摘要本文通过对水准网进行自由网平差，来比较经典平差和自由网平差方法运用在变形监测中效果，并对结果进行分析，通过与自由网平差结果对比表明，在经典间接平差中，必须有足够的初始数据的秩等于观测值的数量是必不可少的，其系数是一个对称矩阵的满秩，即方程有唯一解.秩亏自由网不参与初始数据和待点参数的测量或使用附加条件探讨和传统的测量平差的观点，是从广义逆矩阵的线性代数的角度谈但在在变形测量分析中，有的时候由于条件的原因，很难找到稳定的基准点，这时秩亏自由网平差将会产生一定的作用，秩亏自由网平差无论选择什么样的约束条件都不会对平差结果产生影响，也可以解算出变形量。两种平差计算得到的单位权中误差相差不大，本文认为拟稳平法更适合于监测网数据处理的变形，经典平差可以看做一种特殊的拟稳平差。39519
毕业论文关键词：水准网，变形监测，自由网平差，拟稳平差
Abstract
This article through the free net adjustment of leveling network, compared to the classical adjustment and free network adjustment method used in deformation monitoring results, and the results were analyzed by comparing the results, with the adjustment of free network, the classic indirect adjustment, there must be enough initial data rank is equal to the number of observations is essential, it is a full rank coefficient of a symmetric matrix, the equation has a unique solution. Rank defect free network does not participate in the initial data and the measured parameters or the use of additional conditions on the traditional adjustment point of view, is the inverse matrix from generalized linear algebra perspective but in analysis in deformation measurement, sometimes because of the reasons, it is difficult to find a stable reference point, then the rank defect free network adjustment will have a certain role, rank defect free network adjustment regardless of the choice of what kind of constraints have no influence on the adjustment results, can also calculate the deformation. Two adjustment calculation of unit weight error difference, this paper argues that the quasi steady method is more suitable for deformation monitoring network data processing, the classical adjustment can be seen as a kind of special quasi stable adjustment.
Keywords: Leveling network, deformation monitoring,free adjustment, to be stable adjustment
目录
摘要    I
Abstract    II
１　绪论    1
1.1研究进程    1
1.2选题目的    1
1.3研究问题和解决方案    1
1.3.1 研究的问题    1
1.3.2 研究途径    1
２　秩亏自由网平差    2
2.1  问题的提出    2
2.2  秩亏自由网平差原理    4
2.3  S的具体形式    6
3  平差方法分析及比较    7
3.1  重心基准的秩亏自由网平差    7
3.2  拟稳平差    8
3.3  最小范数准则    9
3.4  秩亏自由网的广义逆解法    10
3.5  分析与比较    13
4　实例分析    14
4.1　例1    14
4.2　例2    17
结论    20
致谢    21
参考文献22
１　绪论
1.1  研究进程
秩亏自由网平差法普遍应用在大地测量和工程测量中，其中，在变形监测中的使用中颇受眷注。这种调整一般是由伪逆N +奇异系数矩阵的求解。目前，对于如何申请？似乎还有不同看法。
一种意见认为，变形观测中应用此法, 主要应发扬其点位误差小且均匀, 分辨变形的灵敏度较高的优点。但是,由于估计的 有偏性,对于如何发扬其优点,以及优良的程度怎么样，还需研究 水准网的秩亏自由网平差比较及应用:http://www.youerw.com/shuxue/lunwen_39843.html