C. F. N. Cowan

Orthogonal least squares learning algorithm for radial basis function networks

The radial basis function network offers a viable alternative to the two-layer neural network in many applications of signal processing. A common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular-value decomposition to solve for the weights of the network. Such a procedure has several drawbacks, and, in particular, an arbitrary selection of centers is clearly unsatisfactory. The authors propose an alternative learning procedure based on the orthogonal least-squares method. The procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed. In the algorithm, each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill-conditioning problems. The orthogonal least-squares learning strategy provides a simple and efficient means for fitting radial basis function networks. This is illustrated using examples taken from two different signal processing applications.

Practical identification of NARMAX models using radial basis functions

A wide class of discrete-time non-linear systems can be represented by the nonlinear autoregressive moving average (NARMAX) model with exogenous inputs. This paper develops a practical algorithm for identifying NARMAX models based on radial basis functions from noise-corrupted data. The algorithm consists of an iterative orthogonal-forward-regression routine coupled with model validity tests. The orthogonal-forward-regression routine selects parsimonious radial-basisTunc-tion models, while the model validity tests measure the quality of fit. The modelling of a liquid level system and an automotive diesel engine are included to demonstrate the effectiveness of the identification procedure.

Adaptive equalization of finite non-linear channels using multilayer perceptions

Abstract Adaptive equalization of channels with non-linear intersymbol interference is considered. It is shown that difficulties associated with channel non-linearities and additive noise correlation can be overcome by the use of equalizers employing a multi-layer perceptron structure. This provides further evidence that the neural network approach proposed recently by Gibson et al. is a general solution to the problem of equalization in digital communications systems.

Parallel recursive prediction error algorithm for training layered neural networks

A new recursive prediction error algorithm is derived for the training of feedforward layered neural networks. The algorithm enables the weights in each neuron of the network to be updated in an efficient parallel manner and has better convergence properties than the classical back propagation algorithm. The relationship between this new parallel algorithm and other existing learning algorithms is discussed. Examples taken from the fields of communication channel equalization and nonlinear systems modelling are used to demonstrate the superior performance of the new algorithm compared with the back propagation routine.

Reconstruction of binary signals using an adaptive radial-basis-function equalizer

Abstract This paper investigates the application of a non-linear structure to the adaptive channel equalization of a bipolar signal passed through dispspersive channel in the presence of additive noise. It is shown that the optimal equalization solution under the classical architecture of making decisions symbol-by-symbol is an inherently non-linear problem and therefore some degree of non-linear decision making ability is desirable in the equalizer structure. The radial-basis-function structure is considered as an adaptive equalizer and simulation examples are included to compare its performance with the optimal equalization solution. A brief comparison with the maximum likelihood sequence estimation is given and it is demonstrated that the non-linear filter approach can also be applied to the decision feedback equalizer.

Non-linear systems identification using radial basis functions

This paper investigates the identification of discrete-time non-linear systems using radial basis functions. A forward regression algorithm based on an orthogonal decomposition of the regression matrix is employed to select a suitable set of radial basis function centers from a large number of possible candidates and this provides, for the first time, fully automatic selection procedure for identifying parsimonious radial basis function models of structure-unknown non-linear systems. The relationship between neural networks and radial basis functions is discussed and the application of the algorithms to real data is included to demonstrate the effectiveness of this approach.

Linearization of analog-to-digital converters

A signal processing technique called threshold tracking is presented; it can improve the linearity of any A/D conversion circuit. The linearization system is described, and the accuracy and signal requirements in the presence of training signal noise are shown. Techniques that can reduce the memory required to implement the linearization system to a level that permits practical realization are developed. >

Textural and spectral features as an aid to cloud classification

Abstract The problem of classifying clouds seen on meteorological satellite images into different types is one which requires the use of textural as well as spectral information. Since multi-spectral features are of prime importance, textural features must be considered as augmenting, rather than replacing, spectral measures. Several textural features are studied to determine their discriminating power across a number of cloud classes including those which have previously been found difficult to separate. Although several features in the frequency domain are tested they are found to be less useful than those in the spatial domain with only one exception. The specific features recommended for use in classification depend on the type of classification to be undertaken. Specifically, different features should be used for a multi-dimensional feature space analysis than for a binary-tree rule-based classification.

Performance comparison of least squares and least mean squares algorithms as HF channel estimators

In this paper a comparison is made between the convergence and tracking properties of Least Squares (LS) and Least Mean Squares (LMS) algorithms as high frequency (HF) channel estimators. Theoretical results are derived for the asymptotic error achieved by the LS algorithms under white-input conditions in the HF channel. This result is more accurate than previous analyses of LS algorithms in a nonstationary enviroment [5,8,9]. Utilising a state space definition of the channel model a minimum variance Kalman estimator is derived using the a-priori knowledge of the parameters which define the Markov process.

Non-linear system modelling : Concept and application

The existing theory relating to the analysis and modelling of non-linear systems relies on the Wiener model which is unnecessarily complex in many practical situations. This paper presents a non-linear system modelling technique based on the 3-section block model which may be reconfigured to represent the non-linearities present in many practical situations.