3:30, SPTM-L5.1
A FULLY ADAPTIVE NORMALIZED NONLINEAR GRADIENT DESCENT ALGORITHM FOR NONLINEAR SYSTEM IDENTIFICATION
I. KRCMAR, D. MANDIC
A fully adaptive normalized nonlinear gradient descent (FANNGD) algorithm for neural adaptive filters employed for nonlinear system identification is proposed. This full adaptation is achieved using the instantaneous squared prediction error to adapt the free parameter of the NNGD algorithm. The convergence analysis of the proposed algorithm is undertaken using contractivity property of the nonlinear activation function of a neuron. Simulation results show that a fully adaptive NNGD algorithm outperforms the standard NNGD algorithm for nonlinear system identification.

3:50, SPTM-L5.2
VOLTERRA FILTERS USING MULTIRATE SIGNAL PROCESSING AND THEIR APPLICATION TO LOUDSPEAKER SYSTEMS
S. KINOSHITA, Y. KAJIKAWA, Y. NOMURA
In this paper, we propose two methods for reducing the computational complexity of Volterra filters. First, a method reducing the computational complexity of Volterra filters is proposed. This method can be realized by incorporating multirate signal processing into the Volterra filters. Hence, it is possible to operate the band-limited Volterra filter at a low sampling rate and with a short system length. Second, we also propose a method to replace the conventional Volterra filter with one including many zeros by using multirate signal processing. The conventional Volterra filter is band-limited in order to avoid aliasing so that waste arithmetic is done. In contrast, the Volterra filter including many zeros can eliminate such waste arithmetic.We demonstrate the effectiveness in their application to loudspeaker systems. Even though the processed frequency band is limited, the proposed method has about 0.03 times as many computational complexities as the conventional method.

4:10, SPTM-L5.3
BLIND IDENTIFICATION OF BILINEAR SYSTEMS
P. KOUKOULAS, V. MATHEWS, N. KALOUPTSIDIS
This paper is concerned with the blind identification of bilinear systems excited by higher-order white noise. Unlike prior work that restricted the bilinear system model to simple forms and required the excitation to be Gaussian distributed, the results of this paper are applicable to a more general class of bilinear systems and for the case when the excitation is non-Gaussian. We describe an estimation procedure for the computation of the system parameters using output cumulants of order less than four.

4:30, SPTM-L5.4
NONLINEAR MODELLING OF AIR POLLUTION TIME SERIES
R. FOXALL, I. KRCMAR, G. CAWLEY, S. DORLING, D. MANDIC
An analysis of predictability of a nonlinear and nonstationary ozone time series is provided. For rigour, the DVS analysis is first undertaken to detect and measure inherent nonlinearity of the data. Based upon this, neural and linear adaptive predictors are compared on this time series for various filter orders, hence indicating the embedding dimension. Simulation results confirm the analysis and show that for this class of air pollution data, neural, especially recurrent neural predictors, perform best.

4:50, SPTM-L5.5
BAYESIAN MCMC NONLINEAR TIME SERIES PREDICTION
T. KURIHARA, T. MATSUMOTO, Y. NAKADA
An MCMC(Markov Chain Monte Carlo) algorithm is proposed for nonlinear time series prediction with Hierarchical Bayesian framework. The algorithm computes predictive mean and error bar by drawing samples from predictive distributions.The algorithm is tested against time series generated by (chaotic) Rossler system and it outperforms quadratic approximations previously proposed by the authors.

5:10, SPTM-L5.6
SOURCE SEPARATION IN STRUCTURED NONLINEAR MODELS
A. TALEB
This paper discusses several issues related to blind source separation in nonlinear models. Specifically, separability results show that separation in the general case is impossible, however, for specific nonlinear models the problem does have a solution. A specific set of parametric nonlinear mixtures is considered, this set has the Lie group structure. In the parameter set, a group operation is defined and a relative gradient is defined. The latter is applied to design stochastic algorithms for which the equivariance property is shown.