Uncertainty quantification of the eigensystem realization algorithm using the unscented transform

In this study, we present a systematic procedure to compute the identified model parameter uncertainties as functions of the statistics of input and output experimental data obtained using the celebrated Eigensystem Realization Algorithm (ERA). An Unscented Transformation (UT) is applied to map the error statistics from the input-output test signal space of the test data to the plant parameter space. It is shown that a computationally efficient algorithm is obtained by an application of the unscented transformation in a high dimensional space. Outputs of the algorithm include the mean and covariance estimates of the identified plant parameters obtained through the Observer/Kalman Filter Identification (OKID) calculations followed by ERA. Numerical simulations and comparisons with Monte-Carlo error statistics demonstrate the efficacy of the unscented transformation presented in this paper.