Input richness and zero buffering in time-domain identification

We consider the notion of persistency within a deterministic, finite-data context, namely, in terms of the rank and condition number of the regressor matrix, which contains input and output data. The novel contribution of this work is the technique of zero buffering, in which the input signal begins with a sequence of zeros. We show that the degree of persistency of the input, which is the order of the minimal AR model that can generate the input signal, is increased by zero buffering. We then demonstrate the effectiveness of zero buffering in increasing the degree of persistency of a Schroeder-phased signal, which, without zero buffering, yields a poorly conditioned regressor matrix. We also investigate the feasibility of estimating the dynamic order in terms of the singular values of the regressor matrix by showing that the rank of the regressor matrix is related to the degree of persistency of the input, the order of the model, and the order of the true system. Under reasonable signal to noise ratios, this technique provides a useful estimate of the true system order.