Table 1 - uploaded by Marek Hubert Zienkiewicz
Content may be subject to copyright.
The results of the precise leveling measurements obtained in the five campaigns.
Source publication
The paper presents monitoring of the geodetic displacements using the Msplit(q) estimation method. Generally, the approach is based on a multi split functional model of geodetic observations. A typical property of Msplit(q) estimation is that the estimates of the controlled point coordinates are determined by using one observation set in all measur...
Similar publications
In aerial multi-view photogrammetry, whether there is a special positional distribution pattern among candidate homologous pixels of a matching pixel in the multi-view images? If so, can this positional pattern be used to precisely confirm the real homologous pixels? These problems have not been studied at present. Therefore, the study of the posit...
Citations
... The different variants of M split estimation have been applied in deformation analysis [127,128,133,[137][138][139][140][141][142], detection of unstable points in GNSS networks [143], processing laser scanning data [89,[144][145][146][147][148][149], direct identification of gross errors [150], S-transformation [151,152], robust coordinate transformation [153], linear regression analysis [128,133], and marine navigation [103,154]. ...
Outlying observations are undesirable but possible elements of geodetic measurements. In such a context, the primary and trivial solution is to repeat “suspected” observations. The question arises: what if the measurements cannot be performed again, or if one cannot flag outliers easily and efficiently? In such a case, one should process data by applying methods that consider the possible occurrence of outlying observations. Historically, except for some previous attempts, the statistical approach to robust estimation originates in the 60s of the 20th century and refers to the pioneer papers of Huber, Tukey, Hampel, Hodges, and Lehmann. Also, the statistical procedures known as data snooping (data dredging) were developed at a similar time. It took not a long time before robust procedures were implemented for processing geodetic observations or adjustment of observation systems. The first works of Baarda and Pope encouraged other scientists or surveyors to elaborate robust procedures adapted for geodetic or surveying problems, which resulted in their rapid development in the last two decades of the 20th century. The question for the 21st century is whether robustness is still an important issue relating to modern measurement technologies and numerical data processing. One should realize that modern geodetic techniques do not decrease the probability of outlier occurrence. Considering measurement systems that yield big data, it is almost certain that outliers occur somewhere. The paper reviews different approaches to robust processing of geodetic observations, from the data snooping methods, random sampling, M-estimation, R-estimation, and Msplit estimation to robust estimation of the variance coefficient. Such a variety reflects different natures, origins, or properties of outliers and the apparent fact that there is no best and most efficient and universal robust approach. The methods presented are indeed the basis for future solutions based on, e.g., machine learning.
... Another variant of Msplit estimation is the absolute Msplit estimation (AMS), which is based on the L1 norm condition [24,25]. The development of Msplit estimation has led to some modifications of SMS or AMS methods [26][27][28][29][30], which have already been applied in deformation analysis and displacement detection [23,25,[27][28][29][30][31][32][33][34]. ...
Deformation analysis or point movement checking is the basis for monitoring ground or engineering structures. There are several approaches to conducting deformation analysis, which differ from each other in measurement techniques or data processing. Usually, they are based on geodetic observables conducted in at least two epochs. As such measurements are not “immediate”, it might so happen that a point (or some points) displaces during measurement within one epoch. The point movements might be continuous or sudden. This study focuses on the latter case, where rockburst, mining damages, or newly formed construction faults might cause displacement. To study this, an observation set consisting of measurements performed before and after point displacements is needed. As the actual observation division stays unknown, this can be called pseudo epochs. Such a hypothetical observation set requires special estimation methods. In this work, we examined Msplit estimation and robust methods. The first approach’s advantage is that it provides two variants of the network point coordinates (before and after point movements), hence showing dynamic changes in the geodetic network. The presented empirical analyses confirm that Msplit estimation is a better choice that results in better and more realistic outcomes.
... Thus, it was necessary to know the real surface and its deformation, hence the necessity of data simulation. The applications of M split estimation to determine terrain profiles or geodetic network deformation using real data can be found in other papers [36,40,53,56]. ...
Terrestrial laser scanning (TLS) is a modern measurement technique that provides a point cloud in a relatively short time. TLS data are usually processed using different methods in order to obtain the final result (infrastructure or terrain models). Msplit estimation is a modern method successfully applied for such a purpose. This paper addresses the possible application of the method in processing TLS data from two different epochs to model a vertical displacement of terrain resulting, for example, from landslides or mining damages. Msplit estimation can be performed in two variants (the squared or absolute method) and two scenarios (two point clouds or one combined point cloud). One should understand that point clouds usually contain outliers of different origins. Therefore, this paper considers the contamination of TLS data by positive or/and negative outliers. The results based on simulated data prove that absolute Msplit estimation provides better results and overperforms conventional estimation methods (least-squares or robust M-estimation). In practice, the processing of point clouds separately seems to be a better option. This paper proved that Msplit estimation is a compelling alternative to conventional methods, as it can be applied to process TLS data disturbed by outliers of different types.
... M split estimation was applied inter alia in the analysis of geodetic network deformation Wiśniewski 2012, 2014;Zienkiewicz 2014;Zienkiewicz et al. 2017;Wiśniewski and Zienkiewicz 2016). In these problems, M split estimation is particularly effective in identifying stable potential reference points (PRPs) (Nowel 2019). ...
Msplit estimation is a method that enables the estimation of mutually competing versions of parameters in functional observation models. In the presented study, the classical functional models found in it are replaced by errors-in-variables (EIV) models. Similar to the weighted total least-squares (WTLS) method, the random components of these models were assigned covariance matrix models. Thus, the proposed method, named Total Msplit (TMsplit) estimation, corresponds to the basic rules of WTLS. TMsplit estimation objective function is constructed using the components of squared Msplit and WTLS estimation objective functions. The TMsplit estimation algorithm is based on the Gauss–Newton method that is applied using a linear approximation of EIV models. The basic properties of the method are presented using examples of the estimation of regression line parameters and the estimation of parameters in a two-dimensional affine transformation.
... A method called Msplit estimation was created to estimate the location parameters (more generally, the parameters of the split functional models) when an observation set consists of the subsets mentioned before. The method has already been applied in deformation analysis (Wiśniewski, 2009;Zienkiewicz et al., 2017;Wyszkowska and Duchnowski, 2019). ...
Various measurement techniques and data processing are applied to determine point displacements and deformation of geodetic networks or buildings. Considering classical measurements and analysis of the network deformation, we should realize that the measurements are not “immediate.” The question arises: what happens if a point (or some points) displaces between particular measurements within one epoch. In such a case, the observation set would consist of the observations before and after point displacement, and such hypothetical observation groups can be regarded as related to two (or more) pseudo epochs. The paper's main objective is to examine some estimation methods that would probably deal with such a problem, namely Msplit estimation (in two variants, the squared and the absolute Msplit estimation) and chosen robust methods, namely Huber’s method (example M-estimation) and the Hodges-Lehmann weighted estimation (basic R-estimation). The first approach can provide two (or more) variants of the network point coordinates (here, before and after point movements), providing information about two (or more) states of the network during measurements. In contrast, the robust methods can only decrease the influence of the outliers on the computed network point coordinates. Thus, estimation results would concern only one network state in such a case. The presented empirical analyses show that the better and more realistic results are obtained by applying Msplit estimation. Huber’s method can also provide acceptable results (describing the network state at the epoch beginning) only if the number of observations conducted after the point displacements is not too high.
... Applications of M split estimation concerned so far not only processing of TLS data (presented in [1,15,22,31]) but also deformation analyses [29,30,[32][33][34][35][36], direct identification of gross errors [37], linear regression analyses [30,34], robust coordinate transformation [38], S-transformation [39] and marine navigation [40]. Most of these applications applied only the squared M split estimation (SMS), of which the objective functions stem from the assumption that observation errors are normally distributed. ...
This paper presents an application of an Msplit estimation in the determination of terrain profiles from terrestrial laser scanning (TLS) data. We consider the squared Msplit estimation as well as the absolute Msplit estimation. Both variants have never been used to determine terrain profiles from TLS data (the absolute Msplit estimation has never been applied in any TLS data processing). The profiles are computed by applying polynomials of a different degree, determining which coefficients are estimated using the method in question. For comparison purposes, the profiles are also determined by applying a conventional least squares estimation. The analyses are based on simulated as well as real TLS data. The actual objects have been chosen to contain terrain details (or obstacles), which provide some measurements which are not referred to as terrain surface; here, they are regarded as outliers. The empirical tests prove that the proposed approach is efficient and can provide good terrain profiles even if there are outliers in an observation set. The best results are obtained when the absolute Msplit estimation is applied. One can suggest that this method can be used in a vertical displacement analysis in mining damages or ground disasters.
... Until now, practical application was found for such a version of M split estimation, in which the components of function (1) take the forms ρ (1) [10,11,16,27,52,53]. This version associated with the assumption that the observation y i is the realisation of either of its random variables Y i (1) ...
The paper presents Msplit estimation as an alternative to methods in the class of robust M-estimation. The analysis conducted showed that Msplit estimation is highly efficient in the identification of observations encumbered by gross errors, especially those of small or moderate values. The classical methods of robust estimation provide then unsatisfactory results. Msplit estimation also shows high robustness to single gross errors of large values. The presented analysis of Msplit estimators’ robustness is of a chiefly empirical nature and is based on the example of a simulated levelling network and a real angular-linear network. Using the Monte Carlo method, mean success rates for outlier identification were determined and the courses of empirical influence functions were specified. The outcomes of the analysis were compared with the relevant values achieved via selected methods of robust M-estimation.
... The studies (Chrzanowski A., et al., 2007;Chrzanowski, A, et al., 2003;Chrzanowski, A., 1981;Chrzanowski, A., et al., 1992;Chrzanowski, A., et al., 1983;Chrzanowski, A., et al., 1986) are encyclopedic. New research on deformation analysis by (Ebeling, A., et al., 2009;Ebeling, A., 2014;Zienkiewicz, Marek, 2014;Zienkiewicz MH, et al., 2017;Han, Junqiang et al., 2018;Герасименко, М.Д., et al., 2017;Savšek, Simona, et al., 2010;Tsanovski, Yuri, 2017;Sušić, Zoran et al., 2015;Shahar, L., and Even-Tzur, G., 2014;Savšek, Simona, 2017;Savšek-Safić S., et al., 2008;Marković, Marko et al., 2015) only within a years have taken the theory and practice of this field to a new level. The deformation analysis is a process of statistical testing of rejection or acceptance of deformation. ...
This monograph defines the place, role, and importance of engineering surveying in the field of deformation monitoring, deformation surveys, and geotechnical monitoring. Тhe monograph represents the author’s experience in this field-the presentation of deformation ellipsoid in a topocentric (local level) coordinate system for deformation analysis, strain analysis, common processing of GPS and terrestrial measurements, determining the tilting of buildings and facilities, and preliminary and optimal design of deformation monitoring schemes. This work also represents the achievements of world-renowned specialists and schools. GPS measurements are of primary importance among other instrumental methods for deformation surveying. GNSS networks are used from small surveying engineering networks to large country geodynamic networks. A special part is dedicated to GPS (GNSS) technology, because as a universal geodetic tool GPS measurements allows to be combined with total positioning systems and classical methods. The theoretical and practical researches presented in this monograph clearly show the nature and capabilities of engineering surveying and confirm the geodetic methods as leading for deformation monitoring and surveys.
This monograph is an attempt to collect from the world literature all the deformation surveying methods and deformation analysis concepts known to human civilization and keep the tremendous scientific heritage in this field.
... EKK yönteminin modeldeki bozucu etkiyi yayması sonucunda periyotlar arasındaki yer değiştirmeler dengeleme sonuçlarına tam olarak yansımamakta ve analiz sonuçlarının güvenilirliği beklenenden düşük çıkmaktadır (Hekimoğlu, Erdoğan & Butterworth, 2010). Bu nedenle kestirici olarak robust yöntemler kullanılarak daha güvenilir sonuçlar elde edilmek istenmektedir (Duchnowski & Wiśniewski, 2014;Nowel & Kamiński, 2014;Nowel, 2016;Wiśniewski & Zienkiewicz, 2016;Zienkiewicz, Hejbudzka & Dumalski, 2017). ...
... Therefore, the numerical case considered in this paper presents a potential application of the binding's general case for eliminating the reversal-point effect. Such a solution may be especially useful when a greater number of measurement epochs is considered in the shift analysis ( Zienkiewicz et al. 2017). ...
In this paper, the use of the parameter estimation method in a split functional model in the analysis of geodetic network deformation is presented. Special attention is drawn to the situation when competitive parameters fulfill certain independent conditions in the systems of observation equations. It is also proposed that the so-called reversal-point effect can be eliminated from the Msplit estimation using conditional equations binding the competitive parameters. It is shown that the introduced extension of the Msplit estimation method does not deprive the studied method of its qualities, including its robustness.
