Obtaining accurate confidence regions for the estimated zeros and poles in system identification problems

System identification techniques allow to obtain actual numbers for the parameters of a device under test (DUT). However, of almost equal importance is to know how accurate these calculated values are. When modelling the DUT by a rotational function in the frequency domain, the covariance matrix of the coefficients can be approximated pretty well, and this matrix defines a confidence ellipsoid in the coefficient space in which the true coefficients must lie with a given probability. When calculating the zeros and the poles of this model, one would also like to know how precise these zeros and poles are; with possibly a graphical representation of their confidence region. However, until now the uncertainty of the zeros and poles was calculated by a linearization of the nonlinear transformation between the coefficients and the roots. It will be shown that this approach may significantly underestimate the uncertainty of the zero/pole estimates. An algorithm will be presented that calculates confidence regions which match very well the true uncertainty regions of the zero/pole estimates. Simulations are included to show its effectiveness.