p
With SPN/GEANS the basic and relatively simple error model presented earlier
in equation (21), supplemented perhaps in the bundle adjustment by an auto-
regressive treatment of stochastic errors, holds promise of suppressing
residual build-up of positional error to a level of less than ] meter per
100 kilometers. Accordingly, when the bundle adjustment with self-calibration
is considered in conjunction with such rapidly developing technologies as
doppler surveying and inertial navigation, the following scenario begins
to emerge for the execution of very large mapping projects in the not-too-
distant future. First, a basic, but sparse, control net is established to
accuracies of 0.5 meters or better by doppler surveying — here, stations
might well be spaced at 75 to 100 km intervals. Using the doppler stations
as control points, an inertial surveying system is then employed to densify
the doppler survey, particularly around the perimeter of the block to be
flown (a spacing of 15 to 25 km along the perimeter might be appropriate
for a photo scale of 1:50,000). An inertial system, most likely the very
same unit as was used for first level densification of the doppler survey,
is then mounted in the mapping aircraft in proximity to the aerial camera.
Here, the unit functions both as a precise flight-line navigator and as an
auxiliary sensor (perhaps along with a statoscope). In the latter capacity
it provides a readout of inertial position corresponding to each photographic
exposure. The coefficients of the error model of the inertial navigator
(and statoscope) are then carried as strip-invariant parameters in the
bundle adjustment along with error coefficients for the camera, which are
carried as block-invariant parameters (or as sub-block invariant parameters,
when more than one camera is employed to cover the block). Through the use
of the inertial unit both on the ground and in the mapping aircraft, maximum
economic benefits are realized from what might otherwise be a prohibitively
expensive unit (at present, cost of a suitable unit with recommended spare
parts approaches $500,000, but is likely to be reduced to less than half this
amount by 1980).
Another development that may well have an impact on photogrammetric
triangulation in the 1980's is the Global Positioning System (GPS). This
system is being developed by the U.S. Air Force and will ultimately involve
a total of 24 satellites so arranged that at least four suitably distributed
satellites are to be visible at all times from all points on the earth.
Simultaneous reception of signals from four satellites will enable a moving
observer to determine his position in real-time to an absolute accuracy of
10 to 20 meters. With special refinements consisting mainly of the exploi-
tation of doppler tracking and the use of appropriate error models in the
bundle adjustment, the possibility exists for GPS to yield positions of the
mapping aircraft to accuracies of a few decimeters. Here again, implemen-
tation of the process of self-calibration would lead to sets of strip-invariant
error coefficients resident in the border of the normal equations.
Again and again reference is made in the foregoing discussions to
the border of the banded-bordered system of normal equations. Without the
border, the practical development of the bundle method would have remained
essentially frozen at its status of a decade ago when recursive partitioning
was first applied to the reduced normal equations. The border, more than
anything else, provides the foundation for the recent development of the
bundle method. To this point in the present discussion the border has been
applied only to parameters in error models for the photographic coordinates
or external sensors (or both). This is far from the limit of the utility
of the border in photogrammetric adjustment. As shown in Brown (1974), the
border can be exploited to introduce new information into the bundle adjust-
ment without altering the essential character of the banded-bordered form of
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