基于F-范数的不确定性平差模型的解算方法

摘要

In order to improve the calculation efficiency of adjustment models with uncertainty based on F-norm,a directly iterative algorithm is developed.The algorithm does not use singular value decomposition (SVD),is simple in the concept,and is easy to program.Another algorithm of SVD-equations is also given when the iterative algorithm is divergent.The results of the binary linear fitting and AR model in settlement observation illustrate that the two proposed algorithms could be practiced and are equivalent to the algorithm of SVD-iteration.The directly iterative algorithm is more suitable when the iterative algorithm is convergence,which has faster convergence rate and higher calculation efficiency.Moreover,the algorithm of SVD-equations can be used when the iterative algorithm is divergent.%为提高基于F-范数的不确定性平差模型的解算效率,给出直接迭代算法进行参数估计.该算法无需SVD,解算过程简单且易于编程计算,同时给出迭代不收敛时的SVD-解方程算法.二元线性拟合及沉降观测AR模型的算例结果表明,这2种算法正确可行,与SVD-迭代算法具有等价性.当迭代收敛时,宜使用直接迭代算法,收敛速度更快,解算效率更高;当迭代不收敛时,可采用SVD-解方程算法.