A unifying theorem for three subspace system identification algorithms (Q1911278)

The paper deals with the identification of linear combined deterministic-stochastic systems by subspace methods. A general unifying theorem is given, showing strong similarities between three existing algorithm, worked out earlier. It is indicated that the determination of the system order and the extended observability matrix from input-output data in a first step of the subspace methods is generally obtained by an oblique projection. The only difference between the particular algorithms lies, in fact, in the use of special weighting matrices for each algorithm. Apart from strong proofs also an intuitive interpretation of the results is provided and an illustrative simulation example is included.