Quantity properties of variate and coefficient in errors-in-variables model under Gaussian noise

Abstract

Total least-squares (TLS) aims to estimate the unknown parameters of an errors-in-variables (EIV) model from noisy observations when the coefficients are also perturbed by errors. It is helpful to know whether more variates and coefficients lead to more accurate estimation for TLS. In this study, our motivation was to reveal the relationship between the estimation performance and the number of variates or coefficients. The challenge was how to observe a performance change when using additional variates/coefficients. First, the Cramér–Rao bound (CRB) and the hybrid Bhattacharyya–Barankin (HBB) bound were derived for the multivariate EIV model under Gaussian noise typical to most systems. Second, we theoretically affirmed the properties by validating the analytical CRB that additional variates/coefficients were favorable. Third, the quantity properties were verified by simulation about CRB and HBB, considering the source direction estimation using time difference of arrival as an example. We conclude that the estimation performance can be improved if additional variates/coefficients are available. The multivariate TLS should be superior to the univariate one. The conclusions have significance for guiding practical system development.