Optimal inputs for FIR system identification

In this paper we consider the problem of input design for open loop identification of linear single input single output finite impulse response systems, under the assumption of full-order modeling. We provide analytic formulas for the information matrix of the optimal input when the design is intended to identify a scalar function of the impulse response coefficients. In particular, we characterize the cases when the optimal information matrix is singular and the optimal input is necessarily a multisine signal. Our results have surprising consequences for the robustness properties of optimal input designs. We show that, contrary to intuition, the choice of an optimal regular information matrix might pose robustness problems if there exist also singular solutions.