TABLE OF CONTENTS In this chapter we described several subspace identification methods. These methods are based on deriving a certain subspace that contains information about the system, from structured matrices constructed from the input and output data. To estimate this subspace, the SVD is used. The singular values obtained from this decomposition can be used to estimate the order of the system.
First, we described subspace identification methods for the special case when the input equals an impulse. In these cases, it is possible to exploit the special structure of the data matrices to get an estimate of the extended observability matrix. From this estimate it is then easy to derive the system matrices (A, B, C, D) up to a similarity transformation.
Next, we described how to deal with more general input sequences. Again we showed that it is possible to get an estimate of the extended observability matrix. From this estimate we computed the system matrices A and C up to a similarity transformation. The corresponding matrices B and D can then be found by solving a linear least-squares problem. We showed that the RQ factorization can be used for a computationally efficient implementation of this subspace identification method.
We continued by describing how to deal with noise. It was shown that, in the presence of white noise at the output, the subspace identification method for general inputs yields asymptotically unbiased estimates of the system matrices. This subspace method is therefore called the MOESP...
