scholarly journals TREATMENT OF GEODETIC SURVEY DATA AS FUZZY VECTORS

2015 ◽  
Vol XL-3/W3 ◽  
pp. 29-33
Author(s):  
G. Navratil ◽  
E. Heer ◽  
J. Hahn
Keyword(s):  
Normal Distribution ◽  
Least Squares ◽  
Survey Data ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Measurement Data ◽  
Geodetic Survey ◽  
Present Measurement ◽  
A Value ◽  
Light Signals

Geodetic survey data are typically analysed using the assumption that measurement errors can be modelled as noise. The least squares method models noise with the normal distribution and is based on the assumption that it selects measurements with the highest probability value (Ghilani, 2010, p. 179f). There are environment situations where no clear maximum for a measurement can be detected. This can happen, for example, if surveys take place in foggy conditions causing diffusion of light signals. This presents a problem for automated systems because the standard assumption of the least squares method does not hold. A measurement system trying to return a crisp value will produce an arbitrary value that lies within the area of maximum value. However repeating the measurement is unlikely to create a value following a normal distribution, which happens if measurement errors can be modelled as noise. In this article we describe a laboratory experiment that reproduces conditions similar to a foggy situation and present measurement data gathered from this setup. Furthermore we propose methods based on fuzzy set theory to evaluate the data from our measurement.

Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data

2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf
Keyword(s):  
Least Squares ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Measurement Data ◽  
Ordinary Least Squares ◽  
Total Least Squares ◽  
Position Measurement ◽  
Point Position ◽  
Ordinary Least Squares Method

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

scholarly journals A comparison of X-ray stress measurement methods based on the fundamental equation

2016 ◽  
Vol 49 (2) ◽  
pp. 426-432 ◽  
Author(s):  
Toshiyuki Miyazaki ◽  
Toshihiko Sasaki
Keyword(s):  
Least Squares ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Stress Measurement ◽  
Fundamental Equation ◽  
Measurement Methods ◽  
X Ray Diffraction ◽  
Diffraction Vector ◽  
X Ray ◽  
Fundamental Equations

Stress measurement methods using X-ray diffraction (XRD) methods are based on so-called fundamental equations. The fundamental equation is described in the coordinate system that best suits the measurement situation, and so making a comparison between different XRD methods is not straightforward. However, by using the diffraction vector representation, the fundamental equations of different methods become identical. Furthermore, the differences between the various XRD methods reside in the choice of diffraction vectors and the way of calculating the stress from the measured data. The stress calculation methods can also be unified using the general least-squares method, which is a common least-squares method of multivariate analysis. Thus, the only difference between these methods turns out to be in the choice of the set of diffraction vectors. In the light of these ideas, three commonly used XRD methods are compared: the sin2ψ method, the XRD2 method and the cosα method, using the estimation of the measurement errors. The XRD2 method with 33 frames (data acquisitions) shows the best accuracy. On the other hand, the accuracy of the cosα method with three frames is comparable to that of the XRD2 method.

scholarly journals Statistical Inference for Stochastic Differential Equations with Small Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liang Shen ◽  
Qingsong Xu
Keyword(s):  
Differential Equations ◽  
Normal Distribution ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Asymptotic Distribution ◽  
Asymptotic Property ◽  
Stable Distribution ◽  
Least Squares Method ◽  
Regularity Conditions ◽  
Drift Parameter

This paper proposes the least squares method to estimate the drift parameter for the stochastic differential equations driven by small noises, which is more general than pure jumpα-stable noises. The asymptotic property of this least squares estimator is studied under some regularity conditions. The asymptotic distribution of the estimator is shown to be the convolution of a stable distribution and a normal distribution, which is completely different from the classical cases.

scholarly journals Uncertainty Analysis and Experimental Validation of Identifying the Governing Equation of an Oscillator Using Sparse Regression

2022 ◽  
Vol 12 (2) ◽  
pp. 747
Author(s):  
Yaxiong Ren ◽  
Christian Adams ◽  
Tobias Melz
Keyword(s):  
Least Squares ◽  
Domain Knowledge ◽  
Least Squares Method ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Estimation Method ◽  
Excitation Amplitude ◽  
Coefficient Of Determination ◽  
Sparse Regression ◽  
Single Mass

In recent years, the rapid growth of computing technology has enabled identifying mathematical models for vibration systems using measurement data instead of domain knowledge. Within this category, the method Sparse Identification of Nonlinear Dynamical Systems (SINDy) shows potential for interpretable identification. Therefore, in this work, a procedure of system identification based on the SINDy framework is developed and validated on a single-mass oscillator. To estimate the parameters in the SINDy model, two sparse regression methods are discussed. Compared with the Least Squares method with Sequential Threshold (LSST), which is the original estimation method from SINDy, the Least Squares method Post-LASSO (LSPL) shows better performance in numerical Monte Carlo Simulations (MCSs) of a single-mass oscillator in terms of sparseness, convergence, identified eigenfrequency, and coefficient of determination. Furthermore, the developed method SINDy-LSPL was successfully implemented with real measurement data of a single-mass oscillator with known theoretical parameters. The identified parameters using a sweep signal as excitation are more consistent and accurate than those identified using impulse excitation. In both cases, there exists a dependency of the identified parameter on the excitation amplitude that should be investigated in further research.

scholarly journals Asymptotic normality of a simple linear EV regression model with martingale difference errors

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1817-1825
Author(s):  
Guo-Liang Fan ◽  
Tian-Heng Chen
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Error Variance ◽  
Martingale Difference ◽  
Errors In Variables ◽  
Ev Regression Model ◽  
Biased Estimators ◽  
Better Than

This paper considers the estimation of a linear EV (errors-in-variables) regression model under martingale difference errors. The usual least squares estimations lead to biased estimators of the unknown parametric when measurement errors are ignored. By correcting the attenuation we propose a modified least squares estimator for a parametric component and construct the estimators of another parameter component and error variance. The asymptotic normalities are also obtained for these estimators. The simulation study indicates that the modified least squares method performs better than the usual least squares method.

On the geometry of a modern imaging diffractometer

1999 ◽  
Vol 55 (3) ◽  
pp. 543-557 ◽  
Author(s):  
W. A. Paciorek ◽  
M. Meyer ◽  
G. Chapuis
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Measurement Data ◽  
Modern Imaging

The geometry of a modern imaging diffractometer is discussed in detail. A method to find all relevant instrument parameters from the control single-crystal measurement data is proposed and the limitations of such a procedure are indicated. Optimization of the instrument parameters by the least-squares method is presented.

scholarly journals The Positioning of the Aircraft Using GPS/GLONASS Data

2019 ◽  
Vol 49 (3) ◽  
pp. 65-96
Author(s):  
Kamil Krasuski ◽  
Ewelina Kobiałka ◽  
Janusz Ćwiklak ◽  
Marek Grzegorzewski
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Measurement Data ◽  
Reference Trajectory ◽  
Flight Trajectory ◽  
Differential Technique ◽  
Stochastic Processing ◽  
Test Flight ◽  
Research Experiment

Abstract The article presents the results of aircraft positioning using GPS/GLONASS data in air navigation. In the work, the flight trajectory of the Cessna 172 aircraft was determined on the basis of GPS, GLONASS and GPS/GLONASS data. The coordinates of the Cessna 172 were determined using the least squares method in a stochastic processing compliant with the ICAO recommendations. In the air test, the Cessna 172 made a test flight over EPDE military airfield in Dęblin. The GPS, GLONASS and GPS/GLONASS measurement data from the Topcon HiperPro on-board aircraft installed on the Cessna 172 aircraft were used in the research experiment. The coordinates of the Cessna 172 in the geocentric XYZ and ellipsoidal BLh were compared with the precise flight reference trajectory determined from the differential technique RTK-OTF.

scholarly journals MULTIPURPOSE MEASUREMENT MODELS FOR ADJUSTMENT BY THE LEAST-SQUARES METHOD

2021 ◽  
Vol 82 (2) ◽  
pp. 29-37
Author(s):  
Iuriy Kuzmenko ◽  
◽  
O. M. Samoilenko ◽  
Serhiy Tsiporenko ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Measurement Errors ◽  
Interlaboratory Comparison ◽  
Least Squares Method ◽  
Measurement Model ◽  
Linear Type ◽  
Measurement Models ◽  
Measurement Results ◽  
Large Scope ◽  
Simultaneous Adjustment

The development of multipurpose measurement models is the precondition for software development for simultaneous adjustment of the large scope and complicated combinations of the measurement results by the least-squares method. Multipurpose measurement models for software can be a helpful tool for processing the final measurement results provided by different measurement methods applying the mentioned software; processing the measurement results of measurement standards comparisons, interlaboratory comparison, and calibration procedures; estimating the additive and multiplicative systematic components of measurement errors and their uncertainty; processing complicated combinations by binding or linking up of the interlaboratory comparison and calibration results in the time; simultaneous processing of the measurement results obtained by various methods e.g. by the method of direct measurements and comparisons; fast-changing the multipurpose measurement models from linear to non-linear type. Processing of the results by software based on the multipurpose measurement model algorithm can help to established a comprehensive measurement traceability network by pooling the single traceability chains.

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