42,242 research outputs found
Distributed estimation from relative measurements of heterogeneous and uncertain quality
This paper studies the problem of estimation from relative measurements in a
graph, in which a vector indexed over the nodes has to be reconstructed from
pairwise measurements of differences between its components associated to nodes
connected by an edge. In order to model heterogeneity and uncertainty of the
measurements, we assume them to be affected by additive noise distributed
according to a Gaussian mixture. In this original setup, we formulate the
problem of computing the Maximum-Likelihood (ML) estimates and we design two
novel algorithms, based on Least Squares regression and
Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and
performs the estimation from relative measurements, the soft classification of
the measurements, and the estimation of the noise parameters. The second
algorithm (Distributed LS-EM) is distributed and performs estimation and soft
classification of the measurements, but requires the knowledge of the noise
parameters. We provide rigorous proofs of convergence of both algorithms and we
present numerical experiments to evaluate and compare their performance with
classical solutions. The experiments show the robustness of the proposed
methods against different kinds of noise and, for the Distributed LS-EM,
against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction
A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation
Stochastic approximation techniques play an important role in solving many
problems encountered in machine learning or adaptive signal processing. In
these contexts, the statistics of the data are often unknown a priori or their
direct computation is too intensive, and they have thus to be estimated online
from the observed signals. For batch optimization of an objective function
being the sum of a data fidelity term and a penalization (e.g. a sparsity
promoting function), Majorize-Minimize (MM) methods have recently attracted
much interest since they are fast, highly flexible, and effective in ensuring
convergence. The goal of this paper is to show how these methods can be
successfully extended to the case when the data fidelity term corresponds to a
least squares criterion and the cost function is replaced by a sequence of
stochastic approximations of it. In this context, we propose an online version
of an MM subspace algorithm and we study its convergence by using suitable
probabilistic tools. Simulation results illustrate the good practical
performance of the proposed algorithm associated with a memory gradient
subspace, when applied to both non-adaptive and adaptive filter identification
problems
Bibliographic Review on Distributed Kalman Filtering
In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud
The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area
Robust Decentralized State Estimation and Tracking for Power Systems via Network Gossiping
This paper proposes a fully decentralized adaptive re-weighted state
estimation (DARSE) scheme for power systems via network gossiping. The enabling
technique is the proposed Gossip-based Gauss-Newton (GGN) algorithm, which
allows to harness the computation capability of each area (i.e. a database
server that accrues data from local sensors) to collaboratively solve for an
accurate global state. The DARSE scheme mitigates the influence of bad data by
updating their error variances online and re-weighting their contributions
adaptively for state estimation. Thus, the global state can be estimated and
tracked robustly using near-neighbor communications in each area. Compared to
other distributed state estimation techniques, our communication model is
flexible with respect to reconfigurations and resilient to random failures as
long as the communication network is connected. Furthermore, we prove that the
Jacobian of the power flow equations satisfies the Lipschitz condition that is
essential for the GGN algorithm to converge to the desired solution.
Simulations of the IEEE-118 system show that the DARSE scheme can estimate and
track online the global power system state accurately, and degrades gracefully
when there are random failures and bad data.Comment: to appear in IEEE JSA
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