Kullback–Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability

This paper addresses distributed state estimation over a sensor network wherein each node–equipped with processing, communication and sensing capabilities–repeatedly fuses local information with information from the neighbors. Estimation is cast in a Bayesian framework and an information-theoretic a...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 50; no. 3; pp. 707 - 718
Main Authors: Battistelli, Giorgio, Chisci, Luigi
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.03.2014
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Consensus filters
Control theory. Systems
Data processing. List processing. Character string processing
Distributed state estimation
Exact sciences and technology
Information retrieval. Graph
Memory organisation. Data processing
Modelling and identification
Networked estimation
Sensor networks
Software
Theoretical computing
Sensor networks
Distributed state estimation
Networked estimation
Consensus filters
Density estimation
Density measurement
Error estimation
Probability density
Relative entropy
Graph connectivity
Observer
Probability density function
System identification
State estimation
Observability
Bayes estimation
Capability index
Estimation error
Stability
Network flow
Computer simulation
Interconnected power system
Distributed system
Consensus
Requirement
Linear system
Filter
Data fusion
Sensor array
Information theory
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Description
Summary:This paper addresses distributed state estimation over a sensor network wherein each node–equipped with processing, communication and sensing capabilities–repeatedly fuses local information with information from the neighbors. Estimation is cast in a Bayesian framework and an information-theoretic approach to data fusion is adopted by formulating a consensus problem on the Kullback–Leibler average of the local probability density functions (PDFs) to be fused. Exploiting such a consensus on local posterior PDFs, a novel distributed state estimator is derived. It is shown that, for a linear system, the proposed estimator guarantees stability, i.e. mean-square boundedness of the state estimation error in all network nodes, under the minimal requirements of network connectivity and system observability, and for any number of consensus steps. Finally, simulation experiments demonstrate the validity of the proposed approach.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.11.042