A computationally efficient and interference tolerant nonparametric algorithm for LTI system identification based on higher order cyclostationarity

Abstract

A new nonparametric algorithm for the identification of linear time-invariant systems is proposed. The method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal. Consequently, although it exploits the higher order cyclostationarity properties of the input and output signals, its computational complexity is comparable with that of methods based on second-order statistics. The proposed estimator of the system transfer function is inherently immune to the presence of noise and interference on both input and output signal measurements and turns out to be asymptotically unbiased and consistent. Moreover, bias and variance of the estimate exhibit a rate of convergence to zero equal to that of estimates based on second-order statistics. Finally, simulation results show that the proposed algorithm significantly outperforms, in terms of both bias and variance of the estimates, several nonparametric identification algorithms previously presented in the literature.