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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
23 Fast Ambiguity Convergence and Resolution
In precise point positioning, carrier phase ambiguities can be
treated as float terms. However, the float ambiguity solutions
may require long convergence times before centimetre-level
accuracy can be obtained, ranging from several tens of minutes
to several hours. Since convergence is a crucial issue for real-
time applications, long convergence times may prevent the PPP
approach from fulfilling the necessary accuracy requirements.
As such, fast ambiguity convergence methods and algorithms
should be developed.
Integer ambiguities must be treated as integers and
subsequently must be resolved in order to fully realize the
accuracy of carrier phase observations. Real-time centimetre
level accuracy will be supported if integer values of the carrier
phase ambiguities can be determined On-The-Fly (OTF) over
short time intervals. The ionospheric-free observation
combination models presented in Section 2.1 allow for the
exploitation of the integer property and new ambiguity
resolution methods are required with un-differenced GPS
observations.
3. UNIVERSITY OF CALGARY'S P? SOFTWARE
A software package called P^ has been developed at the
University of Calgary to support precise point positioning using
un-differenced GPS code and carrier phase observations. The
software can be used to assess the performance of different data
processing models as well as the influence of different error
sources on positioning results.
Processing in P? can be done in post mission or in real-time,
and the program can be run in either static or kinematic mode.
Two point positioning modes are available: Single Point
Positioning (SPP), which only makes use of code
measurements, and Precise Point Positioning (PPP), which
makes use of code and phase measurements along with precise
satellite orbit and clock corrections. P^ also supports forward
and backward data processing.
The software lists various values for each processed epoch and
displays a sky plot and a residual plot during processing. After
processing is completed, a variety of graphs may be displayed,
including the trajectory and velocity, the estimation of the
receiver clock offset and zenith tropospheric delay, and the
number of satellites and DOP values. A sample screenshot of
the software during processing is shown in Figure 1.
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Figure 1: P? Software Sample Screenshot
847
4. RESULTS AND ANALYSIS
Two airborne kinematic data sets were post-processed using the
3 : ^ 3
P^ software. A 10? elevation angle cut-off was used for all P
processing results.
4.1 Aircraft — Low Dynamics (~300 km/h)
The first data set was flown on August 23, 2003, with a flight
duration of approximately 4.75 h. Maximum aircraft speed did
not exceed 310 km/h. Precise orbit and clock data was provided
from JPL, at resolutions of 15 minutes and | second,
respectively. The positioning results obtained using P? software
were then compared to JPL's GIPSY/OASIS II solution, since it
is the only software package that we found in the market that
performs un-differenced carrier phase processing with a single
receiver.
The number of satellites and PDOP, the altitude of the aircraft,
and an estimation of the zenith tropospheric delay for the
forward and backward pass is shown in Figures 2, 3 and 4,
respectively. Finally, the position errors from backward
processing (with respect to the GIPSY OASIS II solution) are
shown in Figure 5. The position error statistics are listed in
Table 1.
The estimation of the zenith tropospheric delay is relatively
stable, as shown in Figure 4. This is because of the relatively
constant flying altitude, shown in Figure 3. Figure 5 and the
statistics in Table 1 show good agreement between the two PPP
solutions, despite the remaining sinusoidal effect that still
remains in the height component.
NumSVs & PDOP
11:23 11:56 12:30 13.03 13:36 14:10
Locai Time (hh:mm)
1443 1516
pads do
| — NumSVs | i
{= Poor +
9
Number of SVs / PDOP
Uu o
>
A À pens d te
401000 403000 405000 407000 409000 411000 413000 415000
GPS Time (s)
Figure 2: Number of Satellites and PDOP
Height Local Time (hh:mm)
s 6 1230 1303 1336 1410 1443 — 1516
ioo. 1123 11:5 ;
Height (m)
e eate Lesern - ade mecre dM Lo ”
"401000 403000 405000 407000 409000 411000 413000 415000
GPS Time (s)
Figure 3: Altitude
