隐式标度因子的总体最小二乘估计方法

Scaled Total Least Squares Method with Implicit Scaled Factor

分析指出了标度总体最小二乘方法(STLS)存在的问题,提出了一种隐式标度因子的标度总体最小二乘方法(Im STLS)。区别于现有STLS方法在平差准则中引入标度因子,Im STLS方法在EIV函数模型中顾及标度因子,从而解决了现有STLS平差准则形式与标度因子实际表征的平差结果不一致的问题。此外,利用所建函数模型的重构表达式推导的Im STLS估计量及其方差-协方差阵,与经典最小二乘平差理论具有形式同构性。最后,验证了所提方法统一表达LS,DLS和TLS的正确性,并讨论给出了标度因子对平差结果的影响及确定方法。

The defect of the existing scaled total least squares （STLS） method is investigated in detail, and then a scaled total least squares method with implicit scaled factor （short for ImSTLS） is proposed. To solve the problem that adjustment criterion form with scaled factor employed by the existing STLS method is inconsistent with actual adjustment result at specific scaled factor, the ImSTLS method establishes the new EIV function model using implicit scaled factor which is a creative way to achieve that problem. Moreover, ImSTLS estimation and its variance -covariance matrix derived from a reconstruction form of the function model can be completely formulated by standard least squares theory. Finally, experiment results show the validity of the proposed method for generalizing LS, DLS and TLS is verified, and both determination method and influence of the implicit scaled factor on the adjustment result are discussed in detail.