It is pointed out, finally, that the case of blocks with cross-
strips, which is here generally favoured, behaves best if com-
pared with the other cases which allow free parameters. It
is closest to the ideal case in which GPS camera positioning
gives direct absolute positioning, with respect to the national
reference system.
4.4 Influence of GPS camera station ac-
curacy and of datum transformations
The previous investigations have shown that it is sufficient
to concentrate on medium block size (6 x 21). They have also
shown that the variation of ground control accuracy has no
very significant influence on the blockadjustment results, at
least not within realistic conditions. We assume, therefore,
in the following investigations for the ground control coordi-
nates standard errors of 0gcp = 30 cm. That corresponds, for
the photo scale 1 : 30000, to the photogrammetric measur-
ing accuracy, projected into ground units (cp = Go). That
assumption is not particularly restrictive. Such control point
accuracy is the least which must be asked in standard pho-
togrammetric practice for aerial triangulation (unless larger
errors are tolerable for secondary reasons). It is further as-
sumed that the measuring precision of ground control point
image coordinates in the photographs is the same as for im-
age tie-points (cep: — 00).
On that basis of standardized assumptions we can now in-
vestigate the influence of GPS camera station positioning ac-
curacy on the results of combined blockadjustment, in com-
bination with the main cases of ground control and drift cor-
rections. It is the central part of the theoretical investigation
into the accuracy of GPS supported aerial triangulation.
We distinguish in particular the 3 cases of ground control, as
defined in fig. 1 (c : 4 XYZ control points; a : as c, + 2 chains
of vertical control; b : as c, + 4 vertical control points + 2
cross-strips). They are combined with 3 according cases of
drift corrections, namely (1) with no correction at all (case
c ), (2) with drift correction per block (case c), and (3), (4)
with drift corrections per strip (case a, b). From a practical
point of view the case b (block with 2 cross-strips) is the
most interesting one.
For a number of blocks the resulting theoretical accuracy has
been computed (by inversion of the normal equation matri-
ces). The results are summarized in fig. 6 and fig. 7 which
show the horizontal and vertical r.m.s. values px,y and uz
of the horizontal and vertical standard coordinate errors, of
all adjusted tie-points.
A discussion and interpretation of the results may distin-
guish between the cases of precise and less precise GPS cam-
era positioning. Let us look first at the lower left parts of the
functions in fig. 6 and 7, as specified by oçps < 30 cm resp.
Japs < 00. That parts of the curves show that, starting from
Jgps = 0, the GPS errors are quadratically added, in some
cases at a reduced rate. The main result is, however, that
the different cases of control and drift corrections determine
the results.
The ideal case is represented by the curves (1). They refer
to the case that no drift corrections are applied at all. The
results are determined by the internal block accuracy, based
on 209, and by the absolute GPS positioning. Case c includes
4 ground control points, but their effect is negligible, as here
no free drift or datum parameters are applied. The curves (1)
refer to consistent absolute GPS positioning, as long as there
are no datum of drift effects at all. In that case there is very
little propagation of errors in the block, and the resulting
r.m.s. accuracy of < 1.069 and < 1.66, for horizontal and
vertical coordinates, respectively, is practically determined
by the mere intersection errors of rays and the minor effects
of the tilt errors of the blockadjustment.
As soon as one set of free datum or drift parameters is ap-
plied (curves (2), case c) the errors of the 4 control points
are added to the basic block accuracy of the previous case.
There is practically no adjustment effect, with 4 control
points only. The block is transformed onto the ground control
points practically as a unit. Their errors are almost indepen-
dently superimposed. That basic situation remains valid in
all cases, in which the datum transformations are determined
via ground control points.
If independent drift parameters are applied per strip, the ge-
ometry of the block is weakened further, as is evident from
the curves (3) which refer to the case a of additional vertical
control points. The blocks with 2 cross-strips, which are back
to minimum control (except for 4 additional vertical control
points), are subject to the same principle, that additional
parameters weaken the geometry. Fortunately, however, the
cross-strips counteract effectively to the extent that amongst
all cases which apply free datum or drift corrections, blocks
with 2 cross-strips give best results, even if drift corrections
are applied per strip. This strengthens the previous recom-
mendation for cross-strips also from the accuracy point of
view.
The results, as far as they refer to precise GPS camera po-
sitioning (GGps X 9o) can be condensed in very simple rules
which can serve for the planning of GPS aerial triangula-
tions. They are summarized in table 1, together with 2 more
cases from an earlier investigation. In case GPS camera posi-
tioning is precise to ocps < 0.300, as can easily be reached in
combination with medium scale photography, the values of
table 1 can be reduced by about 10%. The derived relations
suggest that GPS camera positioning is effectively applica-
ble also for large scale aerial triangulation and for large scale
mapping.
If we now look at the main parts of the relationships in fig. 6
and 7 it can be seen how the accuracy of GPS blocks reacts to
poorer accuracy of GPS camera positioning, i.e. to larger val-
ues of ogps. All relations increase monotonously with Ogps
at roughly similar rates, except for the curves (2) and (4) in
fig. 7, which react more sensitive to GPS positioning errors.
The overall remarkable feature is, however, that the r.m.s.
errors of blocks increase at considerable slower rates than
the GPS positioning errors. If the GPS camera position ac-
curacy is as poor as ggps = 3 m, for instance, which is for 1
: 30000 photo scale equivalent to gps = 10 99, the accuracy
of the adjusted blocks is still about 1 m (3.5 Gy) or better
horizontally and about 1.5 m (5 a9) or better vertically. The
explanation is given by the well known averaging effect if
a block has many control points. It can be concluded that
rather large GPS camera positioning errors can be tolerated
if the required block accuracy needs to be, for instance, only
2.5 Gy in x, y or 3 0$ or 0,295, h in z.
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