Experiment design for impulse response identification with signal matrix models

This paper formulates an input design approach for impulse response identification in the context of implicit model representations recently used as basis for many data-driven simulation and control methods. Precisely, the FIR model considered consists of a linear combination of the columns of a data matrix. An optimal combination for the case of noisy data was recently proposed using a maximum likelihood approach, and the objective here is to optimize the input entries of the data matrix such that the mean-square error matrix of the estimate is minimized. A least-norm problem is derived, which is shown to solve all the classic A-, D-, and E- optimality criteria typically considered in the experiment design literature. Numerical results finally showcase the improved estimation fit achieved with the optimized input.