Best conditioned parametric identification of transfer function models in the frequency domain

It is shown that rational transfer function models based on orthogonal Forsythe polynomials minimize the condition number of the Jacobian of estimators in a least-squares framework. As a result, very high order linear time-invariant systems can be identified. The numerical stability of the estimation of the parameters and their derived quantities (zeros, poles, …) are obtained. Statistical uncertainty bounds are provided. The method is illustrated on a 100th order simulated system and a 120th order measured beam-structure