Nonparametric frequency response function estimators based on nonlinear averaging techniques

Nonparametric frequency response function (FRF) estimators based on nonlinear averaging techniques are proposed. The suitability of such estimators for FFT based signal analyzers is studied. Under mild assumptions, it is shown that their bias is a function of the fourth-order moments of the perturbing errors on the input-output Fourier coefficients while the bias of the classical H₁ estimator is a function of the second-order moments. The performances of these estimators are analyzed in different situations: uncorrelated input-output perturbing errors (i.e., open-loop measurements), mutually correlated input-output disturbances (i.e., closed-loop measurements) and in presence of outliers. Analytical expressions are given for the bias when the input-output errors are zero-mean normal distributed (and mutually correlated)