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".