Least-correlation estimates for errors-in-variables models

This paper introduces an estimator working on errors-in-variables models whose all variables are corrupted by noise. The necessary and sufficient condition minimizing the criterion, defined by the square of empirical correlation between residuals with a non-zero time interval, gives the least-correlation estimates. The method of least correlation can be interpreted as a generalization of the least-squares. Analysis shows that the estimator has a capability to find out the best fit without bias from noisy measurements even contaminated by colored noise as the number of observations increases. Monte Carlo simulations for numerical examples support the consistency of the estimator. The least-correlation estimate is not an orthogonal projection but an oblique projection. We discuss interesting geometric properties of the estimate. Finally recursive realizations of the estimator in continuous-lime domain as well as in discrete-time are mentioned briefly.