24 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
Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization
Dual decomposition has been successfully employed in a variety of distributed
convex optimization problems solved by a network of computing and communicating
nodes. Often, when the cost function is separable but the constraints are
coupled, the dual decomposition scheme involves local parallel subgradient
calculations and a global subgradient update performed by a master node. In
this paper, we propose a consensus-based dual decomposition to remove the need
for such a master node and still enable the computing nodes to generate an
approximate dual solution for the underlying convex optimization problem. In
addition, we provide a primal recovery mechanism to allow the nodes to have
access to approximate near-optimal primal solutions. Our scheme is based on a
constant stepsize choice and the dual and primal objective convergence are
achieved up to a bounded error floor dependent on the stepsize and on the
number of consensus steps among the nodes
On a registration-based approach to sensor network localization
We consider a registration-based approach for localizing sensor networks from
range measurements. This is based on the assumption that one can find
overlapping cliques spanning the network. That is, for each sensor, one can
identify geometric neighbors for which all inter-sensor ranges are known. Such
cliques can be efficiently localized using multidimensional scaling. However,
since each clique is localized in some local coordinate system, we are required
to register them in a global coordinate system. In other words, our approach is
based on transforming the localization problem into a problem of registration.
In this context, the main contributions are as follows. First, we describe an
efficient method for partitioning the network into overlapping cliques. Second,
we study the problem of registering the localized cliques, and formulate a
necessary rigidity condition for uniquely recovering the global sensor
coordinates. In particular, we present a method for efficiently testing
rigidity, and a proposal for augmenting the partitioned network to enforce
rigidity. A recently proposed semidefinite relaxation of global registration is
used for registering the cliques. We present simulation results on random and
structured sensor networks to demonstrate that the proposed method compares
favourably with state-of-the-art methods in terms of run-time, accuracy, and
scalability