用主成分法求解秩亏自由网的研究

Researches in Adjusting Rank Defect Free Nets by Principal Component Estimate

结合多数平差和主成分估计理论，导出误差方程中含多重共线性关系时求解未知数的公式，并证明主成分估计的解是最小二乘最小范效解。由此，将主成分估计推广到秩亏自由网平差中，导出求解未知多数及其协因数的公式，并据主成分估计演绎出用附有条件的参数平差法求解秩亏自由网的条件方程（基准在达式）。

Integrating the parameter adjustment with the pricipal component estimate theory, in the paper, the solution formula of estimated parameters is given when the multi-collinearity is in observation equations; and to prove that the solutions of principal component estimate is the least squares and minimum nomal ones. Therefore, the principal component estimate is applied to rank defect free net adjustment, and deduce the calculation formula of inverse weight matrix of estimated parameters, as well as deduce the constraints (datum expressions ) that rank defect free net adjustment must meet with.