约束秩亏间接平差模型的解法及其应用

Application and Algorithm of Indirect Adjustment Model with Constrained Rank-defect

约束秩亏间接平差模型的基础方程的系数矩阵为一分块矩阵,由于其左上角的子矩阵秩亏,无法直接计算分块矩阵的逆矩阵.经过矩阵运算,构建了一个新的可以直接求逆的分块矩阵,并通过常规的分块矩阵求逆方法,推算出基础方程的系数矩阵的逆矩阵直接显性表达公式.通过数值实验和其他模型计算结果比较,验证了算法和公式的正确性.

The coefficient matrix of the basic equation of the indirect adjustment model with constrained rank-defect is a block matrix. Because of the rank-defect of the sub-matrix in the upper left corner, it is impossible to directly calculate its inverse matrix. A new block matrix which can be directly inversed is constructed by matrix operations. And the direct and explicit formula for the inverse matrix of the coefficient block matrix of the basic equation is deduced by the conventional block matrix inversion method. By comparing the results of numerical experiments and other models, the correctness of the algorithm and formula is verified.