Distributed Kalman filtering based on consensus strategies

In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and on the estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a...

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Bibliographic Details
Published in:IEEE journal on selected areas in communications 2008-05, Vol.26 (4), p.622-633
Main Authors: Carli, R., Chiuso, A., Schenato, L., Zampieri, S.
Format: Article
Language:English
Subjects:
Convergence
Data processing
Dynamical systems
Estimates
Exchanging
Filtering
Gain
Kalman filters
Messages
Optimization
Performance evaluation
Sampling
Sampling methods
Spread spectrum communication
State estimation
Statistical distributions
Strategy
Studies
Wireless sensor networks
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Summary:In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and on the estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain for scalar systems. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we show that although the joint optimization of the consensus matrix and the Kalman gain is in general a non-convex problem, it is possible to compute them under some relevant scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.
ISSN:0733-8716
1558-0008
DOI:10.1109/JSAC.2008.080505