Least-correlation estimates for errors-in-variables models

Abstract

This paper introduces an estimator for errors-in-variables models in which all measurements are corrupted by noise. The necessary and sufficient condition minimizing a criterion, defined by squaring the empirical correlation of residuals, yields a new identification procedure that we call least-correlation estimator. The method of least correlation is a generalization of least-squares since the least-correlation specializes to least-squares when the correlation lag is zero. The least-correlation estimator has the ability to estimate true parameters consistently from noisy input–output measurements as the number of samples increases. Monte Carlo simulations also support the consistency numerically. We discuss the geometric property of the least-correlation estimate and, moreover, show that the estimate is not an orthogonal projection but an oblique projection. Finally, recursive realizations of the procedure in continuous-time as well as in discrete-time are mentioned with a numerical demonstration. Copyright © 2006 John Wiley & Sons, Ltd.