Abstract
A study is presented on relationships between subspace approaches and conventional parameter estimation schemes. We focus on identification of single-input-single-output(SISO) systems via the Subspace State Space Identification (4SID) method. We show that an intermediate vector which appears in the 4SID procedure is equal to the parameter of the system pulse transfer function if the model set includes the system with noise free measurements. We also show explicitly, in a elementary way, that the intermediate vector is also equivalent to the estimate via the eigenvector method in the case that the column size of the extended observability matrix is equal to ᾿(the order of the model) + 1᾿. Furthermore, we demonstrate that using a modified cost functional in the Eigenvector method corresponds to the IV-4SID method and hence gives a consistent estimate even for colored noise.
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