172 research outputs found
Gossip and Distributed Kalman Filtering: Weak Consensus under Weak Detectability
The paper presents the gossip interactive Kalman filter (GIKF) for
distributed Kalman filtering for networked systems and sensor networks, where
inter-sensor communication and observations occur at the same time-scale. The
communication among sensors is random; each sensor occasionally exchanges its
filtering state information with a neighbor depending on the availability of
the appropriate network link. We show that under a weak distributed
detectability condition:
1. the GIKF error process remains stochastically bounded, irrespective of the
instability properties of the random process dynamics; and
2. the network achieves \emph{weak consensus}, i.e., the conditional
estimation error covariance at a (uniformly) randomly selected sensor converges
in distribution to a unique invariant measure on the space of positive
semi-definite matrices (independent of the initial state.)
To prove these results, we interpret the filtered states (estimates and error
covariances) at each node in the GIKF as stochastic particles with local
interactions. We analyze the asymptotic properties of the error process by
studying as a random dynamical system the associated switched (random) Riccati
equation, the switching being dictated by a non-stationary Markov chain on the
network graph.Comment: Submitted to the IEEE Transactions, 30 pages
Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs
The paper considers gossip distributed estimation of a (static) distributed
random field (a.k.a., large scale unknown parameter vector) observed by
sparsely interconnected sensors, each of which only observes a small fraction
of the field. We consider linear distributed estimators whose structure
combines the information \emph{flow} among sensors (the \emph{consensus} term
resulting from the local gossiping exchange among sensors when they are able to
communicate) and the information \emph{gathering} measured by the sensors (the
\emph{sensing} or \emph{innovations} term.) This leads to mixed time scale
algorithms--one time scale associated with the consensus and the other with the
innovations. The paper establishes a distributed observability condition
(global observability plus mean connectedness) under which the distributed
estimates are consistent and asymptotically normal. We introduce the
distributed notion equivalent to the (centralized) Fisher information rate,
which is a bound on the mean square error reduction rate of any distributed
estimator; we show that under the appropriate modeling and structural network
communication conditions (gossip protocol) the distributed gossip estimator
attains this distributed Fisher information rate, asymptotically achieving the
performance of the optimal centralized estimator. Finally, we study the
behavior of the distributed gossip estimator when the measurements fade (noise
variance grows) with time; in particular, we consider the maximum rate at which
the noise variance can grow and still the distributed estimator being
consistent, by showing that, as long as the centralized estimator is
consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page
On Robustness Properties in Empirical Centroid Fictitious Play
Empirical Centroid Fictitious Play (ECFP) is a generalization of the
well-known Fictitious Play (FP) algorithm designed for implementation in
large-scale games. In ECFP, the set of players is subdivided into equivalence
classes with players in the same class possessing similar properties. Players
choose a next-stage action by tracking and responding to aggregate statistics
related to each equivalence class. This setup alleviates the difficult task of
tracking and responding to the statistical behavior of every individual player,
as is the case in traditional FP. Aside from ECFP, many useful modifications
have been proposed to classical FP, e.g., rules allowing for network-based
implementation, increased computational efficiency, and stronger forms of
learning. Such modifications tend to be of great practical value; however,
their effectiveness relies heavily on two fundamental properties of FP:
robustness to alterations in the empirical distribution step size process, and
robustness to best-response perturbations. The main contribution of the paper
is to show that similar robustness properties also hold for the ECFP algorithm.
This result serves as a first step in enabling practical modifications to ECFP,
similar to those already developed for FP.Comment: Submitted for publication. Initial Submission: Mar. 201
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