Experimental design and identifiability for non-linear systems

Leontaritis, I. J.; Billings, S.A.

doi:10.1080/00207728708963958

Cited by 102 publications

(30 citation statements)

References 5 publications

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“…Model (5) was simulated by setting the input   ut as a Pesudo-Random Binary Sequence (PRBS) [32]. The variance of the noise   et was chosen to be 0.04, and this made the signal-to-noise ratio to be around 13 dB.…”

Section: Simulation Examplementioning

confidence: 99%

Time-varying model identification for time–frequency feature extraction from EEG data

Wei

Billings

et al. 2011

Journal of Neuroscience Methods

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A novel modelling scheme that can be used to estimate and track time-varying properties of nonstationary signals is investigated. This scheme is based on a class of time-varying AutoRegressive with an eXogenous input (ARX) models where the associated time-varying parameters are represented by multi-wavelet basis functions. The orthogonal least square (OLS) algorithm is then applied to refine the model parameter estimates of the time-varying ARX model. The main features of the multi-wavelet approach is that it enables smooth trends to be tracked but also to capture sharp changes in the time-varying process parameters. Simulation studies and applications to real EEG data show that the proposed algorithm can provide important transient information on the inherent dynamics of nonstationary processes.

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Section: Simulation Examplementioning

confidence: 99%

Time-varying model identification for time–frequency feature extraction from EEG data

Wei

Billings

et al. 2011

Journal of Neuroscience Methods

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“…Difficulties in online identification of a nonlinear channel model, on the other hand, should not be underestimated. Even when the nonlinear form fh is given, it is not always possible to identify all the parameters in the model unless the system input signal is persistently exciting [15]. For a linear channel model, persistent excitation means that s( t) should contain sufficient frequency components.…”

Section: A Comparison With Other Nonlinear Equalizersmentioning

confidence: 99%

A clustering technique for digital communications channel equalization using radial basis function networks

Chen

Mulgrew

Grant

1993

IEEE Trans. Neural Netw.

674

303

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Abstruct-The paper investigates the application of a radial basis function network to digital communications channel equalization. It is shown that the radial basis function network has an identical structure to the optimal Bayesian symbol-decision equalizer solution and, therefore, can be employed to implement the Bayesian equalizer. The training of a radial basis function network to realize the Bayesian equalization solution can be achieved efficiently using a simple and robust supervised clustering algorithm. During data transmission a decision-directed version of the clustering algorithm enables the radial basis function network to track a slowly time-varying environment. Moreover, the clustering scheme provides an automatic compensation for nonlinear channel and equipment distortion. This represents a radically new approach to the adaptive equalizer design. Computer simulations are included to illustrate the analytical results.

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“…This kind of AR processes may not be sufficiently exciting for ARX and NARX model structure selection (Leontaritis and Billings 1987).…”

Section: Two Examplesmentioning

confidence: 99%

Model structure selection using an integrated forward orthogonal search algorithm assisted by squared correlation and mutual information

Wei

Billings

2008

IJMIC

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Published paperMappin Street, Sheffield, S1 3JD, UK Abstract: Model structure selection plays a key role in nonlinear system identification. The first step in nonlinear system identification is to determine which model terms should be included in the model. Once significant model terms have been determined, a model selection criterion can then be applied to select a suitable model subset. The well known orthogonal least squares type algorithms are one of the most efficient and commonly used techniques for model structure selection. However, it has been observed that the orthogonal least squares type algorithms may occasionally select incorrect model terms or yield a redundant model subset in the presence of particular noise structures or input signals. A very efficient integrated forward orthogonal search (IFOS) algorithm, which is assisted by the squared correlation and mutual information, and which incorporates a generalised cross-validation (GCV) criterion and hypothesis tests, is introduced to overcome these limitations in model structure selection.

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Experimental design and identifiability for non-linear systems

Cited by 102 publications

References 5 publications

Time-varying model identification for time–frequency feature extraction from EEG data

Time-varying model identification for time–frequency feature extraction from EEG data

A clustering technique for digital communications channel equalization using radial basis function networks

Model structure selection using an integrated forward orthogonal search algorithm assisted by squared correlation and mutual information

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