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site in flight 1 and flight 2 and not consistent between campus site
and the Highway 30 site in flight 2. This is due to the highway 30
site is about 25 kilometers from Base 2, and lack of good targeted
pass and control points.
As discussed earlier, in order to do strip adjustment using airborne
GPS without any ground control we need to determine the omega
orientation angle by airborne GPS. Previous tests have shown that:
Il
6, 7 à, * (a cos Ks * b sin Kc) Va + ¢ Og (4)
where — à, — omega by photogrammetry
©; = omega by GPS
Q, — a constant parameter
The. variable 4, was added as the camera's swing motion was
locked.
Table 6 shows the results of the least squares fit of the above
equation using the campus site flight 1 and flight 2 data. The
standard error of 0.0005 indicates that the accuracy of & is better
than or equal to 0.0005 radians and is acceptable for highway
application using 1500 feet or 500 meters in flying height photos.
Table 6 shows the transformation parameters for transferring à to
G, obtained from campus site data. They are not suitable for the
Highway 30 site.
In order to test the feasibility of using the transformation parameters
from the campus site to the Highway 30 site, a combined adjustment
of flights 1 and 2 was done using the "Calib" software. By trial and
error, a satisfactory solution was found by assigning different
weights to interior orientation elements (x,, y,, f) (see Table 7),
Airborne GPS coordinates (X,, Y,, Z.) and ground control. The
parameters from the campus site were used to obtain à, from @g in
the Highway 30 site strip. When these values were used in the
Highway 30 site strip adjustment, even without ground control, they
gave satisfactory pass point coordinates. This suggests a self
calibration for a site (eg. Highway 30) can be used to convert à, to
^
Q,.
Table 5 shows the error of (K, - K;) is about 0.0005 radians and
(6, - 65) is about 0.001 radians even though the distance between
the camera antenna and the forward antenna is only 1 meter. This
suggests that the relative error of GPS coordinates is better than 1
millimeter and that D; and K, can be used to rectify aerial photos
and also produce orthophoto. The error in ( K, - K;) is better than
(0, - $5) because the determination of K by photogrammetry is
more accurate than $,.
Because of the possibility of small errors in the initial data, steps
were taken to refine the ground control, the photogrammetric
coordinates, and the GPS data.
The refined data for the nine photos were then adjusted by "Calib".
The difference in camera coordinates for the campus site (photos 1-
7), see Table 8, clearly show that the airborne GPS coordinates are
better than 10 centimeters irrespective of the flight altitude and
flights. The error in the z direction of 0.7 meters for the Highway
30 site is probably due to integer ambiguity resolution by the PNAV
software because the Highway 30 site is more than 10 kilometers
from the reference station Base 2.
Table 5 shows that the difference in orientation angles between
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
GPS and photogrammetry are constant for flight 1 and flight 2 on
the campus site. However, the orientation angles from GPS for the
Highway 30 and campus site appear to be different. Again, this is
because the Highway 30 site is more than 10 kilometers away from
the reference station Base 2. This suggests the importance of
having the reference station within 10 kilometers of the site or of
knowing the elevation difference for two or more points in the y
direction perpendicular to the flight to determine the transformation
parameter when obtaining à, from Gg.
Table 9 shows that the standard error of the fit between @,, from
refined data and à is 0.00008 radians. The accuracy of 0.0001
radians in Q is sufficient for drawing 2 foot contours either from
1500 or 3000 feet flying height photos.
Table 10 shows the difference between Ad, ^ ó;- à, of flight 1
and Ad, = d- 0, of the flight 2. The table also shows the second
difference, AQ,, - AQ - AQ . The standard error of AW , is
0.00003 radians which agrees with the expected error of 0.00002
for a height difference of 0.2 millimeters at 10 meters apart.
CONCLUSION AND RECOMMENDATION
The airborne GPS is feasible. The coordinates of the camera
antenna can be determined with an accuracy better than + 10
centimeters or better provided the base reference station is within 10
kilometers of the photographic site. This is acceptable for mapping
at all scales.
The PNAV software resolves the integer ambiguity satisfactorily for
fast static computation provided the rover receiver is within 10
kilometers of the base station.
Camera, wings and foresight are suitable for antenna location.
However the tail is not. The motion of the left and wing antennas
are symmetrical and can be used for computing the angle of rotation.
The accuracy of the Z12 GPS receiver is 0.2 millimeters and the
noise due to multipath at the camera, foresight and wing locations
is negligible. The accuracy of the w obtained from left and right
wing antennas at a separation of 10 meters is better than 20.0001
radians. This is acceptable for 2 foot contours using 3000 feet or
lower flying heights.
For a block with more than one strip, no ground control is required.
The base station has to be within 10 kilometers of the block and
local geoid undulation must be applied to the elevations.
For a strip, self calibration is required for transferring og to Q).
This calibration is valid for projects within 10 kilometers. In order
to determine the true parameters which will give true ground values,
the self calibration has to be designed to eliminate linear dependency
between interior orientation elements and exterior orientation
elements, as well as within the interior orientation elements. This
can be accomplished by a self calibration using Airborne GPS with
a minimum quadruplet of photos (see Fig. 11); two in the direction
of flight, one perpendicular to the flight and another at low altitude
flying height. This self calibration can be done every 10 Km along
the strip. Since no additional targeting is required and only
observation in additional two photos for every 10 Km is required the
method is economically feasible.
Further research is required to obtain o, from wg with accuracy of
+0.00002 radians. GPS is capable of providing this accuracy.
FE a HR RY E
