1484 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975
Cs = X. = Mt, = Xe = 0
C, = Ye 7 Mt, = Ys = 0 (15)
G = Ze = M, + 2e = 0
In a least squares solution this means:
8C, 8C, ac, 9C, 8C, .
X, dX, + dX da + o do =F db do = Or dk + V x = 0
oC aC oC oC aC
ZL dy, + Ldn + 2 : : =
àY, Nr lasts yt dit V, = 0 ac
ac, oC oC oC oC
e : 2 + z e 2 =
az. dz. + SX dX = do + 99 de + fret de + V. = 0
As mentioned before, the actual adjustment is done in a step by step iterative procedure.
In the first step the observation equations are:
Ve = G (X.’, Y. de X ve 2 œ', b', K',
o", o", KT a Ve; zl Xo yc", Zeil
Vr = FX. Y. De‘; e, $', K')
Vr — Fo eX Y o Zz. œ, o", kx"
where the first Equation of (17) is obtained by combining Equations (5) with (3) and (4) and
linearizing it by developing into a Taylor series.
The other two equations in Equations (17) are obtained according to Equation (16). Then
the weighted square sum of the corrections V is minimized.
In the second iteration step the function G in Equation (17) is replaced by
Vy = H 1x, Y. Ze. X." Y Ze œ', o ke œ”, d K^,
’ / ’ " " " !
ke > kı > ko > ks’, k, > kı > ka > ks", n. pa', (18)
" " ! ! " "
21. 2, A', B', A", B").
Its linearized form is again adjusted together with V;, and V;, (see Equation (17)).
Iteration continues, using alternatively V; and V;, until the differences between sub-
sequent results are less than 1078 mm and 1075 radians respectively. This usually takes
approximately four iterations.
Due to the fact that the normal equation matrix is fully occupied, the program requires a
considerable amount of cpu-time. This is the main reason why the ground control is consid-
ered presently as fixed rather than incorporated as an observed quantity in a combined
parametric-condition adjustment as in thé optional case where collinearity equations are used
for the control points?. An expansion in this direction is planned.
Perhaps it should be pointed out that there is no need for full X,Y,Z control points, as the
control restraint can utilize horizontal and vertical control points separately.
PRACTICAL TrsrTs
Several test objects have been photographed using a Nikomat-FT 35 mm camera with a 50
mm Nikkor—4 lens and evaluated using 2, 3, 4, or 6 photographs, forming 1,3, 6, and 13 (more
practically : 11) photogrammetric models. The method does not necessarily require conver-
gent photography which however provides better stereo coverage.
There are 17 unknowns per photograph in the second iteration step, which leads to the
minimum number of common points to be measured in each photograph as shown in Table 1.
It is quite apparent that more than four photographs become uneconomical as they require
much more measuring and computing effort.
All these combinations were evaluated using ten each horizontal and vertical control points
and many object points. Both a full calibration (including all distortions and affinity and using
V, and V, alternatively) and a partial calibration (using V; only) were carried out. Further-
