Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

Wyszkowska, Patrycja; Duchnowski, Robert; Dumalski, Andrzej

doi:10.3390/rs13010031

Cited by 7 publications

(4 citation statements)

References 43 publications

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“…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].…”

Section: Split Estimationmentioning

confidence: 99%

Robust procedures in processing measurements in geodesy and surveying: a review

Duchnowski,

Wyszkowska

2024

Meas. Sci. Technol.

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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.

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Section: Split Estimationmentioning

confidence: 99%

Robust procedures in processing measurements in geodesy and surveying: a review

Duchnowski,

Wyszkowska

2024

Meas. Sci. Technol.

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“…In many practical applications of M split estimation, we apply only one observation set, namely the set consisting of two (or more) observation groups. Such an approach is natural for M split estimation and advisable in many surveying problems (Błaszczak-Bąk et al Nowel, 2019;Guo et al, 2020;Wyszkowska et al, 2021). It could also be involved in deformation analysis (Zienkiewicz, 2015;.…”

Section: Numerical Examplementioning

confidence: 99%

“…Such an estimation method allows us automatically isolate observation subsets and estimate their location parameters. That feature might be advisable when processing TLS point clouds that include outliers (Wyszkowska et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Assessing vertical terrain displacement from TLS data by applying Msplit estimation – theoretical analysis

Wyszkowska

Duchnowski

2022

Proceedings of the 5th Joint International Symposium on Deformation Monitoring - JISDM 2022

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Terrestrial laser scanning (TLS) is a measurement technique that has become popular in the last decades. Measurement results, usually as a point cloud, contain many points measured. When the TLS technique is used to determine terrain surface (e.g., by determining terrain profiles), one should realize that some points measured do not concern the terrain surface itself, but trees, shrubs, or generally the vegetation cover. Considering terrain surface determination, they should be regarded as outliers. Some other observations can also be outliers of different origins; for example, they might be disturbed by gross errors. We should consider such observation types when the data are processed. Two leading solutions in such a context are data cleaning and the application of robust estimation methods. Robust M-estimation is the most popular for the latter approach. As an alternative, one can also consider the application of Msplit estimation, in which the functional model is split into two competing ones. Hence, the paper aims to analyze how Msplit estimation can assess vertical terrain displacement based on terrain profile determination from TLS data. We consider processing data in separate sets (two measurement epochs) or one combined set, a natural approach in Msplit estimation. The analyses based on simulated TLS data proved that the first solution seems better. Furthermore, the application of Msplit estimation can also provide more satisfactory results than the classical methods used in such a context.

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“…A similar problem is also analysed in a study by Janicka et al (2020), where M split estimation was proposed as a means of detecting and determining the displacements of adjacent planes. Laser scanning data also provided the basis for determining the terrain profiles using M split estimation (Błaszczak-Bąk et al 2015;Wyszkowska et al 2021).…”

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confidence: 99%

Total Msplit estimation

Wiśniewski

2022

J Geod

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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.

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Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

Cited by 7 publications

References 43 publications

Robust procedures in processing measurements in geodesy and surveying: a review

Robust procedures in processing measurements in geodesy and surveying: a review

Assessing vertical terrain displacement from TLS data by applying Msplit estimation – theoretical analysis

Total Msplit estimation

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