55 research outputs found
1-Bit Matrix Completion under Exact Low-Rank Constraint
We consider the problem of noisy 1-bit matrix completion under an exact rank
constraint on the true underlying matrix . Instead of observing a subset
of the noisy continuous-valued entries of a matrix , we observe a subset
of noisy 1-bit (or binary) measurements generated according to a probabilistic
model. We consider constrained maximum likelihood estimation of , under a
constraint on the entry-wise infinity-norm of and an exact rank
constraint. This is in contrast to previous work which has used convex
relaxations for the rank. We provide an upper bound on the matrix estimation
error under this model. Compared to the existing results, our bound has faster
convergence rate with matrix dimensions when the fraction of revealed 1-bit
observations is fixed, independent of the matrix dimensions. We also propose an
iterative algorithm for solving our nonconvex optimization with a certificate
of global optimality of the limiting point. This algorithm is based on low rank
factorization of . We validate the method on synthetic and real data with
improved performance over existing methods.Comment: 6 pages, 3 figures, to appear in CISS 201
Connection Between System Parameters and Localization Probability in Network of Randomly Distributed Nodes
This article deals with localization probability in a network of randomly
distributed communication nodes contained in a bounded domain. A fraction of
the nodes denoted as L-nodes are assumed to have localization information while
the rest of the nodes denoted as NL nodes do not. The basic model assumes each
node has a certain radio coverage within which it can make relative distance
measurements. We model both the case radio coverage is fixed and the case radio
coverage is determined by signal strength measurements in a Log-Normal
Shadowing environment. We apply the probabilistic method to determine the
probability of NL-node localization as a function of the coverage area to
domain area ratio and the density of L-nodes. We establish analytical
expressions for this probability and the transition thresholds with respect to
key parameters whereby marked change in the probability behavior is observed.
The theoretical results presented in the article are supported by simulations.Comment: To appear on IEEE Transactions on Wireless Communications, November
200
Non Parametric Distributed Inference in Sensor Networks Using Box Particles Messages
This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times
Soft-connected Rigid Body Localization: State-of-the-Art and Research Directions for 6G
This white paper describes a proposed article that will aim to provide a
thorough study of the evolution of the typical paradigm of wireless
localization (WL), which is based on a single point model of each target,
towards wireless rigid body localization (W-RBL). We also look beyond the
concept of RBL itself, whereby each target is modeled as an independent
multi-point three-dimensional (3D), with shape enforced via a set of
conformation constraints, as a step towards a more general approach we refer to
as soft-connected RBL, whereby an ensemble of several objects embedded in a
given environment, is modeled as a set of soft-connected 3D objects, with rigid
and soft conformation constraints enforced within each object and among them,
respectively. A first intended contribution of the full version of this article
is a compact but comprehensive survey on mechanisms to evolve WL algorithms in
W-RBL schemes, considering their peculiarities in terms of the type of
information, mathematical approach, and features the build on or offer. A
subsequent contribution is a discussion of mechanisms to extend W-RBL
techniques to soft-connected rigid body localization (SCW-RBL) algorithms
Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees
This paper addresses the problem of ad hoc microphone array calibration where
only partial information about the distances between microphones is available.
We construct a matrix consisting of the pairwise distances and propose to
estimate the missing entries based on a novel Euclidean distance matrix
completion algorithm by alternative low-rank matrix completion and projection
onto the Euclidean distance space. This approach confines the recovered matrix
to the EDM cone at each iteration of the matrix completion algorithm. The
theoretical guarantees of the calibration performance are obtained considering
the random and locally structured missing entries as well as the measurement
noise on the known distances. This study elucidates the links between the
calibration error and the number of microphones along with the noise level and
the ratio of missing distances. Thorough experiments on real data recordings
and simulated setups are conducted to demonstrate these theoretical insights. A
significant improvement is achieved by the proposed Euclidean distance matrix
completion algorithm over the state-of-the-art techniques for ad hoc microphone
array calibration.Comment: In Press, available online, August 1, 2014.
http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal
Processing, 201
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