scholarly journals Polar motion from ILS observations with least-squares collocation

1988 ◽  
Vol 128 ◽  
pp. 215-220
Author(s):  
R. Verbeiren
Keyword(s):  
Least Squares ◽  
Observational Data ◽  
Polar Motion ◽  
Parameter Determination ◽  
Large Set ◽  
Powerful Method ◽  
Least Squares Collocation ◽  
Computational Step

Least-squares collocation is a powerful method for combining interpolation, filtering and parameter determination in one single computational step. We show that the method is applicable to the computation of polar motion values from a very large set of basic observational data. In this study, we use the ILS observations from 1900 to 1978.

A priori noise and regularization in least squares collocation of gravity anomalies

2013 ◽  
Vol 62 (2) ◽  
pp. 199-216 ◽  
Author(s):  
Wojciech Jarmołowski
Keyword(s):  
Least Squares ◽  
Spatial Resolution ◽  
Gravity Data ◽  
A Priori ◽  
Gravity Anomalies ◽  
Geopotential Model ◽  
Large Set ◽  
Least Squares Collocation ◽  
Gravity Field Model ◽  
Two Parameters

Abstract The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes significantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity field model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

scholarly journals The least-squares collocation method in the mechanics of deformable solids

2021 ◽  
Vol 1715 ◽  
pp. 012029
Author(s):  
Sergey Golushko ◽  
Vasily Shapeev ◽  
Vasily Belyaev ◽  
Luka Bryndin ◽  
Artem Boltaev ◽  
...  
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Least Squares Collocation ◽  
Deformable Solids ◽  
Mechanics Of Deformable Solids

scholarly journals On the uncertainty of height anomaly differences predicted by least-squares collocation

2020 ◽  
Vol 10 (1) ◽  
pp. 53-61
Author(s):  
E. Mysen
Keyword(s):  
Least Squares ◽  
Spatial Separation ◽  
Height Anomaly ◽  
Surface Model ◽  
Least Squares Collocation ◽  
Normal Heights ◽  
Gravimetric Quasigeoid ◽  
The Difference ◽  
Grid Interpolation ◽  
Gps Observations

AbstractA network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

Application of Fitting Estimation Method in GPS Height Fitting

2013 ◽  
Vol 694-697 ◽  
pp. 2545-2549 ◽  
Author(s):  
Qian Wen Cheng ◽  
Lu Ben Zhang ◽  
Hong Hua Chen
Keyword(s):  
Least Squares ◽  
Estimation Method ◽  
Least Square ◽  
Least Squares Collocation ◽  
Normal Height ◽  
Geodetic Height ◽  
The Given ◽  
Surveying And Mapping

The key point researched by many scholars in the field of surveying and mapping is how to use the given geodetic height H measured by GPS to obtain the normal height. Although many commonly-used fitting methods have solved many problems, they all value the pending parameters as the nonrandom variables. Figuring out the best valuations, according to the traditional least square principle, only considers its trend or randomness, which is theoretically incomprehensive and have limitations in practice. Therefore, a method is needed not only considers its trend but also takes randomness into account. This method is called the least squares collocation.

NURBS Surface Reconstruction From a Large Set of Image and World Data Points

1993 ◽  
Author(s):  
Vassilios E. Theodoracatos ◽  
Vasudeva Bobba
Keyword(s):  
Least Squares ◽  
Vision System ◽  
Physical Object ◽  
Free Form ◽  
Approximation Technique ◽  
Global Coordinate System ◽  
Large Set ◽  
Affine Invariant ◽  
Nurbs Surface ◽  
Data Points

Abstract In this paper an approach is presented for the generation of a NURBS (Non-Uniform Rational B-splines) surface from a large set of 3D data points. The main advantage of NURBS surface representation is the ability to analytically describe both, precise quadratic primitives and free-form curves and surfaces. An existing three dimensional laser-based vision system is used to obtain the spatial point coordinates of an object surface with respect to a global coordinate system. The least-squares approximation technique is applied in both the image and world space of the digitized physical object to calculate the homogeneous vector and the control net of the NURBS surface. A new non-uniform knot vectorization process is developed based on five data parametrization techniques including four existing techniques, viz., uniform, chord length, centripetal, and affine invariant angle and a new technique based on surface area developed in this study. Least-squares error distribution and surface interrogation are used to evaluate the quality of surface fairness for a minimum number of NURBS control points.

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