithm also allows for increased robustness of the sensor network in the
case of node failures. We show that our distributed algorithm converges, and
simulation results suggest that our method achieves an accuracy close to the
centralized EM algorithm. We apply the distributed EM algorithm to a set of
experimental measurements with a network of four nodes, which confirm that the
algorithm is able to localize a RF target in a realistic non-line-of-sight
scenario.Comment: 30 pages, 11 figure
Distributed Maximum Likelihood for Simultaneous Self-localization and Tracking in Sensor Networks
We show that the sensor self-localization problem can be cast as a static
parameter estimation problem for Hidden Markov Models and we implement fully
decentralized versions of the Recursive Maximum Likelihood and on-line
Expectation-Maximization algorithms to localize the sensor network
simultaneously with target tracking. For linear Gaussian models, our algorithms
can be implemented exactly using a distributed version of the Kalman filter and
a novel message passing algorithm. The latter allows each node to compute the
local derivatives of the likelihood or the sufficient statistics needed for
Expectation-Maximization. In the non-linear case, a solution based on local
linearization in the spirit of the Extended Kalman Filter is proposed. In
numerical examples we demonstrate that the developed algorithms are able to
learn the localization parameters.Comment: shorter version is about to appear in IEEE Transactions of Signal
Processing; 22 pages, 15 figure
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
On the structural nature of cooperation in distributed network localization
We demonstrate analytically that the contribution of cooperation in improving the accuracy of distributed network localization has a fundamentally structural nature, rather then statistical as widely believed. To this end we first introduce a new approach to build Fisher Information Matrices (FIMs), in which the individual contribution of each cooperative pair of nodes is captured explicitly by a corresponding information vector. The approach offers new insight onto the structure of FIMs, enabling us to easily account for both anchor and node location uncertainties in assessing lower bounds on localization errors. Using this construction it is surprisingly found that in the presence of node location uncertainty and regardless of ranging error variances or network size, the Fisher information matrix (FIM) terms corresponding to the information added by node-to-node cooperation nearly vanish. In other words, the analysis reveals that the key contribution of cooperation in network localization is not to add statistical node-to-node information (in the Fisher sense), but rather to provide a structure over which information is better exploited
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