Bootstrapped Total Least Squares estimator using (circular) overlap for Errors-In-Variables identification

Abstract

The identification of linear dynamic system in a frequency domain Errors-In-Variables (EIV) framework often assumes the knowledge of a nonparametric noise model prior to parametric identification. This noise model can be extracted for periodic excitations using various sample mean/sample variance techniques starting from at least P = 4measured periods. The use of overlap and circular-overlap methods were recently introduced to increase the efficiency of the sample maximum likelihood (SML) estimator. This enabled halving the number of required periods while maintaining the efficiency loss of 1.46dB for P = 2 periods with respect to Maximum Likelihood (ML) estimates with known covariance matrix. In this paper, the overlap and circular-overlap methods are applied to the sample BTLS method. A Monte Carlo analysis on a typical low-pass system shows that the efficiency loss with respect to the ML is only 0.12dB when P = 2 periods are available. In addition, the example shows that the efficiency loss for P = 1.2 periods is smaller than the loss introduced by the circular-overlap SML with P = 4 periods.