Wiener system identification with generalized orthonormal basis functions
For researchers in nonlinear system identification, this work provides a convergent approximation scheme with explicit convergence rates, though it is incremental over existing OBF-based methods.
This paper proposes a method for identifying Wiener systems using generalized orthonormal basis functions (GOBFs) and polynomial nonlinearities, achieving convergence in probability with rates of O_p(N_F^{-n_rep/2}).
Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs is needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infinite impulse response dynamics and a polynomial nonlinearity. We propose to use a limited number of generalized OBFs (GOBFs). The pole locations, needed to construct the GOBFs, are estimated via the best linear approximation of the system. The coefficients of the multivariate polynomial are determined with a linear regression. This paper provides a convergence analysis for the proposed identification scheme. It is shown that the estimated output converges in probability to the exact output. Fast convergence rates, in the order $O_p({N_F}^{-n_{rep}/2})$, can be achieved, with $N_F$ the number of excited frequencies and $n_{rep}$ the number of repetitions of the GOBFs.