Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

Considering the situation that the weight matrix of observation vector and coefficient matrix may be inaccurate, an available algorithm is introduced in this paper, which is derived on the basis of combining the Helmert variance component estimation with a kind of fast weighted total least squares algorithm in the errors-in-variables models. And the derivative process of the fast weighted total least squares is described in detail and the comparison with three other algorithms is implemented in this paper. Using the fast weighted total least squares algorithm combining Helmert variance component estimation derived in this paper, the stochastic model and the unknown parameters of the functional model can be solved simultaneously. Three empirical examples, two straight line fitting and one linear parameter estimation, are also used to investigate the application of posteriori estimation of stochastic model on weighted total least squares problem. Results show that the algorithm is very effective.