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An augmented complex least mean square (ACLMS) algorithm for complex domain adaptive filtering which utilises the full second order statistical information is derived for adap-tive prediction problems. This is achieved based on some recent advances in complex statistics and by using widely linear modelling in. This way, both circular and non–circular(More)
An extension of the fast independent component analysis algorithm is proposed for the blind separation of both Q-proper and Q-improper quaternion-valued signals. This is achieved by maximizing a negentropy-based cost function, and is derived rigorously using the recently developed HR calculus in order to implement Newton optimization in the augmented(More)
—A class of second-order complex domain blind source extraction algorithms is introduced to cater for signals with noncircular probability distributions, which is a typical case in real-world scenarios. This is achieved by employing the so-called augmented complex statistics and based on the temporal structures of the sources, thus permitting widely linear(More)
A new class of complex domain blind source extraction algorithms suitable for the extraction of both circular and non-circular complex signals is proposed. This is achieved through sequential extraction based on the degree of kurtosis and in the presence of non-circular measurement noise. The existence and uniqueness analysis of the solution is followed by(More)
Blind extraction of quaternion-valued latent sources is addressed based on their local temporal properties. The extraction criterion is based on the minimum mean square widely linear prediction error, thus allowing for the extraction of both proper and improper quaternion sources. The use of the widely linear adaptive predictor is justified by the(More)
A novel method for online tracking of the changes in the non-linearity within complex–valued signals is introduced. This is achieved by a collaborative adaptive signal processing approach by means of a hybrid ¿lter. By tracking the dynamics of the adaptive mixing parameter within the employed hybrid ¿ltering architecture, we show that it is possible to(More)
An online blind extraction algorithm, suitable for the generality of complex-valued sources, both complex circular and noncircular, is introduced. This is achieved based on higher order statistics of latent sources, and using the deflation approach. The novelty of the proposed approach is that the cost function is designed so as to be robust to both(More)
An extension of the FastICA algorithm is proposed for the blind separation of both Q-proper and Q-improper quaternion-valued signals. This is achieved by maximising a negentropy-based cost function, and is implemented using the Newton method in the augmented quaternion statistics framework. It is shown that the use of augmented statistics and the associated(More)
—A Regularised Normalised Augmented Complex Least Mean Square (RNACLMS) algorithm is proposed for widely linear adaptive filtering in the complex domain ℂ. Based on augmented complex statistics, the RNACLMS is shown to utilise complete second order information in ℂ, thus being suitable to deal with both circular and noncircular complex signals. Furthermore,(More)