引用本文: 王乐洋, 许光煜. 加权总体最小二乘平差随机模型的验后估计[J]. 武汉大学学报 ( 信息科学版), 2016, 41(2): 255-261.
WANG Leyang, XU Guangyu. Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem[J]. Geomatics and Information Science of Wuhan University, 2016, 41(2): 255-261.
 Citation: WANG Leyang, XU Guangyu. Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem[J]. Geomatics and Information Science of Wuhan University, 2016, 41(2): 255-261.

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

• 摘要: 针对随机模型中观测向量和系数矩阵存在定权不准确的问题,提出了一种加权总体最小二乘随机模型验后估计方法。将赫尔默特方差分量估计方法应用于EIV(errors-in-variables)模型中,结合本文推导的加权总体最小二乘方法,对平差问题的函数模型和随机模型同时进行求解。通过采用真实和模拟数据的三个算例对该方法的有效性进行了验证,结果表明随机模型的验后估计方法在解决加权总体最小二乘问题时更合理、有效。

Abstract: 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.

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