nd 
of 
SS 
Symposium, problems of ill-conditioning are circumvented by the following 
procedure: 
(2) first, apriori reasoning may be invoked to suppress certain 
parameters at the outset: for example, those in group (e) 
would never be exercised with normal vertical photography 
over flat to moderate terrain because of their almost per- 
fect coupling with coordinates of the exposure stations; 
on the other hand, they may be held in reserve for possible 
application in special circumstances warranting their 
exercise (e.g., with highly convergent photographs); 
(it) in an initial reduction, each parameter to be provisionally 
exercised may be regarded as having an apriori value of 
zero governed by an arbitrary, rather loose apriori variance 
(chosen, for example, to allow the term involving the 
parameter to assume a maximum absolute value of perhaps 
100um within the format); 
(iii) by virtue of the imposition of the aforementioned loose 
apriori constraints, determinacy of the initial reduction 
is assured and the covariance matrix of the adjusted error 
parameters can be evaluated; 
(iv) from the correlation matrix generated from the covariance 
matrix those terms that are inherently inseparable in the 
problem at hand will immediately be evident by virtue of 
their very high correlations (typically on the order of .99); 
(v) of each pair (or group) of coefficients exhibiting excessively 
high correlation, all but an arbitrarily selected one can 
Justifiably be suppressed (through exercise of tight apriori 
variances) in a repetition of the reduction. 
Carried to completion, the above process leads rather automatically to a 
reduced set of separable parameters and avoids problems with ill-conditioning. 
As applied to the Vermont block, it led to the suppression of the following 
coefficients (in addition to the presuppressed SXp, SYp, 8c): (13,055 015 02, Ds; 
C1, C5, 6s, Ki, P4, P5. 
Of the 46 available horizontal control points shown in Figure 6 
only 3 were of first order accuracy while 35 and 8, respectively, were of 
second and third order accuracy. The apriori standard deviations assigned 
to the three respective classes of control points were: 0.5 ft., 1.0 ft., 
and 3.0 ft. The bundle adjustment was executed both with and without the 
exercise of self-calibration. In both reductions, all control points were 
carried in the adjustment subject to the just mentioned apriori constraints. 
The most remarkable results of the comparative reductions are those presented 
in Table 1 which lists the horizontal corrections developed for each contro] 
point by each of the two reductions. One sees that the corrections arising 
from the bundle adjustment without self-calibration are decidedly large in 
comparison with their apriori standard deviations and are strongly systematic. 
With second order control points, for instance, the Root Mean Square. (RMS) 
values of the corrections in X and Y are 4.9 ft. and 3.9 ft, respectively, 
as compared with the assigned, apriori one sigma value of 1.0 ft. (at plate 
scale the corrections amount to 24 and 19um, respectively). This, of 
course, is indicative of the presence of a severe internal strain in the 
17