约束秩亏间接平差模型的虚拟观测算法

约束秩亏间接平差模型的法方程系数矩阵为分块矩阵,其左上角的子块矩阵秩亏,因此无法直接计算分块矩阵的凯利逆矩阵。利用矩阵运算,构建一个能直接求凯利逆的分块矩阵,进而推算出约束秩亏间接平差模型法方程系数矩阵的凯利逆的直接显性表达式。提出将约束条件看作虚拟观测,和原有的秩亏间接平差模型组合成新的误差方程,再和约束条件组成约束间接平差模型进行解算的虚拟观测值算法。该方法和前述推算的直接显性表达式的计算结果是一样的。通过数值实验和不同算法的比较,证明文中推算出的算式及算法是正确的。

The virtual observation algorithm of rank-defective indirect adjustment model with constrains

The coefficient of the normal equation of the rank-defective indirect adjustment model with constrains is a block matrix whose sub-matrix in the upper left corner is rank-deficient,so its Kelly inverse matrix cannot be calculated directly.A new block matrix which can be directly inversed is constructed by matrix operations and the formula for the Kelly inverse of the block matrix of the normal equation is deduced.A virtual observation algorithm is proposed,in which the constraint condition is regarded as virtual observation,and a new error equation is composed by it and the original indirect adjustment model of rank deficiency and the indirect adjustment model with constraint condition is composed by the new error equation and the constraint condition.The result of virtual observation algorithm is the same as that of the direct formula.Through numerical experiments and comparison of different algorithms,it is proved that the formulas and algorithms are correct.