If on the other hand, the conditional equations are rather simple
'expressions as e.g. in formulas (47), (48) and (51), it is more practical
to use these equations to eliminate certain unknowns in the corresponding
observational equations, Thus, the coefficients in the By matrix as given.
with (41) have to be replaced by:
(L)
DI -E,(IIT, -, II14) "PF,
* If for points of type 3 the unknowns
A X and À Y are eliminated
L) =D III, -B (LII, -I, IIT - F '
(y 7 ny yn rr
I TT
"H H
and (J) =F_ === -D (K) =F == =-E
x x 11, X * XH X | Ir for points of type 4 the
t i ITR unknown AZ is eliminated
al faire D X) F z-E :
mr EX CES
In ease the systematic errors present in the control data are rather large,
it may be desirable to adjust them in such a way that only a specific residual
V is obtained for any given control coordinate, independent of the number of.
rays intersecting at such a point. Such a solution may be obtained by adding
to the normal equation system (21), corresponding conditional equations. In
general nomenclature, such a conditional equation is, with regard to formulas
6 an
(15), (16), (34) and (40), (55)
9
2) 2
Thus it 1s possible to establish for each of the independent combinations of
Vs p^ (ak, + bk
the intersecting rays by pairs, a conditional equation between the two group
i and k,
(55) separately for each given control coordinate. In this way all normal
of associated k values, by equalizing the corresponding expressions
equations associated with a specific point will become interlocked in the
AP^lAT matrix and the process of stepwise accumulation of the reduced
normal equation system (32) or (37) will be rendered much more cumbersome,
Numerically speaking, in such cases it appears simpler, and from the theo-
retical standpoint sufficiently rigorous, to accomplish the adjustment in
two separate steps. In the first step a least squares adjustment will be
38
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