ON THE RANK DEFICIENCY OF THE LEAST SQUARES RESIDUALS IN SUBSPACE IDENTIFICATION

摘要

Subspace identification methods for linear time-invariant stochastic systems basically consist of two steps. In the first step, which is an orthogonal projection, followed by a Singular Value Decomposition (SVD), typically (non-steady state) Kalman filter states sequences are obtained directly from output data. In the second step, the system model matrices are identified in a least squares estimation step, which is asymptotically unbiased. For an infinite amount of data points, the measurement-process noise covariances are rank deficient, since the system is identified in innovation form. However, due to finite sample errors, this rank deficiency property is generically not satisfied when identifying on a finite number of measurement data. The required rank deficiency is achieved by replacing the least squares step by a total least squares estimate with exact row.