Robust M-Estimation in Analysis of Control Network Deformations: Classical and New Method

An alternative approach to testing displacements in a geodetic network

“…IWST-metode zagotavljajo dobro oceno vektorja premikov za posamezno točko v postopku robustne S-transformacije (Chen et al, 1990). V literaturi je predstavljena alternativna M-ocena za določitev vektorja premikov neposredno iz razlik »surovih« neizravnanih meritev (Nowel, 2015;Nowel, 2016). Metoda je še posebej učinkovita, kadar se pričakujejo mali premiki, ki le malo presežejo merske pogreške.…”

Accuracy of the Hodges–Lehmann estimates computed by applying Monte Carlo simulations

“…Thus, we will check the stability of five potential reference points. Such a network was already considered as an example in some previous publications (see , Caspary 2000;Nowel 2015), which gives us possibility to compare the final results of different approaches to deformation analysis. The detailed description of the network can be found in the mentioned papers, here let us summarize that we consider two measurement epochs, and the two observation sets consist of five arcs of horizontal directions with the assumed standard deviation r a ¼ 3 cc and six distances with r d ¼ 0:3 ½mm.…”

“…This can be performed by applying new Monte Carlo simulations or in the simplified way, namely with application the factors c, which were already computed and which were listed in Table 4. The estimation results are presented in Table 6, which also presents the results obtained by applying the classical method (Caspary 2000) or the method which is based on robust M-estimation (Nowel 2015). Now let us find stable reference frame within PRPs.…”

Geometric deformation analysis in free geodetic networks: case study for Fruska Gora in Serbia

“…If ≤ , , , the point is stable, otherwise ( > , , ) the point is unstable. Detailed explanations concerning the robust methods can be found in contributions of the following authors: (Chen, 1983;Caspary and Borutta, 1987;Setan and Singh, 2001;Nowel and Kamiński, 2014;Nowel, 2015Nowel, , 2016aNowel, , 2016b.…”

“…IWST and LAS are based on the S transformation for the purpose of detecting the movement trend of the points. The robust estimation of deformation from observation differences (REDOD and its generalization GREDOD) is especially recommended when the observation plan is completely the same for both measurement epochs in order to keep constant possible non-random errors for one geometric network element in both epochs under control (Nowel and Kamiński, 2014;Nowel, 2015). In the literature one can find applications in deformation analyses of the R-estimation (Duchnowski, 2009 and2013), as well as of the M split estimation (Wiśniewski, 2009;Zienkiewicz, 2014;Zienkiewicz and Baryla, 2015;Zienkiewicz et al, 2017).…”