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| In this paper we exploit the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm. Two particular forms of the extended RLS algorithm are considered, one pertaining to a system identiication problem and the other pertaining to the tracking of a chirped sinusoid in(More)
—In this paper, constructive approximation theorems are given which show that under certain conditions, the standard Nadaraya-Watson regression estimate (NWRE) can be considered a specially regularized form of radial basis function networks (RBFN's). From this and another related result, we deduce that regularized RBFN's are m.s. consistent, like the NWRE(More)
| This paper is composed of two parts. The rst part surveys the literature regarding optimum nonlinear l-tering from the (continuous-time) stochastic analysis point of view, and the other part explores the impact of recent applications of neural networks (in a discrete-time context) to nonlinear ltering. In particular, the results obtained by using a(More)
Pattern classiication may be viewed as an ill-posed, inverse problem to which the method of regularization be applied. In doing so, a proper theoretical framework is provided for the application of radial basis function (RBF) networks to pattern classiication, with strong links to the classical kernel regression estimator (KRE)-based classiiers that(More)
A dynamic network of regularized Gaussian radial basis functions (GaRBF) is described for the one-step prediction of nonlinear, nonstationary autoregressive (NLAR) processes governed by a smooth process map and a zero-mean, independent additive disturbance process of bounded variance. For N basis functions, both full-order and reduced-order updating(More)
In this paper, constructive approximation theorems are given which show that, under certain conditions, the standard Nadaraya-Watson regression estimate (NWRE) can be considered a specially regularized form of radial basis function networks (RBFNs). From this and another related result, we deduce that regularized RBFNs are m.s. consistent, like the NWRE,(More)
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