奇异值分解法在秩亏自由网平差中的应用

Application of singular value decomposition in rank defect free network adjustment

在经典测量平差中,按间接平差法列出的误差方程系数阵为列满秩,所得到的法方程系数阵为一个对称的满秩矩阵,法方程组具有唯一解。而当控制网中没有必要的起算数据时,则按间接平差法所列出的误差方程系数阵是非列满秩的,其对应的法方程系数阵也是一个秩亏的奇异阵。探讨了秩亏自由网的法方程系数阵的一种解算方法。

In classical adjustment, the normal equations have a unique solution if the error equation coefficient matrix achieved by indirect adjustment is a full column rank, and the normal equation coefficient matrix achieved by the same method is a sym-metrical full rank matrix. When there is no necessary initial data in control network, the error equation coefficient matrix by indi-rect adjustment is a non-full column rank and the corresponding normal equation is also a rank deficient singular matrix. The paper discusses the solution for normal equation coefficient matrix in the rank defect free network.