超大规模大地网分区平差快速解算方法

A Fast Method of Solving Partitioned Adjustment for Super Large-scale Geodetic Network

针对超大规模大地网平差解算这一难题,首先按常规将大规模大地网分解成多个子网,并组成相应子网的误差方程和法方程,然后提出了用解算约化代替求逆约化的新算法,解算约化采用Cholesky分解法,计算过程中对联系误差方程进行压缩存储,并进行相应的有效算法。如此可大大节省大型大地网平差的计算时间,利用PentiumⅣ个人计算机即可解算全国范围的约5万个点(约18万个未知参数)的超大型大地网的整体平差问题,且计算时间只需3h左右。

Aiming at the difficulties of solving the adjustment problem for super largescale geodetic network, we propose a new fast method of solving partitioned adjustment, on the basis of Cholesky decomposition principle. The largescale geodetic network is partitioned into several subnetworks, the corresponding error equations are decomposed into subequations and connected equations. Then the reduction processes of inversing normal matrices are replaced by solving reduction processes. The coefficients of the connection error equations are stored by compact and condensed technique. A lot of null and void computations of the normal equations are avoided. Thus the computation time of the adjustment process for the largescale geodetic network is tremendously reduced. By using a personal computer, Pentium Ⅳ, we have successfully carried out the integrated threedimensional adjustment of the nationwide geodetic network with about 50 thousand stations and 180 thousand unknown parameters with about 3 hours.