A variance based confidence criterion for ERA identified modal parameters

The realization theory is developed in a systematic manner for the Eigensystem Realization Algorithm (ERA) used for system identification. First, perturbation results are obtained which describe the linearized changes in the identified parameters resulting from small change in the data. Formulas are then derived that can be used to evaluate the variance of each of the identified parameters, assuming that the noise level is sufficiently low to allow the application of linearized results. These variances can be converted to give confidence intervals for each of the parameters for any chosen confidence level.