Prediction for the processes with almost cyclostationary structure

Nonparametric identification of Wiener system with a subclass of wide‐sense cyclostationary excitations

“…14,[29][30][31][32] Many published estimators with more general assumptions have not been analytically proven to be statistically consistent. 18,24,[33][34][35] Important relaxation of prior restrictions was made in References 36 and 37, where consistent nonparametric estimates of nonlinear characteristics of the Wiener system are proposed. Nevertheless, these algorithms suffer from curse-of-dimensionality and the convergence rate is rather slow.…”

“…First attempts to Wiener system modeling required specially generated input signal (deterministically sinusoidal or stochastically Gaussian) and usually were limited to the class of invertible nonlinearities 14,29‐32 . Many published estimators with more general assumptions have not been analytically proven to be statistically consistent 18,24,33‐35 . Important relaxation of prior restrictions was made in References 36 and 37, where consistent nonparametric estimates of nonlinear characteristics of the Wiener system are proposed.…”

“…§§ Other References 16,35,42‐45 identifies an unknown system that itself is cyclo‐stationary. That mathematics differs fundamentally from the present case where the cyclostationary input is observed. References 34,46 and 47 are also not included in the table. They do not seem to be relevant enough to our investigation (given signal is modeled therein and no input‐output pairs are involved). References 22,23,48‐50 are restricted to linear systems only.…”

“…References 34,46 and 47 are also not included in the table. They do not seem to be relevant enough to our investigation (given signal is modeled therein and no input‐output pairs are involved).…”