| 导线网方差分量估计的综合研究 |
| |
| 引用本文： | 王仲锋.导线网方差分量估计的综合研究[J].武汉大学学报(信息科学版),2001,26(2):112-117. |
| |
| 作者姓名： | 王仲锋 |
| |
| 作者单位： | 长春工程学院地质与测绘工程系, |
| |
| 基金项目： | 长春工程学院科研发展基金资助项目(3200134)。 |
| |
| 摘 要： | 提出方差分量估计的多余观测分量平均匹配方式；总结出导线网方差分量估计定权的基本规律，并给出其权增量循环算法和特征根法以及将两个实对称矩阵同时对角化的实用方法。
|
| 关 键 词： | 导线网 方差分量估计 多余观测分量 定权规律 特征根法 权增量循环算法 |
| 文章编号： | 1000-050X(2001)02-0112-06 |
| 修稿时间： | 2000年11月23 |
Synthetical Study to
Estimate the Variance Components of Traverse Nets |
| |
| Wang Zhongfeng.Synthetical Study to
Estimate the Variance Components of Traverse Nets[J].Geomatics and Information Science of Wuhan University,2001,26(2):112-117. |
| |
| Authors: | Wang Zhongfeng |
| |
| Institution: | WANG Zhongfeng 1 |
| |
| Abstract: | This paper gives the function model to estimate the viarance components of traversenets, narrates the basic processes of viarance components estimate simply, and enumerates the formulae to estimate the viarance components in common use. Supposing every measured values have the same redundant observation components, a new simplified formula to estimate viarance components is advanced. In Tab. 1, the changing law of weights of observed values is depicted when calculating the traverse nets by variance components estimate, d01 and d02 stand for 021 and σ022 respectively, and P )and P ) stand for the weights of jth observed value of traverse angles and legsrespectively in the calculation ofith time. In Eqs. (19) and (20), P1 and P2 stand for weightsmatrix of observed values of traverse angles and legs respectively, p(0)2 ＝ P20 stands for the initialvalue ofP2, ki ＝ k can be calculated by Eq.(17).
Because only the weights of traverse legs are changed in every circulate processes to estimatethe variance components of traverse nets, a circulate calculating method to use the increments ofweights is summed up,and the related formulae are Eqs. (22) to (25) ,as well as the whole circulate calculating processes are listed in Tab. 2. In the formulae or Tab. 2, V10 and V20 stand for thecorrections of traverse angles and legs calculated by initial weights matrix respectively, and theweights increments matrix Ap comes from Eq. (21). the circulate calculating method to use theweights increments has an obvious advantage, which is that the normal equations do not need constituted in every circulate processes.
There are many continued multiplication and inversion and finding trace of matrices inHelmert's formula. These calculations not only are complicated but also need a lot of store spacefor computer. So this paper also advances the characteristic roots method to estimate the viarancecomponents of traverse nets. This method makes complicated calculations between matrices inHelmert' s formula become into the simple calculations between characteristic roots.Besides, thecalculation for characteristic roots is only needed once. In line with the same thought, Forstener' sformula can be simplified too. The calculated method about the characteristic roots can be foundfrom Eqs. (34)～(37).
At the end of this paper, a calculated example is given. It is used to prove that the newmethod to estimate the variance components is effective. Advancing a new simplified formula andthe characteristic roots method for variance components estimate, summing up the basic law to calculate the weights of the observed values for traverse nets in the processes of variance componentsestimate and the method to calculate the variance components of traverse nets using the weightsincrements are the main achievements in the paper. Supplying a practical method to make two realand symmetric matrices become into two diagonal matrices together may be another achievementof this paper. |
| |
| Keywords: | traverse nets variance components estimate redundant observation components law to calculate weights characteristic roots method |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
