Transfer function estimation using elemental sets

Nonlinear least-squares (NLS) fitting of rational transfer functions to frequency response data yields the maximum likelihood estimator (MLE) of the transfer function coefficient vector under mild conditions on the observation noise. Furthermore, the NLS approach is robust to errors in the modeling of data. However the NLS criterion is in general difficult to minimize. Here we show that an asymptotic realization of the NLS estimator can be obtained from the elemental set parameter estimates by simple linear operations. The latter estimates are derived by matching the frequency response data on many "elemental sets" comprising a number of frequencies equal to half the number of unknown parameters.