REVIEW OF STRIP AND BLOCK ADJUSTMENT DURING 1964-1967
5
coordinates and to three rotations) and to the
provisional terrain coordinates. Although the
adjustment has been written as an iterative
procedure, in practice one pass through the
adjustment is found to be sufficient.
Although computation costs will depend
on the computer and on the time and care
spent on the preparation of the program, it is
of interest to notice that a small block re
quired nine times more computer time when
disk storage was used than when only core
storage was used. The adjustment of a block
of 180 photographs took about eight times
longer than that of a block of 90 photographs.
7. THE PROGRAM OF D. BROWN ASSOCIATES,
INC., ([11]-[13])
Here, also, pre-edited input data for the
block adjustment can be provided by other
programs, and the unknowns in the normal
equations are corrections to approximate
coordinates and rotations. The block adjust
ment program computes directly the normal
Equations 2e. An iterative solution is em
ployed which, judging by the number of
iterations that is required, operates on small
submatrices.
On the basis of an investigation of iterative
solutions, the method of successive overrelax
ation is considered to be the only one that
converges sufficiently fast. The acceleration
factor 2/(1 + y/\l — r) ) is used, r being here
the ratio between the largest corrections in
two successive iterations. Especially if r is
close to unity, this leads to an even slower
convergence than is obtained with the factor
l-\-r. Luysternik’s method is rejected because
its use in every iteration causes divergence.
Equation 3 is used for control points and
for photographs with one or more known
parameters. In any second or following pass
through the adjustment, the second part of
this equation is replaced by the sum of the
vectors of corrections obtained earlier. This
makes the formation of the normal equations
more complicated. It is meant to avoid the
complications of the correlation that the pre
ceding adjustment introduces if corrected
approximations are used as new observations.
However, considering the facts that with a
properly organized initial positioning one pass
through the adjustment can be sufficient and
that the correlation of the initial estimates of
unknown parameters of different points or
photographs is already neglected, this modifi
cation of Equation 3 can be dispensed with.
The most recent version of the program
[116] has been used to adjust a block of 162
photographs on a computer with only 8,000
words of core storage and four magnetic tape
units and to adjust a block of 1,000 photo
graphs (5 X200) on a large and fast computer.
8. PROGRAMS EVOLVED FROM ‘THE HERGET
method’ ([ 14]—[19])
The Herget method was initiated in 1954 at
Ohio State University under contract with
the Aeronautical Chart and Information
Centre. It has since gone through a sequence
of modifications most of which were sponsored
by the U. S. Army Engineer research organi
zation at Fort Belvoir (see [14] and [16]).
Herget used only one type of condition
equation for all measurements: that of
coplanarity of vectors. These vectors are the
vectors from the projection centres to the
image points and unit vectors through con
trol points. One photograph at a time was
envisaged to be relaxed in an iterative pro
cedure.
In 1956, separate condition equations for
partial control points and a rather unusual
scale constraint equation for three conjugate
rays were added by McNair. Subsequently,
condition equations for two equal-height
points in the same model and for known air
base were added and a simple simultaneous
solution of the complete set of normal equa
tions was introduced. At this point, the
method became known as the U. S. Geologi
cal Survey’s Direct Geodetic Restraint Method.
A new program for the adjustment of up to
22 photographs and with undisclosed further
modifications was completed in 1965 [17].
A further series of modifications was ini
tiated in 1961. Weighting of the observations
was made possible and a search for an opti
mum pivotal element was introduced in the
direct solution of the normal equations.
In the present version of the program [16],
for control points the collinearity equations
and Equation 3 are used. For pass points
(non-control points), the linearized coplanar
ity equation and a scale constraint equation
have been retained. The latter equation speci
fies that the distance from ground point to
projection centre along the second of three
rays must be the same for the two pairs of
rays. No approximate coordinates of pass
points are needed here. Because such coordi
nates can be easily computed from the coordi
nates of any two image points, this is only a
small advantage. The need to select combina
tions of points for the formation of the ob
servation equations and the resulting occur
rence of a coefficient matrix for the vector v
in Equation 1 which differs from the unit
matrix is a slight disadvantage.