Robust Total Least Squares Method for Multivariable EIV Model

The reliability of the solution to the errors-in-variables (EIV) model can be improved through robust total least square method. The false robust estimation problem that the existed robust total least squares method gives priority to reduce the weights of some columns which have large product of estimated parameters and prior cofactors in the multivariable EIV model is pointed out in detail. To tackle this problem, a new robust estimation strategy is presented based on Huber weight function. This new robust estimation strategy copes with each column variable respectively to avoid the false robust estimation problem. Based on this new robust estimation strategy, a multivariate robust total least squares method is proposed and the corresponding estimation results of parameters and variance-covariance matrix are deduced. Experiment results verify the analysis about false robust estimation problem and show the validity of proposed method in coping with false robust estimation problem and detecting the gross error in multivariable EIV model. And compared with the total least squares method and traditional robust least squares method, the proposed method in this paper gets the nearest parameter estimation results to the real value.