SUBSPACE IDENTIFICATION METHODS

This paper gives a short introduction to and survey of subspace identification algorithms. Deterministic, stochastic and combined deterministic-stochastic subspace identification algorithms are treated. These methods estimate state sequences directly from the given data, either explicitly or implicitly, through an orthogonal or oblique projection of the row spaces of certain block Hankel matrices of data into the row spaces of other block Hankel matrices, followed by a singular value decomposition (SVD) to determine the order, the observability matrix and /or the state sequence. The extraction of the state space model is then achieved through the solution of a least squares problem. Each of these steps can be elegantly implemented using well-known numerical linear algebra algorithms such as the singular value decomposition and the QR decomposition.