A Singular Value Thresholding Algorithm for Order Estimation

The order of a linear system can be determined by computing the rank of a Hankel matrix constructed from its Markov parameters. A plot of the singular values of the Hankel matrix shows a large gap at the singular value whose index is equal to the order of the system. However, a small amount of noise added the Markov parameters can significantly decrease the gap, which complicates the order estimation problem. In this paper, we introduce an algorithm to estimate the order of a linear system from the singular values of the Hankel matrix constructed from the estimated Markov parameters of the system. The proposed algorithm uses two sets of estimated Markov parameters obtained from two distinct input-output data sets to determine the noise level in the singular values, which is used as a threshold to separate true and spurious singular values. The proposed algorithm is demonstrated numerically and experimentally and compared to the nuclear norm minimization approach.