Formulation and implementation of the non-stationary evolutionary Wiener filtering

In this paper we consider solutions to the non-stationary Wiener filtering problem using the evolutionary spectral theory. Two cases of interest resul t from the uncorrelation between the desired signal and the noise. One cons trains the support of the generating kernels of the signals and the other i mposes orthogonality on their innovation processes. The latter condition is more general and our solution coincides with the one presented previously by Abdrabbo and Priestley. For the first case, we develop a new solution th at depends directly on the Wold-Cramer models of the desired and noisy proc esses. Implementation is achieved in both cases by estimating the kernels f or the Wold-Cramer representations from the spectra using the evolutionary maximum entropy spectral estimation. The connections of the Wiener filter w ith the Wiener-Hopf equations and with the special case of stationary proce sses are discussed. Although the developed Wiener filter is non-recursive, an approximate recursive filter is obtained using a nonlinear Kalman system identification method. Examples illustrating the filtering are given. (C) 1999 Elsevier Science B.V. All rights reserved.