自检校光束法区域网平差的相关分析和附加参数显著性检验

本文选用正交的附加参数组对自检校光束法区域网平差进行相关分析和附加参数的显著性检验。主要讨论了区域网平差坐标的理论精度、附加参数的理论精度、附加参数之间及其与坐标未知数之间的相关系数,以及如何由附加参数显著性检验结果决定附加参数的取舍。所有这些讨论均在附加参数取不同的权时进行的。得到的主要结论有:(i)自检校区域网平差中平差坐标和附加参数的理论精度,以及附加参数与坐标未知数之间的相关均与附加参数所选择的权有关。(ii)正交的附加参数组,在一定的几何图形下,它的某些参数也可能与坐标未知数产生强相关。(iii)针对区域网平差的几何图形和所用的附加参数组,采用模拟数据进行相关分析,就可以找出其中可能存在的对权敏感、不易测准的或引起未知参数强相关的附加参数。只要将这些参数剔除或给予一个较大的权,则可保证自检校平差获得可靠的精度改善。此时平差结果对附加参数的权变得不敏感了。(iv)反过来,如果能精确地按照信噪比确定附加参数的权,在不考虑对系统误差的拟合误差时,可免去对平差结果的相关分析和显著性检验,而获得有效的精度改善。文章最后结合文献[1]、[2]的研究结果,对实际生产中如何使用自检校平差提出了具体的建议。

The Correlation Analysis of a Self-Calibrating Bundle Block Adjustment and the Test of Significance of Additional parameters

In this paper,the correlation analysis of a self-calibrating bundle block adjustment and the test of significance of additional parameters are carried out by the use of a selected orthogonal additional parameter set.The main objects of study are namely:the theoretical accuracy of the adjusted coordinates and the additional parameters,the correlation coefficients among the additional parameters and between the additional parameters and the ground point coordinates,the choice of additional parameters according to the test of significance.All of these studies are performed with different weights of additional parameters.The basic conclussions obtained are:(1) The theoretical accuracy of adjusted coordinates and additional parameters as well as the correlation between additional parameters and ground point coordinates are related to the choice of the weight of additional parameters.(2) Under certain geometrical conditions some additional parameters of an orthogonal parameter set might be highly correlated with ground point coordinates.(3) From the correlation analysis by the use of synthetic data for the given geometric figure of the block and the adopted additional parameter,we can find out those parameters which are very sensitive to their weights or which can not be easily determined exactly or which will bring out high correlations among the unknowns.If those parameters are removed from the equations or are given a bigger weight,the self-calibrating adjustment will be able to obtain a reliable accuracy improvement.In this case,the adjusted results will become insensitive to the weight of additional parameters.(4) Vice versa,if the weight of additional parameters can be correctly determined according to their signal-to-noise ratio,the correlation analysis and the test of significance of additional parameters can he exempted from the adjustment procedure when the imitation errors for systematic errors are not considered.Thus,an efficient accuracy improvement can be expected.At the end of this paper some suggestions are made in accordance with the investigations in[1]、[2]and this paper for the proper use of self-calibration in production work.