On simultaneous structure and parameter identification of linear dynamical systems

In the identification of linear systems the model may be of lower or higher dimension than the system. The second case which is of particular interest requires a proper formulation of the model equations to guarantee a finite solution of the parameter estimate. Without noise the solution of the parameter vector is, in general, not unique. With noise at the system output its estimate, though biased, is shown to be unique. If a model of higher dimension is used in conjunction with an algorithm for unbiased estimation, the estimate, though finite, may be nonunique. Numerator and denominator factorization should be used to reveal the excess pairs of poles and zeros which cancel. Thus, the structure of the system can be identified along with its parameters.