A robust whitness test for the identification of discrete-time linear models: Use of orthonormal transfer functions

A novel whiteness test of residuals is proposed, which makes use of generalized bases of orthonormal transfer functions. It can be viewed as a robustified version of the classical whiteness test in the sense that it reduces the risk of type II errors, by introducing a frequency weighting in the assessment of the flatness in the residual power spectrum density. This frequency weighting, which depends on the basis poles, can be employed for the validation of reduced order models, when the flatness of the residual power spectrum density is evaluated over a limited frequency band.