Recursive 4SID algorithms using gradient type subspace tracking

Sometimes we obtain some prior information about a system to be identified, e.g., the order, model structure etc. In this paper, we consider the case where the order of a MIMO system to be identified is a priori known. Recursive subspace state-space system identification algorithms presented here are based on the gradient type subspace tracking method used in the array signal processing. The algorithms enable us to estimate directly the subspace spanned by the column vectors of the extended observability matrix of the system to be identified without performing the singular value decomposition. Also, a new convergence proof of the gradient type subspace tracking is given in this paper. Under the condition of a step size between 0 and 1, we prove the convergence property of the recursive equation of the gradient type subspace tracking. A numerical example illustrates that our algorithm is more robust with respect to the choice of the initial values than the corresponding PAST one.