基于EIV模型的稳健估计

Robust estimation based on EIV model

EIV(error-in-variables)模型同时考虑观测向量和系数矩阵的误差,自提出以来便得到广泛应用。目前针对EIV模型的整体最小二乘解法(TLS)假设观测值仅含有偶然误差,当观测值存在粗差时其解并不是最优的。文中通过选定合适的权函数,结合加权整体最小二乘迭代算法,导出基于EIV模型的稳健整体最小二乘迭代解法(RTLS)。线性拟合实验表明,文中方法能对粗差进行定位,且估计量受粗差影响较小,具有稳健性。

EIV （error-in-variables） model has been widely used sin ce it is proposed as taking both me error of the observation vector and the coefficient matrix into account. However, the least squares solution for the EIV model which is called total least squares（TLS） assuming observations only contain accidental error, when there is a gross error in the observations, the solution is not optimal. By selecting an appropriate weight function, combined with the weighted total least squares （WTLS）, a robust estimate called robust total least squares （RTLS） is proposed based on the EIV model. The linear fitting experiments show that the proposed method can locate gross errors, and the estimated amount is less affected by gross error, with robustness.