Total least squares estimation model based on uncertainty theory

Uncertain least squares estimation is one of the important methods to deal with imprecisely observed data, which can solve linear regression equation effectively. However, the least squares estimation does not consider the influence of the error of the given independent variables data on the linear regression equation during the regression analysis. Based on the least squares estimation and uncertainty theory, this paper proposed the uncertain total least squares estimation of linear regression model. The total least squares estimation first corrects the data of the given independent variables and make the given data more precise, then solve for the expected value of the square of each of the residual, and minimize the sum of the expected values, so the regression equation obtained is more reasonable and reliable. Numerical example verify the feasibility of the total least squares estimation, and the data analysis shows that the fitting effect of the linear regression equation is good.