Robust rational approximation for identification

Using vector orthogonal polynomials as basis functions for the maximum-likelihood (ML) frequency domain identification of the rational form of a linear time invariant system is shown to circumvent all the well known numerical conditioning problems. For identification of very high order systems (e.g. 100/100), systems that operate over a wide frequency band, or even in the presence of over- and undermodelling, condition numbers of less than 10 are reported on real measurements and simulation.