scholarly journals Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method

Sensors ◽  
2020 ◽  
Vol 20 (14) ◽  
pp. 3913 ◽  
Author(s):  
Zbigniew Wiśniewski ◽  
Waldemar Kamiński
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Random Noise ◽  
Total Least Squares ◽  
Reference Points ◽  
Deformation Analysis ◽  
Control Network ◽  
Least Squares Adjustment ◽  
Random Fluctuations ◽  
Vertical Deformations

This paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface’s vibrations is also assumed. Such noise disturbs the deformation’s functional models. Surface monitoring with the use of the geodetic levelling network of a free control network class is carried out. Assuming that, in some cases, the control networks are insufficient in surface’s deformation analysis, additional and non–measurable reference points have been provided. The prediction of these points’ displacements and estimation of the free control network points’ displacement are carried out using the collocation method applying the total least squares adjustment. The proposed theoretical solutions were verified by the simulation methods and on the example of a real control network.

scholarly journals Deformation analysis with Total Least Squares

2006 ◽  
Vol 6 (4) ◽  
pp. 663-669 ◽  
Author(s):  
M. Acar ◽  
M. T. Özlüdemir ◽  
O. Akyilmaz ◽  
R. N. Çelik ◽  
T. Ayan
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Transformation Model ◽  
Deformation Analysis ◽  
New Approach ◽  
Main Research ◽  
Research Fields ◽  
Analysis Process ◽  
Alternative Methodology ◽  
Coordinate Changes

Abstract. Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS) technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS) that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS) and the Total Least Squares (TLS), respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.

Bias-Corrected Weighted Total Least-Squares Adjustment of Condition Equations

2015 ◽  
Vol 141 (2) ◽  
pp. 04014013 ◽  
Author(s):  
Xiaohua Tong ◽  
Yanmin Jin ◽  
Songlin Zhang ◽  
Lingyun Li ◽  
Shijie Liu
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Weighted Total Least Squares ◽  
Least Squares Adjustment

Total least-squares adjustment of condition equations

2011 ◽  
Vol 55 (3) ◽  
pp. 529-536 ◽  
Author(s):  
Burkhard Schaffrin ◽  
Andreas Wieser
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Adjustment

scholarly journals A New Method for Vertical Deformation Detection Using Survey Control Networks

2009 ◽  
Vol 4 (1) ◽  
pp. 14
Author(s):  
Mudathir Omer Ahmed
Keyword(s):  
Least Squares ◽  
Confidence Level ◽  
Specific Area ◽  
New Method ◽  
Control Network ◽  
Vertical Deformation ◽  
Control Networks ◽  
Vertical Control ◽  
Vertical Deformations ◽  
Step Localization

Usually, the Survey control networks are used for deformation detection in a specific area using observations taken at different epochs. Where the coordinates obtained from two epochs, using least squares technique, are compared in order to assess if a deformation of a specified magnitude exists. Traditionally, the global congruency test is carried out so as to detect if the area of the network has undergone any movement (uplift or subsidence) due to natural or manmade causes. As a next step, localization methods are used to determine deformations at specific points in case there are changes in shape. In this research a new method is developed to establish deformations at specific points directly. The method is tested using a vertical control network simulated at various epochs of observation. The results obtained are compared with those obtained by another used method. Results obtained using this method indicate that vertical deformations greater than 0.03m using a precision of observation less than 10 can be detected at a minimum significant level of 0.05 (95% confidence level).

scholarly journals Scaled weighted total least-squares adjustment for partial errors-in-variables model

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
J. Zhao
Keyword(s):  
Least Squares ◽  
Variance Component ◽  
Maximum Likelihood Method ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Likelihood Method ◽  
Errors In Variables ◽  
Weighted Total Least Squares ◽  
Least Squares Adjustment ◽  
Observation Vector

AbstractScaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.

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