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.