Stochastic system identification with noisy input-output measurements

Two parametric frequency domain approaches are proposed for estimation of the parameters of linear errors-in-variables models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. One of the approaches is a linear estimator. Using the bispectrum of the input and the cross-bispectrum of the input-output, 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 used to estimate the unknown parameters using an overdetermined linear system of equations. In the second approach a quadratic transfer function matching criterion is optimized by using the linear estimator as an initial guess. Both the parameter estimators are shown to be consistent in any measurement noise that has a symmetric marginal probability density function. The input to the system need not be a linear process but must have nonvanishing bispectrum. Computer simulation results are presented