Reliability Measures for Correlated Observations
Reliability Measures for Correlated Observations
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DOI：
10.1061/(asce)0733-9453(1997)123:3(126
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发表时间：
1997-08
期刊：
影响因子：
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通讯作者：
B. Schaffrin
中科院分区：
文献类型：
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作者：
B. Schaffrin
在W.Baarda的开创性工作之后，测量工程师在高可靠性至关重要的情况下，在平差后定期检查学生化残差。为了检测不相关观测值中的异常值，必须检查残差的余因和相应(未调整的)观测值之间的相对大小。这些比率通常取自所谓的“可靠性矩阵”。正如其他研究人员最近指出的那样，传统的方法在相关观测的情况下崩溃了，已经提出了新的可靠性衡量标准，然而，这些衡量标准并不一定是有界的。因此，我们引入了一个标准化程序，保证我们的新可靠性度量在0到1之间。然后，我们用几个简单的例子展示了它们的行为，然后是一个(模拟的)全球定位系统(GPS)应用程序，它允许以下结论：(1)对于相关的观测，“传统的”冗余数字给出了过于乐观的结果；(2)标准化后，根据以前记录的可靠性度量对观测的排名很可能会颠倒，使“最不可靠”的观测适度可靠，反之亦然。
Following the pioneering work by W. Baarda, surveying engineers routinely inspect the Studentized residuals after an adjustment when high reliability is crucial. To detect outliers among uncorrelated observations, the relative magnitude between the cofactor of the residual and the corresponding (unadjusted) observation has to be checked. These ratios are commonly taken from a so-called “reliability matrix.” As other researchers have pointed out recently, the traditional approach breaks down in the case of correlated observations, and new measures of reliability have been proposed that, however, are not necessarily bounded. Therefore, we introduce a standardization procedure that guarantees our new reliability measures to fall between 0 to 1. We then show their behavior in a few simple examples, followed by a (simulated) global positioning system (GPS) application that allows these conclusions: (1) the “traditional” redundancy numbers give much too optimistic results for correlated observations; and (2) the ranking of observations according to previously recorded reliability measures may well be reversed after the standardization, making the “least reliable” observations moderately reliable, and vice versa.