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.

scholarly journals Adaptive Least-Squares Collocation Algorithm Considering Distance Scale Factor for GPS Crustal Velocity Field Fitting and Estimation

2019 ◽  
Vol 11 (22) ◽  
pp. 2692 ◽  
Author(s):  
Wei Qu ◽  
Hailu Chen ◽  
Shichuan Liang ◽  
Qin Zhang ◽  
Lihua Zhao ◽  
...  
Keyword(s):  
Least Squares ◽  
Covariance Function ◽  
High Reliability ◽  
Scale Factor ◽  
Distance Scale ◽  
Crustal Movement ◽  
Least Squares Collocation ◽  
Crustal Velocity ◽  
Regional Tectonic ◽  
Gps Observations

High-precision, high-reliability, and high-density GPS crustal velocity are extremely important requirements for geodynamic analysis. The least-squares collocation algorithm (LSC) has unique advantages over crustal movement models to overcome observation errors in GPS data and the sparseness and poor geometric distribution in GPS observations. However, traditional LSC algorithms often encounter negative covariance statistics, and thus, calculating statistical Gaussian covariance function based on the selected distance interval leads to inaccurate estimation of the correlation between the random signals. An unreliable Gaussian statistical covariance function also leads to inconsistency in observation noise and signal variance. In this study, we present an improved LSC algorithm that takes into account the combination of distance scale factor and adaptive adjustment to overcome these problems. The rationality and practicability of the new algorithm was verified by using GPS observations. Results show that the new algorithm introduces the distance scale factor, which effectively weakens the influence of systematic errors by improving the function model. The new algorithm can better reflect the characteristics of GPS crustal movement, which can provide valuable basic data for use in the analysis of regional tectonic dynamics using GPS observations.

Astrogravimetric Leveling by Least Squares Collocation

1977 ◽  
Vol 31 (2) ◽  
pp. 133-150
Author(s):  
Gérard Lachapelle
Keyword(s):  
Least Squares ◽  
Fundamental Equation ◽  
Gravity Anomalies ◽  
Least Squares Collocation ◽  
Empirical Formulas ◽  
Covariance Functions ◽  
Rugged Topography ◽  
The Difference ◽  
Geoid Undulations ◽  
Good Agreement

The application of least squares collocation to astrogravimetric leveling is described and the fundamental equation of astrogravimetric leveling in least squares collocation is derived. This method is easier and quicker to use than classical astrogravimetric leveling and is therefore well suited for extensive application. Six different covariance functions for use in flat and rugged topography areas are presented and comparisons are made between the accuracy estimates obtained when using these covariance functions and those obtained when using Bomford’s empirical formulas for astrogeodetic leveling; results are in very good agreement. Two astrogeodetic profiles located in Canada were used for this purpose. Finally, comparisons are made between the accuracy estimates obtained for the difference of geoid undulations calculated by astrogravimetric leveling when using the covariance functions mentioned and different configurations of observed deviations of the vertical and gravity anomalies.

On the advantage of normal heights

2018 ◽  
Vol 939 (9) ◽  
pp. 2-9
Author(s):  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Tide Gauge ◽  
General Term ◽  
Reference Ellipsoid ◽  
Height Anomaly ◽  
Normal Height ◽  
Anomalous Field ◽  
Normal Heights ◽  
Basic Concepts ◽  
Orthometric Heights

The author analyzes the arguments in the report by Robert Kingdon, Petr Vanicek and Marcelo Santos “The shape of the quasigeoid” (IX Hotin-Marussi Symposium on Theoretical Geodesy, Italy, Rome, June 18 June 22, 2018), which presents the criticisms for the basic concepts of Molodensky’s theory, the normal height and height anomaly of the point on the earth’s surface, plotted on the reference ellipsoid surface and forming the surface of a quasigeoid. The main advantages of the system of normal heights, closely related to the theory of determining the external gravitational field and the Earth’s surface, are presented. Despite the fact that the main advantage of Molodensky’s theory is the rigorous determining the anomalous potential on the Earth’s surface, the use of the system of normal heights can be shown and proved separately. To do this, a simple example is given, where the change of marks along the floor of a strictly horizontal tunnel in the mountain massif is a criterion for the convenience of the system. In this example, the orthometric heights show a change of 3 cm per 1.5 km, which will require corrections to the measured elevations due the transition to a system of orthometric heights. The knowledge of the inner structure of the rock mass is also necessary. It should be noted that the normal heights are constant along the tunnel and behave as dynamic ones and there is no need to introduce corrections. Neither the ellipsoid nor the quasi-geoid is a reference for normal heights, because so far the heights are referenced to initial tide gauge. The points of the earth’s surface are assigned a height value; this is similar to the ideas of prof. L. V. Ogorodova about the excessive emphasis on the concept of quasigeoid. A more general term is the height anomaly that exists both for points on the Earth’s surface and at a distance from it and decreases together with an attenuation of the anomalous field.

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

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.

DOES TRUST PROMOTE ENTREPRENEURSHIP IN A DEVELOPING COUNTRY?

2018 ◽  
Vol 63 (05) ◽  
pp. 1385-1403 ◽  
Author(s):  
KITAE SOHN ◽  
ILLOONG KWON
Keyword(s):  
Developing Countries ◽  
Property Rights ◽  
Least Squares ◽  
Developing Country ◽  
Ordinary Least Squares ◽  
Community Level ◽  
Two Stage ◽  
The Us ◽  
The Difference ◽  
The Individual

Trust was found to promote entrepreneurship in the US. We investigated whether this was true in a developing country, Indonesia. We failed to replicate this; this failure was true whether trust was estimated at the individual or community level or whether ordinary least squares (OLS) or two stage least squares (2SLS) was employed. We reconciled the difference between our results and those for the US by arguing that the weak enforcement of property rights in developing countries and the consequent hold-up problem make it more efficient for entrepreneurs to produce generic goods than relationship-specific goods—producing generic goods does not depend on trust.

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