Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Quaternion involutions and anti-involutions
Computers & Mathematics with Applications
The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
IEEE Transactions on Signal Processing
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Properness and widely linear processing of quaternion random vectors
IEEE Transactions on Information Theory
Augmented second-order statistics of quaternion random signals
Signal Processing
A quaternion widely linear adaptive filter
IEEE Transactions on Signal Processing
Second-order statistics of complex signals
IEEE Transactions on Signal Processing
A unified approach to the steady-state and tracking analyses ofadaptive filters
IEEE Transactions on Signal Processing
Quaternion ICA From Second-Order Statistics
IEEE Transactions on Signal Processing
Color image processing by using binary quaternion-moment-preserving thresholding technique
IEEE Transactions on Image Processing
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The strictly linear quaternion valued affine projection algorithm (QAPA) and its widely linear counterpart (WLQAPA) are introduced, in order to provide fast converging stochastic gradient learning in the quaternion domain, for the processing of both second order circular (proper) and second order noncircular (improper) signals. This is achieved based on the recent advances in augmented quaternion statistics, which employs all second order information available, together with the associated widely linear models and through performing rigorous gradient calculation (HR-calculus). Further, mean square error analysis is performed based on the energy conservation principle, which provides a theoretical justification for the WLQAPA offering enhanced steady state performance for quaternion noncircular (improper) signals, a typical case in real world scenarios. Simulations on benchmark circular and noncircular signals, and on noncircular real world 4D wind and 3D body motion data support the analysis.