Robust parametric transfer function estimation using complex logarithmic frequency response data

The statistical properties of a logarithmic least-squares frequency-domain estimator are analyzed in an "error in-variables" framework. It is shown that, contrary to most frequency-domain estimators, the logarithmic least-squares estimator remains "practically" consistent when the variances of the frequency-domain data are not a priori known. If available, the variance at each spectral line of the logarithmic frequency response data can be used to weight the logarithmic least-squares estimator, resulting in parameter estimates with a smaller variability. An estimate of these variances can be derived from the residual errors at the excited spectral lines. Besides its robustness to lack of prior noise information, it is demonstrated that the logarithmic estimator behaves remarkably well in the presence of outliers.>