OPERATIONAL RULES AND ACCURACY MODELS FOR
GPS-AEROTRIANGULATION
F. Ackermann
Institute of Photogrammetry
University of Stuttgart
Keplerstr. 11, D-7000 Stuttgart 1
Tel. 49-711-121-3386, Fax 49-711-1213297
Commission III invited paper
Abstract
Airborne kinematic camera positioning by GPS has reached
a mature state of development. The paper reviews some re-
maining practical problems, like signal discontinuities, cycle
slips, drift errors, datum transformation and derives recom-
mendations which make GPS application to aerial triangula-
tion operationally secure. In the second part the theoretical
accuracy of GPS blocks is analyzed for various cases of over-
lap and control, resulting in simple accuracy models which
can be used for planning GPS supported aerial triangulation.
1 Present status of kinematic
camera positioning
1.1
Airborne kinematic camera positioning, for aerial triangula-
tion purposes, by differential GPS carrier wave phase obser-
vations has recently been thoroughly studied and also exper-
imentally tested. The modern GPS receivers and appropriate
software have been developed to a point that successful prac-
tical application is imminent. In fact, it has started already,
and GPS-supported blockadjustment is expected to become
the standard case of aerial triangulation soon.
State of development
1.2 Accuracy performance
In this paper we refer only to high precision relative kine-
matic camera positioning for aerial triangulation by differ-
ential carrier wave phase observations. Relative positioning
eliminates almost all systematic positioning errors directly
and also reduces greatly the effects of signal degradation by
‘selective availability’ (SA). For operational reasons there are
always and only two GPS receivers involved, one stationary
on a known point in or near the photo-mission area, the other
in the aircraft. Both receivers record simultaneously carrier
wave (L1 and preferably also L2) phase measurements to at
least 4 identical GPS satellites, as well as C/A-code (or P-
691
code) pseudo ranges, at measuring rates of < 1 sec.
The internal r.m.s. precision of ranging by phase observa-
tions has been established empirically to be in the order of
1 mm - 2 mm. This gives a positioning precision in the sta-
tionary mode of 1 cm - 2 cm, depending on the satellite
constellation (PDOP < 10, preferably < 6).Controlled test
flights have shown that relative kinematic camera positioning
in-flight comes rather close to that accuracy. R.m.s. coordi-
nate accuracies of < 5 cm (< 3 cm) have been empirically
confirmed, except for some systematic errors wich will be
discussed below. Thus, kinematic GPS camera positioning is
of greatest interest to aerial triangulation practically for all
conventional photo scales. The computation of the sequence
of GPS antenna positions, which represent the flight trajec-
tory, is a standard, straight forward adjustment procedure
which does not present particular problems.
There are, however, some practical problems which have to
be given attention in order to receive high precision camera
postions by GPS. They are reviewed next.
2 Some practical problems
2.1 Time off-set and spatial off-set
The kinematic GPS positioning gives directly the positions
of the GPS antenna on the aircraft, the time sequence being
given by the GPS measuring rate. The positions have to be
interpolated onto the times of camera exposure and reduced
for the spatial off-set between GPS antenna and the perspec-
tive centre of the camera (outer node of the lens).
The time interpolation is usually based on a signal from the
camera with which the mid-time of exposure is recorded on
the GPS time scale. All modern cameras are equipped for
emitting such a pulse. Old cameras can be equipped with a
light-detector serving the same purpose. The time accuracy
of the pulse must be about 1 msec as it corresponds to a for-
ward movement of the aircraft of 6 cm at a ground speed of
