caa a22 4500 475737687 CHVBK 20180406123451.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1007/s001900000103 doi (NATIONALLICENCE)springer-10.1007/s001900000103 On non-linear low-low SST observation equations for the determination of the geopotential based on an analytical solution [Elektronische Daten] [Ch. Cui, D. Lelgemann] Abstract.: In satellite data analysis, one big advantage of analytical orbit integration, which cannot be overestimated, is missed in the numerical integration approach: spectral analysis or the lumped coefficient concept may be used not only to design efficient algorithms but overall for much better insight into the force-field determination problem. The lumped coefficient concept, considered from a practical point of view, consists of the separation of the observation equation matrix A=BT into the product of two matrices. The matrix T is a very sparse matrix separating into small block-diagonal matrices connecting the harmonic coefficients with the lumped coefficients. The lumped coefficients are nothing other than the amplitudes of trigonometric functions depending on three angular orbital variables; therefore, the matrix N=B T B will become for a sufficient length of a data set a diagonal dominant matrix, in the case of an unlimited data string length a strictly diagonal one. Using an analytical solution of high order, the non-linear observation equations for low-low SST range data can be transformed into a form to allow the application of the lumped concept. They are presented here for a second-order solution together with an outline of how to proceed with data analysis in the spectral domain in such a case. The dynamic model presented here provides not only a practical algorithm for the parameter determination but also a simple method for an investigation of some fundamental questions, such as the determination of the range of the subset of geopotential coefficients which can be properly determined by means of SST techniques or the definition of an optimal orbital configuration for particular SST missions. Numerical results have already been obtained and will be published elsewhere. Springer-Verlag Berlin Heidelberg, 2000 Key words: SST nationallicence Geopotential determination nationallicence Dynamic orbital improvement nationallicence Satellite geodesy nationallicence Analytical solution nationallicence Cui Ch Institute of Geodesy and Geoinformatics, H12, Technical University Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany e-mail: cui@lego.bv.tu-berlin.de, DE aut Lelgemann D. Institute of Geodesy and Geoinformatics, H12, Technical University Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany e-mail: cui@lego.bv.tu-berlin.de, DE aut https://doi.org/10.1007/s001900000103 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900000103 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cui Ch Institute of Geodesy and Geoinformatics, H12, Technical University Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany e-mail: cui@lego.bv.tu-berlin.de, DE aut NATIONALLICENCE 700 1- Lelgemann D. Institute of Geodesy and Geoinformatics, H12, Technical University Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany e-mail: cui@lego.bv.tu-berlin.de, DE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer