Computing the extended observability matrix in the PO-MOESP algorithm: an alternative point of view

The PO-MOESP algorithm is a subspace identification method that employs the extended observability matrix for building state space models. In this algorithm, the matrix Oe is computed from an orthogonal projection onto the null space of input data. However, in order to achieve a consistent estimation of Oe is necessary to employ a special matrix called instrumental variable. In this paper, we propose a different operation scheme of the PO-MOESP based on the calculation of an alternative null space of input data. This approach is conceptually simpler and avoids the explicit use of the instrumental variable matrix for computing Oe.