基于修正Gram-Schmidt算法的GPS基线向量网伪逆平差

Adjustment Method of GPS Base-Line Vectors Network Based on Improved Gram-Schmidt Arithmetic

直接从GPS基线向量法方程系数阵入手,利用修正的Gram-Schmidt算法对法方程系数阵进行三角分解实现最小二乘求解,导出了基于修正的Gram-Schmidt算法求解法方程系数阵广义逆的数学公式和计算步骤,给出了通过广义逆表示的未知数解向量及其协因数阵的数学表达式。计算过程不仅避免了对矩阵的求逆,并从理论上解决了Gram-Schmidt算法由于舍入误差的影响表现出的数值不稳定性,从而很好地解决了具有秩亏系数阵方程组解的不唯一性问题。

Least square solution of GPS network was obtained by triangulation decomposition on its normal equation coefficient matrix using improved Gram-Schmidt algorithm. The math formula and the calculation steps of solving generalized inverse matrix on improved Gram-Schmidt algorithm was deduced. Inverse matrix was not computed in the course of this procedure. The numerical value non-stability of Gram-Schmidt algorithm was carried out theoretically due to affecting of rounding error. Thereby non-uniqueness of equation- group with rank-defect coefficient matrix was solved.