Numerically robust frequency domain identification of multivariable systems

Frequency domain methods are known to suffer from a poor numerical conditioning when the frequency span and/or the model order become large (more than 2 decades and an order more than 20). This numerical problem ruins both the modeling performance and the model order selection capability. This paper presents a modeling approach that leads to (almost) optimal numerical conditioning of the normal equations (condition number = 1). The key idea is to expand the numerator and denominator of the transfer function model in a vector orthogonal basis. The theory is illustrated on a real measurement example.