(Ca,?Yi Ca<2*i)2 a2- (x3) 245 In order to derive the weight coefficient of an orientation bearing for the computation of 0\ the law of propagation of errors is applied to the simplified equation (4) V\ i a\ ;AYi bi iAXi. (14) This gives in symbolical notation: Qvi.i «i.;<2y'i h.iQx1 Qaii (15) or worked out Qvl.ivl.i a2l.iQyjYi 2aI.ibl.iQxY ^I.iQxjXi The covariance between the bearings i and j at I is given by QvjVj al.iaI.iQxiYi («I.i&I.i OLl.jbii) <?XiYj h.ih.jQxiXi- 0-7) The question now arises whether there are any specific orientation bearings 9j.j of length dx i satisfying the centroid condition ca c/, o in formula 13), for which the assumption of equal weights and freedom of correlation, is truly valid. Then 0$ would attain a minimum. The is now left out of consideration. An investigation shows that there is a unique solution for two orienting directions only. We put in this case, omitting the index I for convenience a\Qyy 2«1J1 QXy b\ Qxx p (ïSa) a\ Qyy 2«2^2 Qxy "t" ^2 Qxx P (I8t>) and axa2QYY (aA a2^i) Qxy ^1^2Qxx 0 I1®0) Equation 18c can also be written cos 9j cos <?2QYy (cos 9i sin <p2 cos 92 sin <Pi) Qxy sin 9j sin 92QXx 0 (x8d) from which it is apparent that the freedom of correlation is depend- enl only on the bearings and not on the lengths of 1 From the equations (18) it is derived that Qxx r a\ Qyy C b\ b\ Qxy n A a2b2 Qyy b\ b\ (20) Expressing the centroid conditions as al ®2 2«i.p A (21) and b1 b2 2 blP B (22) it is found by solution of (19), (20), (21) and (22) that

Digitale Tijdschriftenarchief Stichting De Hollandse Cirkel en Geo Informatie Nederland

Tijdschrift voor Kadaster en Landmeetkunde (KenL) | 1963 | | pagina 13