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.

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.

Effect of gravity data coverage on geoid determination: comparison between Stokes and Collocation techniques in Egypt and Austria

2020 ◽  
Author(s):  
Hussein Abd-Elmotaal ◽  
Norbert Kühtreiber
Keyword(s):  
Least Squares ◽  
Covariance Function ◽  
Gravity Data ◽  
Geoid Determination ◽  
Large Area ◽  
Least Squares Collocation ◽  
Function Fitting ◽  
Collocation Technique ◽  
Data Coverage

&lt;p&gt;The coverage of the gravity data plays an important role in the geoid determination. This paper tries to answer whether different geoid determination techniques would be affected similarly by such gravity data coverage. The paper presents the determination of the gravimetric geoid in two different countries where the gravity coverage is quite different. Egypt has sparse gravity data coverage over relatively large area, while Austria has quite dense gravity coverage in a significantly smaller area. Two different geoid determination techniques are tested. They are Stokes&amp;#8217; integral with modified Stokes kernel, for better combination of the gravity field wavelengths, and the least-squares collocation technique. The geoid determination has been performed within the framework of the non-ambiguous window remove-restore technique (Abd-Elmotaal and K&amp;#252;htreiber, 2003). For Stokes&amp;#8217; geoid determination technique, the Meissl (1971) modified kernel has been used with numerical tests to obtain the best cap size for both geoids in Egypt and Austria. For the least-squares collocation technique, a modelled covariance function is needed. The Tscherning-Rapp (Tscherning and Rapp, 1974) covariance function model has been used after being fitted to the empirically determined covariance function. The paper gives a smart method for such covariance function fitting. All geoid are fitted to GNSS/levelling geoids for both countries. For each country, the computed two geoids are compared and the correlation between their differences versus the gravity coverage is comprehensively discussed.&lt;/p&gt;

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.

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