Identification of Linear Time-Invariant Systems From Multiple Experiments

A standard assumption for consistent estimation in the errors-in-variables setting is persistency of excitation of the noise-free input signal. We relax this assumption by considering data from multiple experiments. Consistency is obtained asymptotically as the number of experiments tends to infinity. The main theoretical and algorithmic difficulties are related to the growing number of to-be-estimated initial conditions. The method proposed in the paper is based on analytic elimination of the initial conditions and optimization over the remaining parameters. The resulting estimator is consistent; however, achieving asymptotically efficiency is an open problem.