651 research outputs found
Distributed Maximum Likelihood Sensor Network Localization
We propose a class of convex relaxations to solve the sensor network
localization problem, based on a maximum likelihood (ML) formulation. This
class, as well as the tightness of the relaxations, depends on the noise
probability density function (PDF) of the collected measurements. We derive a
computational efficient edge-based version of this ML convex relaxation class
and we design a distributed algorithm that enables the sensor nodes to solve
these edge-based convex programs locally by communicating only with their close
neighbors. This algorithm relies on the alternating direction method of
multipliers (ADMM), it converges to the centralized solution, it can run
asynchronously, and it is computation error-resilient. Finally, we compare our
proposed distributed scheme with other available methods, both analytically and
numerically, and we argue the added value of ADMM, especially for large-scale
networks
On Sensor Network Localization Using SDP Relaxation
A Semidefinite Programming (SDP) relaxation is an effective computational
method to solve a Sensor Network Localization problem, which attempts to
determine the locations of a group of sensors given the distances between some
of them [11]. In this paper, we analyze and determine new sufficient conditions
and formulations that guarantee that the SDP relaxation is exact, i.e., gives
the correct solution. These conditions can be useful for designing sensor
networks and managing connectivities in practice.
Our main contribution is twofold: We present the first non-asymptotic bound
on the connectivity or radio range requirement of the sensors in order to
ensure the network is uniquely localizable. Determining this range is a key
component in the design of sensor networks, and we provide a result that leads
to a correct localization of each sensor, for any number of sensors. Second, we
introduce a new class of graphs that can always be correctly localized by an
SDP relaxation. Specifically, we show that adding a simple objective function
to the SDP relaxation model will ensure that the solution is correct when
applied to a triangulation graph. Since triangulation graphs are very sparse,
this is informationally efficient, requiring an almost minimal amount of
distance information. We also analyze a number objective functions for the SDP
relaxation to solve the localization problem for a general graph.Comment: 20 pages, 4 figures, submitted to the Fields Institute Communications
Series on Discrete Geometry and Optimizatio
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