Collocation method

The collocation least squares (after the Latin collocatio arrangement, common position), Eng. least squares collocation, is a combined interpolation and equalizing method in which in contrast to the normal compensation calculation data may be processed with very different characteristics.

Who developed the method and its foundations for the first time, has not yet been researched doubt. At the Institute for Computing Technology of the former TH Dresden Horst Kadner developed in 1958 as part of his doctoral thesis collocation methods and habilitated in 1966 to approximate methods for linear equations Integration second type based on the collocation. In 1969, Horst Kadner developed as Professor of Mathematical Cybernetics and Computing Technology at the TU Dresden solution methods for a special class of integral equations on the basis of collocation methods.

In the late 1970s, these methods of geodesics and mathematician Helmut Moritz ( Berlin / Graz) were included for the purposes of integrated geoid determination to handle geometrical and physical data of the earth's shape and gravity field in one pour. Moritz also stated solutions of the collocation of the covariance matrix, and the problem in steps, in order to reduce the computer's calculation time with a large amount of data.

Among other things, extensive applications submitted by Hans Sünkel ( integrated local geoid determination ) and by Christian Tscherning (regional gravimetry). The first astro- geodetic geoid determination by LSC was performed in 1982 at the Technical University of Graz. She could see the accuracy of the Austrian Astrogeoides ( average ± 6 cm from 700 measurement points of deflections of the vertical ) by including a global harmonic gravity model ( RHRapp until 180.Ordnung ) increase by about a quarter and a local isolate data errors. Three years later, the accuracy can be increased by the inclusion of about 10,000 gravity anomalies to ± 4 cm.

Since about 1990, the collocation also serves as the basis for large-scale gravity field modeling with the inclusion of spherical function developments in satellite geodesy, including in two program systems German universities, GRAVSOFT and Opera (geodesy ). Applications in Northern Europe ( Tscherning & Forsberg 1986-93 ), Italy, Spain ( Simo, Catalao & Sevilla 1994) and Turkey ( Ayhan, 1993) showed the benefits of integral calculations accuracy increases by about a third compared to individual solutions.

The peculiarity of these applications is to minimize the average error of the measurements used by all data configurations can be created by a rotation of Geozentrum each other ( hence the name collocation ).

The collocation method is now also in the chemical thermodynamics application.