*9 or ev GfrG«v U^KP whence, as Gx$ gap gPY 8Y I if a f, and o if a y e«=U°K. (9) In other words: The corrections e of the original problem can be regarded as corrections to uncorrelated observations of equal weights, to be submitted to the condition-equations UpRa=Up. These equations are now solved by the orthogonalization method. VI. Example The sequence of the calculations will be shown. A triangulation is given as in fig. 6. All directions are observed with equal weights and are assumed to be uncorrelated. In this case the cofactors- tensor is: g«P=i (a p) and g°$= o (a (J) a (3 I 62. The adjustment will be performed in three steps. In all there are 17 triangle-conditions and 4 side-conditions. a) The first step consists of adjusting 11 angle-conditions. A chain of triangles ischosen in the net e.g.no 1,..,11 incl. Its direc tions are numbered according to the system as under III, A. From formula II, 3 is derived: e1=+K1 e2 Kx e3 -\-Kx K2 etc. The correlatives are immediately known as the inverse matrix of the normal-equations is given by the rules of III, B and so is the co- factors-tensor. (See III, C, D, and E.) The corrections are computed and applied. b) In the second phase the once corrected directions have now unequal weights and are correlated. This is expressed by the above mentioned tensor. The two triangle-equations 12 and 13 and three side-equations are adjusted. The conditions are given by up P<* up. This set of equations is submitted to a linear transformation (see V) whence XJo ra p. To find the corrections e these equations are solved by the orthog- a p a o a o „0.3 mp 7^0. U9 =up R<* o a o a a

Digitale Tijdschriftenarchief Stichting De Hollandse Cirkel en Geo Informatie Nederland

Tijdschrift voor Kadaster en Landmeetkunde (KenL) | 1957 | | pagina 27