International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
were available for comparing with the adjustment output.
Dual-frequency GPS observations at 2Hz were collected
along with the imagery. Additionally, a dual-frequency
base station in the centre of the block collected GPS ob-
servations at | Hz.
There were several problems with the data set that com-
plicated the generation and analysis of results. Foremost
among these was that only orthometric heights were avail-
able for the check points. Because an accurate geoid model
for the test region was unavailable, these heights could
not be converted into ellipsoidal heights compatible with
the GPS heights determined in the adjustment. In an ad-
mittedly imperfect solution, the vertical datum shift was
solved for in an adjustment that treated all the check points
as control points and used exposure station position ob-
servations generated from the best possible dual-frequency
carrier-phase GPS solution (to solve for the datum shift it
is necessary to constrain both datums). In addition to the
large vertical datum shift, it was felt that there may also
have been small horizontal datum shifts. These were not
solved for, and, if present, contribute to the mean errors
seen in the results presented below. An additional problem
with the data set was that the lens distortion available for
the camera was not in a format compatible with the adjust-
ment software used. Consequently, the lens distortion was
calibrated for using the same adjustment that solved for the
vertical datum shift. This may mean that the standard devi-
ations in the results are somewhat optimistic as the camera
may ‘fit’ the data better than it should.
Before looking at the results available when the GPS mea-
surements are included in the adjustment, it is worthwhile
to get some idea of the noise within the network. Table 1
shows the results from a conventionally controlled adjust-
ment where approximately one-third of the check points
were used as control points. The remaining check points
were used to calculate the statistics in the table. These re-
sults should be an indication of the best possible accuracy
available from the network.
Table 1: Check Point Error Statistics (m): Control Points
Horizontal Vertical
Mean 0.18 -0.19
Std. dev. 0.09 0.45
RMSE 0.20 0.49
Absolute maximum
(mean removed) 0.27 1.00
The comparison of results will primarily be done using the
standard deviations of the check point errors. This in ac-
knowledgement of the fact that a mean error — primarily
due to unmodelled tropospheric delays — will almost cer-
tainly be present in the networks determined using the un-
differenced GPS pseudoranges. It may be tempting to be-
lieve that the GPS errors would 'average out' over the entire
block. Unfortunately, because of the relatively short time-
span in which the imagery was captured, the errors at the
individual GPS stations will be highly correlated (during
this time period, the troposphere and satellite positions do
936
not change significantly). The common errors among GPs
stations will cause the entire network to translate.
Finally, it should be emphasised that in the tests that fol.
low, no ground control points are used. The networks are
controlled entirely by the GPS measurements.
4.1 Broadcast Orbits and Clocks
The first tests were performed using the broadcast satellite
orbits. Table 2 contains the results for when the pseudo-
ranges are included directly in the adjustment. Notably,
the standard deviations of the check point errors are only
slightly worse that those in Table I. In other words, di-
rectly including the GPS pseudoranges in the adjustment
yields object space accuracies that are comparable to those
obtained from the same network controlled via well-distri-
buted ground control points. This is a promising first re-
sult; however, it must be restated that the efforts made to
overcome difficulties with the data may mean that this re-
sult is somewhat optimistic.
Table 2: Check Point Error Statistics (m): Pseudorange
observations, Broadcast Orbits
Horizontal Vertical
Mean 0.98 3.06
Std. dev. 0.21 0.47
RMSE 1.00 3.09
Absolute maximum
(mean removed) 0.46 1.25
Of course, rather than being directly integrated into the
bundle adjustment, the pseudorange measurements can also
be used to generate single-point exposure station positions.
These positions could then be added to the adjustment as
position observations in the typical fashion (see 2.1). Ta-
ble 3 shows the results for when the network is controlled
using such positions. By comparing the results in this table
with those in Table 2, it can be seen that directly including
the pseudoranges in the adjustment yields object space ac-
curacies that are about 30% better than when single-point
position observations are used. Both approaches use ex-
actly the same data, but the closer integration that comes
from directly including the pseudoranges in the adjustment
leads to a significant improvement in accuracy.
Table 3: Check Point Error Statistics (m): Single-point position
observations, Broadcast Orbits
Horizontal Vertical
Mean 1.09 3.07
Std. dev. 0.35 0.69
RMSE {15 3.14
Absolute maximum
(mean removed) 0.63 1.61
In spite of the favourable standard deviations, it should be
noted that, as predicted, large mean errors exist in both
tests shown above. In these tests, the mean error also re-
flects the residual satellite clock error (and, to a lesser ex-
tent, satellite position error) in addition to the unmodelled
tropospheric delay spoke of above.
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