107 research outputs found
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Analysis of incremental augmented affine projection algorithm for distributed estimation of complex-valued signals
This paper considers the problem of distributed estimation in an incremental network when the measurements taken by the node follow a widely linear model. The proposed algorithm which we refer to it as incremental augmented affine projection algorithm (incAAPA) utilizes the full second order statistical information in the complex domain. Moreover, it exploits spatio-temporal diversity to improve the estimation performance. We derive steady-state performance metric of the incAAPA in terms of the mean-square deviation (MSD). We further derive sufficient conditions to ensure mean-square convergence. Our analysis illustrate that the proposed algorithm is able to process both second order circular (proper) and noncircular (improper) signals. The validity of the theoretical results and the good performance of the proposed algorithm are demonstrated by several computer simulations
Variable Step-Size Widely Linear Complex-Valued Affine Projection Algorithm and Performance Analysis
A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence
A novel framework for a unifying treatment of quaternion valued adaptive
filtering algorithms is introduced. This is achieved based on a rigorous
account of quaternion differentiability, the proposed I-gradient, and the use
of augmented quaternion statistics to account for real world data with
noncircular probability distributions. We first provide an elegant solution for
the calculation of the gradient of real functions of quaternion variables
(typical cost function), an issue that has so far prevented systematic
development of quaternion adaptive filters. This makes it possible to unify the
class of existing and proposed quaternion least mean square (QLMS) algorithms,
and to illuminate their structural similarity. Next, in order to cater for both
circular and noncircular data, the class of widely linear QLMS (WL-QLMS)
algorithms is introduced and the subsequent convergence analysis unifies the
treatment of strictly linear and widely linear filters, for both proper and
improper sources. It is also shown that the proposed class of HR gradients
allows us to resolve the uncertainty owing to the noncommutativity of
quaternion products, while the involution gradient (I-gradient) provides
generic extensions of the corresponding real- and complex-valued adaptive
algorithms, at a reduced computational cost. Simulations in both the strictly
linear and widely linear setting support the approach
Data-driven multivariate and multiscale methods for brain computer interface
This thesis focuses on the development of data-driven multivariate and multiscale methods
for brain computer interface (BCI) systems. The electroencephalogram (EEG), the
most convenient means to measure neurophysiological activity due to its noninvasive nature,
is mainly considered. The nonlinearity and nonstationarity inherent in EEG and its
multichannel recording nature require a new set of data-driven multivariate techniques to
estimate more accurately features for enhanced BCI operation. Also, a long term goal
is to enable an alternative EEG recording strategy for achieving long-term and portable
monitoring.
Empirical mode decomposition (EMD) and local mean decomposition (LMD), fully
data-driven adaptive tools, are considered to decompose the nonlinear and nonstationary
EEG signal into a set of components which are highly localised in time and frequency. It
is shown that the complex and multivariate extensions of EMD, which can exploit common
oscillatory modes within multivariate (multichannel) data, can be used to accurately
estimate and compare the amplitude and phase information among multiple sources, a
key for the feature extraction of BCI system. A complex extension of local mean decomposition
is also introduced and its operation is illustrated on two channel neuronal
spike streams. Common spatial pattern (CSP), a standard feature extraction technique
for BCI application, is also extended to complex domain using the augmented complex
statistics. Depending on the circularity/noncircularity of a complex signal, one of the
complex CSP algorithms can be chosen to produce the best classification performance
between two different EEG classes.
Using these complex and multivariate algorithms, two cognitive brain studies are
investigated for more natural and intuitive design of advanced BCI systems. Firstly, a Yarbus-style auditory selective attention experiment is introduced to measure the user
attention to a sound source among a mixture of sound stimuli, which is aimed at improving
the usefulness of hearing instruments such as hearing aid. Secondly, emotion experiments
elicited by taste and taste recall are examined to determine the pleasure and displeasure
of a food for the implementation of affective computing. The separation between two
emotional responses is examined using real and complex-valued common spatial pattern
methods.
Finally, we introduce a novel approach to brain monitoring based on EEG recordings
from within the ear canal, embedded on a custom made hearing aid earplug. The new
platform promises the possibility of both short- and long-term continuous use for standard
brain monitoring and interfacing applications
Study of L0-norm constraint normalized subband adaptive filtering algorithm
Limited by fixed step-size and sparsity penalty factor, the conventional
sparsity-aware normalized subband adaptive filtering (NSAF) type algorithms
suffer from trade-off requirements of high filtering accurateness and quicker
convergence behavior. To deal with this problem, this paper proposes variable
step-size L0-norm constraint NSAF algorithms (VSS-L0-NSAFs) for sparse system
identification. We first analyze mean-square-deviation (MSD) statistics
behavior of the L0-NSAF algorithm innovatively in according to a novel
recursion form and arrive at corresponding expressions for the cases that
background noise variance is available and unavailable, where correlation
degree of system input is indicated by scaling parameter r. Based on
derivations, we develop an effective variable step-size scheme through
minimizing the upper bounds of the MSD under some reasonable assumptions and
lemma. To realize performance improvement, an effective reset strategy is
incorporated into presented algorithms to tackle with non-stationary
situations. Finally, numerical simulations corroborate that the proposed
algorithms achieve better performance in terms of estimation accurateness and
tracking capability in comparison with existing related algorithms in sparse
system identification and adaptive echo cancellation circumstances.Comment: 15 pages,15 figure
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