Time delay estimation in discrete-time state-space models

This paper proposes a method for estimating multiple input delays in systems described by discrete-time state-space models. The proposed method is based on the minimization of a quadratic cost function related to the prediction error of the state variables over a given time frame. It is assumed that the system inputs are known and that noisy measurements of the states are available. The statistical properties of the resulting estimate are used to determine the delay values that are consistent with the observations at a given significance level. Simulation experiments are presented for illustration. As expected, the actual error rate is found to be consistent with the significance level employed in the estimation procedure. The relation between the precision of the estimation and the noise level is also investigated. ► Multiple input delay estimation for discrete-time state-space models. ► A quadratic cost related to the prediction error of the state variables is minimized. ► Confidence sets associated to the delay estimate are determined. ► The trade-off between precision and error rate is investigated.