14,200 research outputs found
An Improved Variable Structure Adaptive Filter Design and Analysis for Acoustic Echo Cancellation
In this research an advance variable structure adaptive Multiple Sub-Filters (MSF) based algorithm for single channel Acoustic Echo Cancellation (AEC) is proposed and analyzed. This work suggests a new and improved direction to find the optimum tap-length of adaptive filter employed for AEC. The structure adaptation, supported by a tap-length based weight update approach helps the designed echo canceller to maintain a trade-off between the Mean Square Error (MSE) and time taken to attain the steady state MSE. The work done in this paper focuses on replacing the fixed length sub-filters in existing MSF based AEC algorithms which brings refinements in terms of convergence, steady state error and tracking over the single long filter, different error and common error algorithms. A dynamic structure selective coefficient update approach to reduce the structural and computational cost of adaptive design is discussed in context with the proposed algorithm. Simulated results reveal a comparative performance analysis over proposed variable structure multiple sub-filters designs and existing fixed tap-length sub-filters based acoustic echo cancellers
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
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
The Generalised Raychaudhuri Equations : Examples
Specific examples of the generalized Raychaudhuri Equations for the evolution
of deformations along families of dimensional surfaces embedded in a
background dimensional spacetime are discussed. These include string
worldsheets embedded in four dimensional spacetimes and two dimensional
timelike hypersurfaces in a three dimensional curved background. The issue of
focussing of families of surfaces is introduced and analysed in some detail.Comment: 8 pages (Revtex, Twocolumn format). Corrected(see section on string
worldsheets), reorganised and shortened slightl
Cosmic optical activity from an inhomogeneous Kalb-Ramond field
The effects of introducing a harmonic spatial inhomogeneity into the
Kalb-Ramond field, interacting with the Maxwell field according to a
`string-inspired' proposal made in earlier work are investigated. We examine in
particular the effects on the polarization of synchrotron radiation from
cosmologically distant (i.e. of redshift greater than 2) galaxies, as well as
the relation between the electric and magnetic components of the radiation
field. The rotation of the polarization plane of linearly polarized radiation
is seen to acquire an additional contribution proportional to the square of the
frequency of the dual Kalb-Ramond axion wave, assuming that it is far smaller
compared to the frequency of the radiation field.Comment: 9 pages, Revtex, no figure
Sensor Networks with Random Links: Topology Design for Distributed Consensus
In a sensor network, in practice, the communication among sensors is subject
to:(1) errors or failures at random times; (3) costs; and(2) constraints since
sensors and networks operate under scarce resources, such as power, data rate,
or communication. The signal-to-noise ratio (SNR) is usually a main factor in
determining the probability of error (or of communication failure) in a link.
These probabilities are then a proxy for the SNR under which the links operate.
The paper studies the problem of designing the topology, i.e., assigning the
probabilities of reliable communication among sensors (or of link failures) to
maximize the rate of convergence of average consensus, when the link
communication costs are taken into account, and there is an overall
communication budget constraint. To consider this problem, we address a number
of preliminary issues: (1) model the network as a random topology; (2)
establish necessary and sufficient conditions for mean square sense (mss) and
almost sure (a.s.) convergence of average consensus when network links fail;
and, in particular, (3) show that a necessary and sufficient condition for both
mss and a.s. convergence is for the algebraic connectivity of the mean graph
describing the network topology to be strictly positive. With these results, we
formulate topology design, subject to random link failures and to a
communication cost constraint, as a constrained convex optimization problem to
which we apply semidefinite programming techniques. We show by an extensive
numerical study that the optimal design improves significantly the convergence
speed of the consensus algorithm and can achieve the asymptotic performance of
a non-random network at a fraction of the communication cost.Comment: Submitted to IEEE Transaction
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