L(2)-overbiased, L(2)-underbiased and L(2)-unbiased Estimation of Transfer-functions

The identification of an undermodeled transfer function from input-output data is stated as a constrained optimization problem. The constraints determine the identification procedure, the residual error and whether on average the magnitude of the frequency response is L2-overbiased, L2-underbiased or L2-unbiased, as measured by a certain weighted L2-bias integral. The L2-unbiased solutions are linear combinations of L2-overbiased and L2-underbiased solutions, which are precisely the classical least squares estimates. They can be obtained from the solution of certain eigenvalue problems.