Weakly Multicollinear Datum Transformations

被引:9
作者
Aktug, Bahadir [1 ,2 ]
机构
[1] Bogazici Univ, Kandilli Observ, TR-34680 Istanbul, Turkey
[2] Earthquake Res Inst, Geodesy Dept, TR-34680 Istanbul, Turkey
关键词
Datum; Transformations; Networks; Reference frames; Multicollinearity; Estimation; RIDGE-REGRESSION; GPS; DEFORMATION; TOMOGRAPHY; EARTHQUAKE; INSAR;
D O I
10.1061/(ASCE)SU.1943-5428.0000086
中图分类号
TU [建筑科学];
学科分类号
0813 ;
摘要
Geodetic network design and optimization is a very well-known concept in geodesy. However, in many cases, the available geodetic network configuration with respect to the estimation model is insufficient because of the physical and financial limitations. For the case of estimating the datum transformation parameters between two datums, the colocated points are only an unevenly and inhomogenously distributed subset of the available national/regional networks. Because the transformation parameters are defined with respect to an earth-centered, earth-fixed (ECEF) frame, very limited geographic coverage of the national/regional networks often leads to a weakly multicollinear estimation problem. Such limited geographical coverage is often coupled with the intrinsic geometrical distortions as well as the relatively lower precision of the observations, in particular, when transforming a terrestrial network into a space-based network. In such cases, the individual parameters become highly correlated and oversensitive to the network configuration, and the individual transformation parameters cannot be estimated reliably. In this study, the concept of an idealized three-dimensional (3D) regional network geometry is introduced, its inverse cofactor matrix is analytically derived, and a regularized estimation method based on the inverse cofactor matrix of an ideal network distribution is presented to deal with the weakly multicollinear datum transformation problem. The efficiency of the proposed method is shown in three realistically simulated networks. The proposed method outperforms the standard least squares in terms of mean square error (MSE) and reduces the correlations among the parameters. DOI: 10.1061/(ASCE)SU.1943-5428.0000086. (C) 2012 American Society of Civil Engineers.
引用
收藏
页码:184 / 192
页数:9
相关论文
共 38 条
[1]   Source parameters for the Mw=6.6, 03 February 2002, Cay Earthquake (Turkey) and aftershocks from GPS, Southwestern Turkey [J].
Aktug, Bahadir ;
Kaypak, Buelent ;
Celik, Rahmi Nurhan .
JOURNAL OF SEISMOLOGY, 2010, 14 (03) :445-456
[2]   Inverse and Compound Datum/Frame Transformations [J].
Aktug, Bahadir .
JOURNAL OF SURVEYING ENGINEERING, 2009, 135 (02) :46-55
[3]  
[Anonymous], TECHNOMETRICS
[4]  
[Anonymous], 1963, Soviet Mathematics Doklady
[5]  
Baarda W., 1968, PUBLICATIONS ON GEOD, V2
[6]   Deformation during the 12 November 1999 Duzce, Turkey, earthquake, from GPS and InSAR data [J].
Bürgmann, R ;
Ayhan, ME ;
Fielding, EJ ;
Wright, TJ ;
McClusky, S ;
Aktug, B ;
Demir, C ;
Lenk, O ;
Türkezer, A .
BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA, 2002, 92 (01) :161-171
[7]  
Bursa M., 1966, FUNDAMENTALS OF THE
[8]  
CAI J, 2004, IAG S, V127, P309
[9]   The systematic analysis of the transformation between the German geodetic reference system (DHDN, DHHN) and the ETRF system (DREF91) [J].
Cai, JQ .
EARTH PLANETS AND SPACE, 2000, 52 (11) :947-952
[10]   Effect of the satellite laser ranging network distribution on geocenter motion estimation [J].
Collilieux, X. ;
Altamimi, Z. ;
Ray, J. ;
van Dam, T. ;
Wu, X. .
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH, 2009, 114