Abstract
In this paper, two approaches, for the estimation of matrices A and C in CV A-type subspace identification algorithms are compared and the differences between the two obtained estimates are analysed. One of the methods, "least squares" based, was proposed in the original CVA algorithm. The other method, inspired in the techniques of the classical Realization Theory and proposed by Verhaegen, is far more efficient. Therefore, although the two methods produce two different estimates, a replacement is proposed and an expression for correction of the estimates is obtained, in order to reduce the loss of accuracy.

Abstract
In this paper, a recursive algorithm is presented, based on the CVA subspace identification algorithm. The main idea was to explore the relations between the orthogonal and oblique projections involved and to provide simpler expressions that allowed a recursive version of the algorithm - guaranteeing most of the advantages of this kind of methods, and still improving the numerical efficiency.

Abstract
In this paper, a new approach to estimate matrices B and D, in subspace methods, is provided. The starting point was one method proposed by Van Overschee and De Moor (1996). We have derived new (and simpler) expressions and we found that the original method can be rewritten as a weighted least squares problem, involving the future outputs and inputs and the observability matrix.

Abstract
In this paper we present two subspace identification methods implemented through sequences of modified Householder algorithm. The main idea was to show that subspace identification methods can be represented as sequences of least squares problems and implemented wing QR factorizations. Therefore, it is possible to develop iterative algorithms with most of the advantages of this kind of methods, and still improve the numerical efficiency, in order to deal with real-tme applications and minimize the computational burden.

Abstract

Abstract