formation can come from additional control points or from
additional photo overlap. In case of standard overlap (par-
allel strips with 20% side overlap) drift parameters per strip
can be solved, if 2 chains of vertical control points, running
across the block at both front ends, are given, in addition
to the standard 4 XYZ control points. If a block has dou-
ble stereo coverage (parallel strips with 60% side overlap, or
double coverage with crossed flight directions), stripwise drift
corrections are possible with only 4 ground control points.
There is a simpler overlap case, however, with which strip-
wise drift parameters can be solved for during the combined
adjustment. Tt is sufficient to run 2 cross-strips, across a stan-
dard block (20% side overlap) at either end, the cross-strips
replacing the 2 chains of vertical control points. In that case
the adjustment can be based on 4 XYZ ground control points
alone, although it is suggested to add one vertical control
point at each corner of the block. That cross-strip version
is highly recommended as the standard case for GPS aerial
triangulation. Cross-strips may not be needed, if there are no
serious signal interruptions. But drift errors can be corrected
with their help, in case necessary. In that sense cross-strips
are an operational precaution, in order to solve for singular-
ities in the combined blockadjustment, in case needed.
3 Combined blockadjustment
The introduction of GPS camera position data into aerial
triangulation constitutes a certain extension of conventional
block adjustment. It is assumed that the aerial triangula-
tion as such is done in the same way as usual, as far as tie-
points, point transfer, measurement of image- or of model-
coordinates, data reduction etc. are concerned. Only the
number of ground control points is considerably less, in gen-
eral.
The GPS camera station coordinates, as obtained from the
kinematic GPS processing and possibly transformed approx-
imately into the national coordinate system, are treated as
additional observations. They are introduced into the com-
bined blockadjustment appropriately weighted. Treating ad-
ditional observations is very well known in blockadjustment
and does not present particular problems. Especially the ma-
trix structure of normal equations is not altered at all.
It is only the unknown drift parameters which require some
attention. Linear drift parameters are treated as unknown
parameters in the combined adjustment. They will extend
the well known matrix structure of observation- and normal
equations, but the standard numerical solution techniques
can still be applied, for instance by reduction to banded-
bordered matrices.
With regard to unknown drift parameters there are 3 cases
to be distinguished which a GPS-blockadjustment program
should have as options: (1) no drift corrections at all, (2) one
set of linear drift correction parameters for the whole block,
(3) several independent sets of parameters for certain subdi-
visions of the GPS trajectory, up to independent corrections
per strip, as the case may demand. Case (1) and (2) can be
handled with the four standard XYZ ground control points,
provided there are no interruptions in the GPS trajectory.
Case (3) takes care of possible interruptions. But it has to
rely on the 2 additional chains of vertical control, or on 2
694
cross-strips, as described in section 2.3, in order to prevent
numerical singularities or near-singularities in the combined
adjustment.
Such computer programs for combined blockadjustment with
additional datum parameters have been developed and are
being applied, for both the bundle method and the indepen-
dent model method of adjustment.
4 Accuracy of adjusted GPS
blocks
4.1 Theoretical investigations
The accuracy features of adjusted GPS blocks are expected
to be highly favourable. The GPS camera stations act es-
sentially as if the camera air stations were ’ground’ control
points. It can be anticipated, therefore, that GPS blocks are
generally very well controlled, even if free drift parameters
will weaken the geometrical strength of a block somewhat. It
can also be anticipated that there is very little propagation
of errors in a block, and that the accuracy of blocks is little
dependent on block size. It is further intuitively evident that
conventional ground control points are not required any more
for stabilizing the accuracy of a block, but only for providing
the datum reference. The conventional accuracy function of
ground control points is taken over by the GPS camera sta-
tion positions. This has been confirmed by early computer
simulations.
That general picture sets the scene for a more detailed inves-
tigation into the accuracy properties of GPS blocks. A com-
prehensive investigation into the effects of various parame-
ters can only be done theoretically, in view of the multitude
of combinations. The theoretical accuracy of a great num-
ber of cases has been worked out, by data simulation and
inversion of the respective normal equation matrices. The
most urgent questions concern the overall accuracy features
of GPS blocks, and the effects of ground control and GPS
camera positioning accuracy on the blocks, in combination
with block size and the various cases of drift corrections. The
main results are here demonstrated and summarized.
Theoretical accuracy studies usually make idealized assump-
tions. Also here flat terrain is assumed, zero-tilts and ide-
ally regular photo-overlap, 9 tie-points per photograph in
the standard positions.
All image coordinates are assumed to be uncorrelated and
have equal accuracy, expressed in the variance factor 02. Sys-
tematic image errors are not considered, they are assumed
to be sufficiently corrected before or during the blockadjust-
ment. Ground control points as well as GPS camera station
coordinates are also treated as uncorrelated observations. All
cases refer to combined bundle-blockadjustment, with GPS
camera station coordinates as additional observations.
The actual investigations concern wide-angle photo-blocks of
photo-scale 1 : 30000, h — 4500 m, and extend to different
block size and different control cases, in relation to different
assumptions about drift corrections. The image coordinate
accuracy is generally assumed to be go = 10um in photo
scale, which corresponds to ó in terrain units. The direct
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