A dynamic regularized radial basis function network for nonlinear,nonstationary time series prediction

In this paper, constructive approximation theorems are given which show that under certain conditions, the standard Nadaraya-Watson (1964) 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 for the one-step-ahead prediction of Markovian nonstationary, nonlinear autoregressive time series generated by an i.i.d. noise processes. Additionally, choosing the regularization parameter to be asymptotically optimal gives regularized RBFNs the advantage of asymptotically realizing minimum m.s. prediction error. Two update algorithms (one with augmented networks/infinite memory and the other with fixed-size networks/finite memory) are then proposed to deal with nonstationarity induced by time-varying regression functions. For the latter algorithm, tests on several phonetically balanced male and female speech samples show an average 2.2-dB improvement in the predicted signal/noise (error) ratio over corresponding adaptive linear predictors using the exponentially-weighted RLS algorithm. Further RLS filtering of the predictions from an ensemble of three such RBFNs combined with the usual autoregressive inputs increases the improvement to 4.2 dB, on average, over the linear predictors     

Adaptive tracking of linear time-variant systems by extended RLSalgorithms

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 identification problem and the other pertaining to the tracking of a chirped sinusoid in additive noise. For both of these applications, experiments are presented that demonstrate the tracking superiority of the extended RLS algorithms compared with the standard RLS and least-mean-squares (LMS) algorithms     

A Simulation Study of Digital Modulation Methods for Wide-Band Satellite Communications

A computer simulation study has been performed to evaluate the performance of a variety of digital modulation techniques in transmitting high-rate digital data over a satellite channel. Results are presented showing comparative performance of various techniques in the form of error-rate curves and signal-to-noise ratio (SNR) degradation curves.     

Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature

In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other nonlinear filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve nonlinear non- Gaussian filtering problems.