Order estimation method for subspace-based system identification

All subspace-based methods for system parameter estimation require an estimate of the order of the system under study. Most typically, the order estimate is obtained by means of ad-hoc thresholding methods, such as those based on the visual inspection of the eigenvalues (or singular values) of an appropriate data covariance matrix. This paper introduces a statistical rule for testing whether the smallest eigenvalue of the covariance matrix is zero. Then, the paper goes on to propose an order estimation method which builds on the aforementioned rank estimation rule. To illustrate the performance of the proposed subspace-based order estimation methodology we apply it to the case of ARMA signals.