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ycle count
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images
Fig. 2 Comparison between
photogrammetrically and GPS determined
projection center coordinates
has to be. Mostly, the variance of the carrier
phase observation is used in statistical tests to
determine wether a set of carrier phase
ambiguities is potentially correct or false.
Further, the computer processing requirements
are very large, because often more than several
hundredthousand possible ambiguity
combinations have to be tested in real-time.
Although, the ambiguity resolution on the fly
has proven its applicability in numerous tests it
is important to mention, that for the time being
the reliability of these algorithms can not be
guaranteed. Especially, if only single frequency
C/A-Code receivers are used and the baselines
between the moving and reference receivers are
large, the convergence to incorrect ambiguity
solutions are very likely. Nevertheless, if one is
able to find the correct ambiguities, GPS carrier
phase observations can provide sufficient
positioning accuracy for all real-time mapping
applications. Figure 2b shows the position
differences of the projection center coordinates
determined with GPS carrier phase observations
and conventional aerial triangulation.
3. REAL-TIME DETERMINATION OF
SENSOR ATTITUDE PARAMETERS
Apart from the determination of the projection
center coordinates of sensors, the reconstruction
of objects on the earth's surface from sensor
information, requires the measurement of the
attitude angles of the sensor with respect to a
known coordinate system. For the direct
measurement of real-time attitude parameters
only a few sensors are available (e.g. INS).
Recent developments of multi-antennae GPS
receivers have added a further potential method
for the real-time, kinematic attitude
determination of sensor systems. Attitude
determination with GPS is based on the
interferometric measurements of GPS carrier
phase data. The phase difference À ® which can
be observed between two antennas results from
the range difference between the satellite to the
antennas. As the distance between an antenna
and the satellite is rather large (> 20000 km)
compared to the short distance between the
antennas (« 20 m), the incoming phase signal
can be assumed to be parallel. Therefore, the
phase difference is just dependent on the
baselength B and the angular position y of the
satellite with respect to the baseline between the
antennas (see Eq. 3).
Ad x)
211*B
Y = arccos
(3)
The phase difference has to be measured with
the highest possible accuracy as small errors in
the phase difference may result, depending on
the baseline length, in large attitude errors
(1cm/10m = 0.1°). The baseline B between the
antennas can be measured prior to the mapping
mission in a calibration measurement with
conventional survey methods. It is clear that the
above equation only holds if the carrier phase
cycle ambiguity for the interferometric
measurement has been determined correctly.
However, here the resolution of the correct
ambiguities is simplified compared to
conventional positioning. In the attitude
computation algorithms, the known baseline
length between the antennas can be used as
187
