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In this paper we provide a different way to estimate matrices B and D, in subspace identification algorithms. The starting point was the method proposed by Van Overschee and De Moor (1996) – the only one applying subspace ideas to the estimation of those matrices. We have derived new (and simpler) expressions and we found that the method proposed by Van Overschee and De Moor (1996) can be rewritten as a weighted least squares problem, involving the future outputs and inputs.

EXPLORING THE LINEAR RELATIONS IN THE ESTIMATION OF MATRICES B AND D IN SUBSPACE IDENTIFICATION METHODS