1,514 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
Large-Scale Sensor Network Localization via Rigid Subnetwork Registration
In this paper, we describe an algorithm for sensor network localization (SNL)
that proceeds by dividing the whole network into smaller subnetworks, then
localizes them in parallel using some fast and accurate algorithm, and finally
registers the localized subnetworks in a global coordinate system. We
demonstrate that this divide-and-conquer algorithm can be used to leverage
existing high-precision SNL algorithms to large-scale networks, which could
otherwise only be applied to small-to-medium sized networks. The main
contribution of this paper concerns the final registration phase. In
particular, we consider a least-squares formulation of the registration problem
(both with and without anchor constraints) and demonstrate how this otherwise
non-convex problem can be relaxed into a tractable convex program. We provide
some preliminary simulation results for large-scale SNL demonstrating that the
proposed registration algorithm (together with an accurate localization scheme)
offers a good tradeoff between run time and accuracy.Comment: 5 pages, 8 figures, 1 table. To appear in Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
Eigenvector Synchronization, Graph Rigidity and the Molecule Problem
The graph realization problem has received a great deal of attention in
recent years, due to its importance in applications such as wireless sensor
networks and structural biology. In this paper, we extend on previous work and
propose the 3D-ASAP algorithm, for the graph realization problem in
, given a sparse and noisy set of distance measurements. 3D-ASAP
is a divide and conquer, non-incremental and non-iterative algorithm, which
integrates local distance information into a global structure determination.
Our approach starts with identifying, for every node, a subgraph of its 1-hop
neighborhood graph, which can be accurately embedded in its own coordinate
system. In the noise-free case, the computed coordinates of the sensors in each
patch must agree with their global positioning up to some unknown rigid motion,
that is, up to translation, rotation and possibly reflection. In other words,
to every patch there corresponds an element of the Euclidean group Euc(3) of
rigid transformations in , and the goal is to estimate the group
elements that will properly align all the patches in a globally consistent way.
Furthermore, 3D-ASAP successfully incorporates information specific to the
molecule problem in structural biology, in particular information on known
substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a
faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a
preprocessing step for dividing the initial graph into smaller subgraphs. Our
extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very
robust to high levels of noise in the measured distances and to sparse
connectivity in the measurement graph, and compare favorably to similar
state-of-the art localization algorithms.Comment: 49 pages, 8 figure
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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