Numerically robust transfer function modeling from noisy frequency domain data

Using vector orthogonal polynomials as basis functions for the representation of the rational form of a linear time invariant system, in frequency domain identification problems, it is shown that the notorious numerical ill conditioning of these maximum likelihood problems can be overcome completely. For the identification of high-order (100/100) systems operating over a wide frequency band, or even in the situation of over- or undermodeling, condition numbers less than ten are reported for real measurements.