LANDMEETKUNDE Ir. P. RICHARDUS, The calculation of cofactors in Tienstra's method of adjustment I. Introduction. The characteristic of Tienstra's method1) of adjusting observa tions according to the principle of the least squares is a split up of the calculations into a number of phases. The original observa tions are accompanied by a tensor of cofactors expressing their weights and amounts of correlation in the first step. In the sub sequent phases the corrected observations are introduced as "new" ones with their newly derived cofactors. It is possible to choose the number of normal-equations every time, but the number of cofactors to be computed depends on the number of observations. In this treatise rules are derived that minimise and simplify these computations in the first standard problem (more unknowns than relations). It will be done partly by tracing regularities in the tensors themselves, partly by changing and transforming the condition-equations. At the end an example is given of the ap plication. II. Syllabus of formulae. As in Tienstra's publication, the Ricci-calculus will be used. The observed quantities P01 (a i n) have to satisfy the equations The observations are p<1the cofactors are ga|3 and the weights gag" Their relation is given by the Kronecker 8 in which 8Y I if a y, and 8Y o if a y. The e<* are the corrections to the observations; these have to be calculated from or upeup uppa tp, (2) in a way that 1S a minimum. The solution is e® u^Kp. (3) Surveying-engineer, Cooma (Australia) u?pa up (p i ->b,b<n). (i) a 1 a k MP (p* ga) MP a o a r v Bulletin Géodésique no. 6, Oct. 1947. Prof. J. M. Tienstra "Extension of the technique of the method of the least squares to correlated obser- vations".

Digitale Tijdschriftenarchief Stichting De Hollandse Cirkel en Geo Informatie Nederland

Tijdschrift voor Kadaster en Landmeetkunde (KenL) | 1957 | | pagina 11