Abstract
Outliers in observation set badly affect all the estimated unknown parameters and residuals, that is because outlier detection has a great importance for reliable estimation results. Tests for outliers (e.g. Baarda's and Pope's tests) are frequently used to detect outliers in geodetic applications. In order to reduce the computational time, sometimes elimination of some unknown parameters, which are not of interest, is performed. In this case, although the estimated unknown parameters and residuals do not change, the cofactor matrix of the residuals and the redundancies of the observations change. In this study, the effects of the elimination of the unknown parameters on tests for outliers have been investigated. We have proved that the redundancies in initial functional model (IFM) are smaller than the ones in reduced functional model (RFM) where elimination is performed. To show this situation, a horizontal control network was simulated and then many experiences were performed. According to simulation results, tests for outlier in IFM are more reliable than the ones in RFM.
Highlights
Outlier detection has a great importance in geodetic networks
The redundancies in initial functional model (IFM) are smaller than the ones in reduced functional model (RFM); this situation is proved in this study
Since the diagonal elements of the cofactor matrix of the residuals in RFM is bigger than the ones in IFM, the standardized residuals or studentized residuals in IFM are bigger than RFM
Summary
The efficacy of the unknown parameters and their standard deviations depends on whether the observation set includes outliers or not. If the observations include more than one outlier, the tests for outliers cannot detect them reliably due to masking effect or swamping effect, especially when the magnitudes of multiple outliers are small (HEKIMOGLU, 2000 and 2005). The number of unknown parameters in geodetic networks should be small so that some unknowns that are not related directly to the coordinates can be eliminated in adjustment model. The following question is investigated: must the outlier detection be applied to RFM or IFM where a group of unknowns is not eliminated? To compare the reliabilities of tests for outliers in RFM and IFM, mean success rate (MSR) is used. The MSR means the estimated power of the test (AYDIN, 2011)
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