200 km/h. The interpolation of the GPS position is usually
linear between the 2 neighbour positions. In 1 sec the aircraft
moves about 55 m, at 200 km/h. Hence the GPS measuring
rate should preferably be shorter than 1 sec, in order to keep
the deviation between the actual flight path and the linearly
interpolated positions small (< 10 cm). Also a more sophis-
ticated interpolation procedure is recommended.
There is a second approach by which the time interpolation
can be avoided. If the signal for camera exposure is given by
the GPS system, it can be arranged that the camera expo-
sure coincides nearly with a GPS observation. In that case
an interpolation is not required at all or it can be kept simple
and safe if it has to bridge only 0.1 sec or less.
The second kind of correction reduces the (interpolated) GPS
antenna position onto the perspective centre of the camera.
For that purpose the off-set coordinate components must be
known. They can be measured directly at the airplane, by
tacheometric ground survey, for instance. The off-set compo-
nents should refer to the axis system of the aircraft.
The computational reduction of the GPS antenna position to
the camera position is wanted with regard to the coordinate
system of the kinematic GPS positioning. For that purpose
the attitude parameters of the aircraft must be known. They
may be measured directly by INS. In connection with aerial
triangulation there is another solution, as the attitude pa-
rameters of the photographs can be derived from the first
iterations of the combined blockadjustment. In that case,
however, the zero-settings of the camera have to be consid-
ered, especially the crab setting, which is to be kept constant
during a flight strip and should be manually or automatically
recorded during the flight.
The off-set corrections do not require precise attitude data.
The reduction is particularly insensitive if the GPS antenna
is mounted more or less directly above the camera. In that
case the horizontal off-set component is small and may be
negligible altogether. The z-correction is then reduced to a
constant and the remaining x- and y-corrections amount to
only 3.5 cm per degree tilt, for a 2 m vertical off-set. Thus
tilt corrections can be neglected in most cases, except for the
high precision demands of large scale photography.
2.2 Ambiguity solution, signal interrup-
tion, drift errors
There is a second group of problems, related to the ambigu-
ity solution of phase observations and the risk of cycle slips
and signal interruptions.
Carrier wave phase observations measure only the phase shift
within one cycle. The total integer number of cycles, the sig-
nal has travelled through from the satellite to the receiver,
remains unknown. Those initial unknown phase ambiguities
are to be solved before the kinematic positioning can start.
In the case of relative positioning by one stationary receiver
on the ground and one receiver in the aircraft the problem
can be solved by stationary recordings of both receivers be-
fore take-off. There are two cases: Either start from a known
base-line (both receivers at known GPS points), or deter-
692
mine an initial base-line from the known stationary receiver
position to the unknown position of the also stationary air-
craft receiver. The simultaneous stationary recordings had
to continue, until recently, for about one hour, in order to
solve safely for all initial phase ambiguities. Recently fast
ambiguity solutions have been developed which reduce the
stationary recording time to a few minutes. Once the initial
phase ambiguities are solved the receivers stay locked on the
satellites! carrier waves during the flight, until an interrup-
tion would occur.
Unfortunately, there are several effects which can cause sig-
nal interruptions during the flight. They are known as cy-
cle slips, signal obstruction by body and wings of a turn-
ing aircraft, and changes of the number and constellation of
recorded satellites. There is no need to go into any details
here, as to the causes of such disturbancies. It suffice here
to state that signal disruptions do occur during the flight
missions and are not likely to be completely avoided.
As direct effect of a signal disruption the ambiguity solu-
tions are lost. In other words, the common system reference
is lost and the continuity of the trajectory is interrupted. Re-
cently, sophisticated software development has succeeded to
bridge such gaps or jumps by applying prediction and filter
techniques. In many cases the interruptions do not affect all
signals, some satellites continue to be recorded with the help
of which the lost signals can be reconnected. Software pro-
grams become available which are capable of bridging signal
interruptions and of reassessing and updating the phase am-
biguity solutions.
There are cases of quite serious signal interruptions which
may extend over 10 sec or more. In such cases it is possible
that the ambiguity solution can be restored only approx-
imately. It is well established that approximate ambiguity
solutions result in GPS drift errors which are, however, linear
in first approximation. This brings us to the general prob-
lem of GPS drift errors. Practically all experimental tests on
kinematic GPS positioning have shown some systematic GPS
drift errors, the typical magnitudes being in the order of 10
cm to 50 cm per hour. It is a matter of controversy amongst
experts what are the causes of systematic GPS drift errors
and whether they can be avoided completely.
From an operational point of view it has to be accepted as a
fact, for the time being, that signal discontinuities may oc-
cur during a flight mission, especially during flight turns. It
has equally to be accepted that there may be small GPS drift
errors, possibly as a result of incomplete phase ambiguity so-
lutions, or for other reasons. Considering on the other hand
that linear GPS drift errors can be assessed and corrected
subsequently, during combined blockadjustment, it can be
concluded that no particular efforts need to be made to avoid
drift errors. They can be just accepted and dealt with dur-
ing the blockadjustment. This is an operational considera-
tion which holds only in connection with aerial triangulation.
It has, however, convenient operational consequences. If we
cannot rule out signal interruptions during the flight with the
consequence of reassessment of phase ambiguities there is no
point in determining the initial phase ambiguities by sta-
tionary recordings before take-off. It can be recommended,
therefore, referring to GPS aerial triangulation flights, not to
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