Stochastic system identification with noisy input-output measurements using polyspectra

Two new classes of parametric, frequency domain approaches are proposed for estimation of the parameters of scalar, linear “errors-in-variables” models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. The first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross-bispectrum or the integrated cross-polyspectrum, the system transfer function is first estimated at a number of frequencies exceeding one-half the number of unknown parameters. The estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations. In the second class of approaches, quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses. Both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used. The proposed parameter estimators are shown to be consistent in Gaussian measurement noise when trispectral approaches are used