應用疊代近乎無偏估計法釐定觀測量方差之研究

• Main Authors: Chen,Ming Tsuan, 陳銘川
• Other Authors: Hsu,Rong Shin
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/30449910801087790215

碩士 === 國立臺灣大學 === 土木工程學研究所 === 87 === The Iterated Almost Unbiased Estimation (IAUE) technique to estimate the variance components of the observations was discussed. The first-order leveling network of Taiwan and a two-dimensional network (excepted from Hirvonen 1979) were used as numerical examples. For the first-order leveling network of Taiwan, the observed elevation differences were grouped according to the standard deviations of individual leveling lines with line-length as parameter. Due to the network geometry, the rigorous IAUE formula caused group redundancies to decrease monotonically when grouping inadequately. As a result, some of the variance factors were unable to converge to unity. On the other hand, the variance factors as estimated by the IAUE approximate formula tended to oscillate at 1 and converged eventually. For the two- dimensional network, the grouping was made according to the lengths of the measured distances and the triangle misclosures of the observed angles. Due to large degree of freedom of the network, and hence more flexible in grouping the observed quantities, all variance factors converged to unity no matter whether the rigorous formula or the approximate one was used. When the Helmert’s method was applied for checking the consistency among the weights as determined by IAUE, it was found that the consistency was always fulfilled among those group variances which were estimated by the rigorous formula provided that the corresponding variance factors converged to unity, and that the consistency was not satisfactory among those group variances which were estimated by the approximate formula. However, such an inconsistency was degraded significantly if the rigorous formula was employed in the first several iterations and then succeeded thereafter with the approximate formula. In addition, three indicators: (1) convergence of variance factors to unity, (2) the a posteriori variance of unity weight being equal to 1, and (3) the highest mean network precision, were proposed to help select the optimum grouping scheme for a network.