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F1G6.9. General form of banded-bordered coefficient matrix.
frames. Under such circumstances, it can be shown that with proper ordering of
parameters the coefficient matrix of the normal equations for photogrammetric
block triangulation can be made to assume a banded form (Brown, 1968b), or more
generally, a banded-bordered form as shown in Figure 9. The band accommodates
all unknown elements of exterior orientation and the border accommodates those
parameters that are common to all frames (i.e., x, (ys reu Ku Kee P P).
Such systems of normal equations can be solved with extraordinary efficiency by
Recursive Partitioning (Gyer, 1967); a method developed originally at DBA Systems
for application to conventional aerotriangulation. It is appropriate to note here
that the process of self-calibration can also be employed effectively (under certain
circumstances) in conjunction with conventional blocks of aerial photography. In
such applications the normal equations again assume the banded-bordered form.
Aerial SMAC may be viewed as that special case of the Method of Self-
Calibration in which apriori coordinates of all targets have zero variances (or
infinite weight). In this case, the band in the banded-bordered system of normal
equations assumes a block diagonal form comprised of 6x6 matrices corresponding
to the elements of exterior orientation of the exposures. Accordingly, the normal
equations can be collapsed still further to the dimensions of the border (i.e., to the
number of parameters of the inner cone being recovered). Even when locations of
targets have been pre-established, Self-Calibration is to be preferred over SMAC
because the coordinates of the targets can be assigned appropriate a priori variances
to reflect their actual accuracies. Targets of unknown location merely constitute
the special subclass in which coordinates have infinite variance (or zero weight).
Some further examples of actual and potential application of the Method of Self-
Calibration are to be found in Kenefick (1971b).
