附不等式约束的总体最小二乘迭代算法

Iteration Algorithm of Total Least Squares with Inequality Constraints

基于惩罚函数和测量平差中权的思想,提出了附不等式约束的总体最小二乘平差模型,即利用惩罚函数对不等式约束方程构造约束权,通过零权和无限权将不等式约束转换为等式约束,从而将不等式约束平差准则转化为传统的测量平差准则。同时,根据非线性最小二乘平差理论,用构造结构矩阵的方法来顾及系数矩阵的结构性,推导了附不等式约束的总体最小二乘迭代算法。该算法迭代格式与传统的间接平差类似,只需经过若干次迭代便能得到最优解。

Based on penalty function and weight of adjustment,an inequality constraints EIV（ICEIV）model is presented.The model utilizes penalty function to construct the constraint weight for the constraint equations and transforms the inequality constraint into the equality constraint by the zero or infinite weight.So,it can transform the inequality constraint adjustment criteria into the classical adjustment criteria.Therefore,a new iteration algorithm of total least squares with inequality constraints is deduced by the nonlinear least squares adjustment theory;the method uses a structured matrix to consider the repetitive elements and constant terms.