On optimal input signal design for frequency response estimation

This paper studies optimal input excitation design for parametric frequency response estimation. We will focus on least-squares estimation of Finite Impulse Response (FIR) models and minimum variance input design. The objective is to minimize the uncertainty of functions of the frequency response estimate at a given frequency. In particular, we are interested in estimating the H-norm of a stable linear system, that is the maximum of the absolute value of the corresponding frequency response. An asymptotic error variance expression for H-norm estimates is derived. The optimal input problem is formulated as a convex optimization problem in the second order statistics of the input signal. We analytically characterize the optimal solution for first order FIR systems, and do a numerical optimization study to obtain insights in the optimal solution for higher order models. We compare the optimal result to the case when a sinusoidal input signal, which gives the same accuracy, is used. For fi...

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Bo Wahlberg, Håkan Hjalmarsson, Petre Stoica
• Keywords: CDC 2010, Control Systems, Input Signal, Optimal Input, Order Fir