Estimation of nonparametric noise and FRF models for multivariable systems—Part I: Theory

This series of two papers presents a method for estimating nonparametric noise and frequency response function models of multivariable linear dynamic systems excited by arbitrary inputs. It extends the results of Schoukens et al. (2006) [1] and Schoukens and Pintelon (2009) [2] from single input, single output systems with known input and noisy output observations (=outputerrorproblem), to multiple input, multiple output systems where both the input and output are disturbed by noise (=errors‐in‐variables problem=errors‐in‐variables problem). In Part I, the theory is developed for linear dynamic multivariable output error problems. The results are supported by simulations. A detailed comparison with the classical spectral analysis based on correlation techniques shows that the proposed procedures are more robust. In Part II (Pintelon et al., 2009) [3], the method first is applied to nonlinear systems, and parametric identification within a generalized output error framework. Next, it is extended to handle errors-in-variables problems, and identification in feedback. Finally, it is illustrated on four real measurement examples.