Beth Jelfs

Collaborative Adaptive Learning using Hybrid Filters

A novel stable and robust algorithm for training of finite impulse response adaptive filters is proposed. This is achieved based on a convex combination of the least mean square (LMS) and a recently proposed generalised normalised gradient descent (GNGD) algorithm. In this way, the desirable fast convergence and stability of GNGD is combined with the robustness and small steady state misadjustment of LMS. Simulations on linear and nonlinear signals in the prediction setting support the analysis.

An adaptive approach for the identification of improper complex signals

A real-time approach for the identification of second-order noncircularity (improperness) of complex valued signals is introduced. This is achieved based on a convex combination of a standard and widely linear complex adaptive filter, trained by the corresponding complex least mean square (CLMS) and augmented CLMS (ACLMS) algorithms. By providing a rigorous account of widely linear autoregressive modelling the analysis shows that the monitoring of the evolution of the adaptive convex mixing parameter within this structure makes it possible to both detect and track the complex improperness in real time, unlike current methods which are block based and static. The existence and uniqueness of the solution are illustrated through the analysis of the convergence of the convex mixing parameter. The analysis is supported by simulations on representative datasets, for a range of both proper and improper inputs.

Characterisation of Signal Modality: Exploiting Signal Nonlinearity in Machine Learning and Signal Processing

A novel method for online tracking of the changes in the nonlinearity within both real-domain and complex–valued signals is introduced. This is achieved by a collaborative adaptive signal processing approach based on a hybrid filter. By tracking the dynamics of the adaptive mixing parameter within the employed hybrid filtering architecture, we show that it is possible to quantify the degree of nonlinearity within both real- and complex-valued data. Implementations for tracking nonlinearity in general and then more specifically sparsity are illustrated on both benchmark and real world data. It is also shown that by combining the information obtained from hybrid filters of different natures it is possible to use this method to gain a more complete understanding of the nature of the nonlinearity within a signal. This also paves the way for building multidimensional feature spaces and their application in data/information fusion.

Modelling of brain consciousness based on collaborative adaptive filters

A novel method for the discrimination between discrete states of brain consciousness is proposed, achieved through examination of nonlinear features within the electroencephalogram (EEG). To allow for real time modes of operation, a collaborative adaptive filtering architecture, using a convex combination of adaptive filters is implemented. The evolution of the mixing parameter within this structure is then used as an indication of the predominant nature of the EEG recordings. Simulations based upon a number of different filter combinations illustrate the suitability of this approach to differentiate between the coma and quasi-brain-death states based upon fundamental signal characteristics.

A Class of Adaptively Regularised PNLMS Algorithms

A class of algorithms representing a robust variant of the proportionate normalised least-mean-square (PNLMS) algorithm is proposed. To achieve this, adaptive regularisation is introduced within the PNLMS update, with the analysis conducted for both individual and global regularisation factors. The update of the adaptive regularisation parameter is also made robust, to improve steady state performance and reduce computational complexity. The proposed algorithms are better suited not only for operation in nonstationary environments, but are also less sensitive to changes in the input dynamics and the choice of their parameters. Simulations in a sparse environment show the proposed class of algorithms offer enhanced performance and increased stability over the standard PNLMS.

Online tracking of the degree of nonlinearity within complex signals

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 filter. By tracking the dynamics of the adaptive mixing parameter within the employed hybrid filtering architecture, we show that it is possible to quantify the degree of nonlinearity within complex-valued data. Simulations on both benchmark and real world data support the approach.

A Unifying Approach to the Derivation of the Class of PNLMS Algorithms

unifying approach to the derivation of the class of proportionate normalised least mean square (PNLMS) algorithms is provided. This is an important class of algorithms where the two most used algorithms are introduced empirically. It is shown that it is possible to derive PNLMS algorithms as a result of an optimisation procedure. This is achieved in a rigorous way, starting from the standard LMS through to the PNLMS with the sparsification factor in both the numerator and denominator of the weight update. The proposed approach is generic and also applies to other LMS types of adaptive algorithms. Simulations on benchmark sparse impulse responses support the approach.

Collaborative adaptive filtering in the complex domain

A novel hybrid filter combining the complex least mean square (CLMS) and augmented CLMS (ACLMS) algorithms for complex domain adaptive filtering is introduced. The ACLMS has been shown to have improved performance in terms of prediction of non-circular complex data compared to that of the CLMS. By taking advantage of this along with the faster convergence of the CLMS, the hybrid filter is shown to give improved performance over both algorithms for both circular and non-circular data. Simulations on complex-valued synthetic and real world data support the effectiveness of this approach.

An online method for detecting nonlinearity within a signal

A novel method for online analysis of the changes in signal modality is proposed. This is achieved by tracking the dynamics of the mixing parameter within a hybrid filter rather than the actual filter performance. An implementation of the proposed hybrid filter using a combination of the Least Mean Square (LMS) and the Generalised Normalised Gradient Descent (GNGD) algorithms is analysed and the potential of such a scheme for tracking signal nonlinearity is highlighted. Simulations on linear and nonlinear signals in a prediction configuration support the analysis. Biological applications of the approach have been illustrated on EEG data of epileptic patients.

Blind extraction of noncircular complex signals using a widely linear predictor

Real valued blind source extraction based on a linear predictor is extended to the complex domain using recent advances in complex domain statistics. It is shown that, in general, the mean square prediction error of the algorithm depends both on the covariance matrix and the pseudo-covariance matrix of the source signals. To fully utilise the available information, it is thus natural to adopt a widely linear predictor to extract the latent sources from the observed mixture. This way, we derive a new algorithm for the extraction of general complex signals and provide simulation results using benchmark complex data.