L(2)-OVERBIASED, L(2)-UNDERBIASED AND L(2)-UNBIASED ESTIMATION OF TRANSFER-FUNCTIONS

The identification of an undermodeled transfer function from input-out put data is stated as a constrained optimization problem. The constrai nts determine the identification procedure, the residual error and whe ther on average the magnitude of the frequency response is L2-overbias ed, L2-underbiased or L2-unbiased, as measured by a certain weighted L 2-bias integral. The L2-unbiased solutions are linear combinations of L2-overbiased and L2-underbiased solutions, which are precisely the cl assical least squares estimates. They can be obtained from the solutio n of certain eigenvalue problems.