Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm

This paper focuses on the development of analytical methods for uncertainty quantification of system matrices obtained by the Eigenvalue Realization Algorithm (ERA) to quantify the effect of noise in the observation data. Starting from first principles, analytical expressions are presented for the probability density function for norm of system matrix by application of standard results in random matrix theory. Assuming the observations to be corrupted by zero mean Gaussian noise, the distribution for the Hankel matrix is represented by the nonsymmetric Wishart distribution. From the Wishart distribution, the joint density function of the singular value of the Hankel matrix are constructed. These expressions enable us to construct the probability density functions for the norm of identified system matrices. Numerical examples illustrate the applications of ideas presented in the paper.