Efficacy of Msplit Estimation in Displacement Analysis

Wiśniewski, Z.; Duchnowski, Robert; Dumalski, Andrzej

doi:10.3390/s19225047

Cited by 13 publications

(9 citation statements)

References 34 publications

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“…The efficacy of the Msplit method has been confirmed by tests carried out on different datasets. The sensitivity of the proposed method was described by the authors of this method in [27]. The size of the displacement is an important issue here.…”

Section: Discussionmentioning

confidence: 99%

Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes

et al. 2020

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Building constructions are exposed to various forces and natural phenomena. Some of them are sudden and violent, e.g., an earthquake or heavy rains, causing a displacement of the ground. Other phenomena affect objects on a longer-term, e.g., vibrations caused by daily road traffic. Sometimes, building structures may have defects due to incorrect construction. In any case, if an engineering object shows changes in the relation to its correct geometry or position, deformation and displacement measurements are required. Engineering objects are also monitored during their construction. Nowadays, it is important to perform measurements quickly and with high accuracy. The use of a Terrestrial Laser Scanning (TLS) allows for the required measurement speed and accuracy. This measurement technology allows a large dataset, which can be arbitrarily elaborated, to be obtained. The structure of building objects can include vertices, lines, planes, and other shapes and can be described using mathematical functions. This allows data processing to be automated. In this article, we present the Msplit method as an effective approach to the processing of data obtained as a result of TLS measurements. The proposed approach is new because until now, the Msplit estimation method has not been used to detect adjacent planes in one-point cloud obtained from TLS. The Msplit estimation method allows a functional model to be split into two or more competitive models and thus two or more entities in a point cloud to be estimated simultaneously. Four different objects measured using TLS are presented: two objects representing vertical displacements and two objects representing horizontal displacements. The test results and analysis confirm that the Msplit estimation method can be successfully applied in the detection of adjacent planes.

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Section: Discussionmentioning

confidence: 99%

Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes

et al. 2020

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“…Such an application of M split estimation would be novel. Currently, such a method was used in the deformation analysis in a different context, namely when the observation set was a disordered mixture of the same object's observations from two different measurement epochs [29,32,35,45].…”

Section: Real Tls Datamentioning

confidence: 99%

Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

2020

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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.

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“…Without loss of generality we can take such an assumption here. The solutions with other weight matrices and regarding to the estimates applied here can be found in (e.g., Yang et al, 2002;Duchnowski, 2013;Wiśniewski et al, 2019). The least squares estimate (LS) of the parameter vector,X LS , is as followŝ…”

Section: Theoretical Foundationsmentioning

confidence: 99%

Systematic bias of selected estimates applied in vertical displacement analysis

Wyszkowska

Duchnowski

2020

Journal of Geodetic Science

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AbstractIn surveying problems we almost always use unbiased estimators; however, even unbiased estimator might yield biased assessments, which is due to data. In statistics one distinguishes several types of such biases, for example, sampling, systemic or response biases. Considering surveying observation sets, bias from data might result from systematic or gross errors of measurements. If nonrandom errors in an observation set are known, then bias can easily be determined for linear estimates (e.g., least squares estimates). In the case of non-linear estimators, it is not so simple. In this paper we are focused on a vertical displacement analysis and we consider traditional least squares estimate, two Msplitestimates and two basic robust estimates, namely M-estimate, R-estimate. The main aim of the paper is to assess estimate biases empirically by applying Monte Carlo method. The smallest biases are obtained for M- and R-estimates, especially for a high magnitude of a gross error. On the other hand, there are several cases when Msplitestimates are the best. Such results are acquired when the magnitude of a gross error is moderate or small. The outcomes confirm that bias of Msplitestimates might vary for different point displacements.

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Efficacy of Msplit Estimation in Displacement Analysis

Cited by 13 publications

References 34 publications

Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes

Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes

Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

Systematic bias of selected estimates applied in vertical displacement analysis

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