- Data from a GPS12 was logged in 7 different days (Jul 3-11)
at the very same spot.
- There were 8 sessions (4 with 10 mins, 3 with 15 min, and 1
with 20 min) from which I generated the corresponding RINEX
- The observation conditions were not specially good. I was a bit
lower than the surrounding terrain, there were trees around
and a building nearby.
- NO external antenna was used.
- As reference station, I used the data published by the
Madrid Deep Space Tracking Station (MAD2 is the EUREF
nickname) in Robledo de Chavela, 35 Km away from my position.
- For the efemerides, I got a set of
in EF18 format.
- For the postprocessing software I used the fully functional 30-day trial
version of GeoGenius.
There are two postprocessing steps. In the first one, the 8 individual
static baselines were processed. The second step (adjustment) receives
those results and gives us a best fit to the data.
When processing an individual baseline GeoGenius gives us three solutions.
The first one is obtained using triple differences. It is quite noisy, but
is quick to compute and doesn't have to solve ambiguities, serving as an
starting point for more refined solutions.
Then a double difference solution is obtained, where the ambiguities are
solved as real numbers, instead of integers. That is called a float
double difference solution.
Finally, the software attemps to fix the integer ambiguities by basically
exploring those integers close to the float ambiguity. If the set of
integers that best explains the observations is significantly better
than the second option, the ambiguities are considered fixed.
In that case, that baseline is considered known to a few milimeters.
Only in five cases (out of eight) the software could resolve
the integer ambiguity.
The problem of a fixed solution is that if we choose the wrong set of
integer ambiguities, the position would be wrong by an amount of one
or several wavelengths (20 cm).
These were the adjusted baselines using each kind of solution:
Baseline || Solution || DX(mt) || DY(mt) || DZ(mt) ||
SigmaDX(mm) || SigmaDY(mm) || SigmaDZ(mm) |
|MAD2-f1 || Triple || 4065.3656 ||34834.0132|| -1984.1105|| 139.5|| 153.1|| 98.8
|MAD2-f1|| Double Float|| 4065.2902|| 34834.3575||-1984.2004||124.3||149.0||81.4
|MAD2-f1|| Double Fixed|| 4064.9740|| 34834.3459|| -1984.1345|| 469.4|| 167.0|| 384.6
You can see the complete results of the triple, double float, and double
fixed solution in these adjustment reports generated by GeoGenius.
- The error given for the adjusted baseline corresponds
to an standard deviation (or a confidence level of about 60%).
Doubling that number will take us to a 95% confidence level.
- The adjusted baseline is very close for all three solutions.
The maximum discrepancy is about 30-35 cm. in any axis.
- The variance in the individual baselines is maximum in the
triple solution and minimum for the fixed double solution as
- Most important: while the error of the individual fixed
solutions is much lower than that of the float ones,
the final adjustment reports a lower variance for the floating
solutions. The most obvious reason would be that the fixed solutions
are probably wrong (probably due to the half-cycle ambiguity of these
receptors). Indeed, the ratio between the chosen candidate and
the second bet is usually rather low (between 2 and 5) indicating
that the fixed solution is not to be trusted.
- Do not try to obtain fixed solutions (this is just as well, because
the free GeoGenius package doesn't perform ambiguity resolution).
- With the stated conditions:
it seems that the computed position in a SINGLE session is within a
meter of the real position.
- Not so good location.
- No planning of observations.
- 10-15 minute session.
- NO external antenna.
- Reference station 30-40 Km away.
- By averaging/adjusting several sessions we can get down to an error
of about 10-20 cm in XYZ.
- A couple persons have also reported than with an external antenna and
a better location they are getting typical errors in the order of 20cm
(against a surveyed monument). This is good since it tells us
that the computed errors can be interpreted as errors from the real
position, not only as errors from a mean (possibly wrong) position.
- It seems that 10-20 cm is the best we can get without solving the
ambiguity. The trouble is, no standard software will work for this,
as they try to find INTEGER ambiguities and in our case it seems
that we can also get HALF-INTEGER ambiguities. Even if we wrote
special soft for the task, we'll face a much larger search space
(by a factor of 2 raised to the number of sats) and lower levels
of confidence (as the possible candidates will be half as close).
In this setup we simulate a small network. Two GPS12 (in the same
conditions as above) were placed 15 mt. apart. Data was logged
simultaneously in two sessions (Jul 10-11). The other point of the
network was the reference station MAD2. Now we had 3 simultaneous
baselines: MAD2 to f1, MAD2 to f2, and f1 to f2.
After the previous experience we only considered floating solutions
to the double difference equations. Here are the final adjusted
Baseline || DX(mt) || DY(mt) || DZ(mt) ||
SigmaDX(mm) || SigmaDY(mm) || SigmaDZ(mm) |
|MAD2-f1 || 4065.3498 || 34834.9477 ||-1983.8023 ||293.2|| 564.8|| 268.0 |
|MAD2-f2 || 4075.7219 ||34843.0945 ||-1995.4062 ||292.8 || 564.1 ||267.6 |
|f1-f2 || -10.3722 || -8.1468 || 11.6039 || 45.7 || 81.6 || 38.0
Again, the sigmas in the previous table correspond to a standard
deviation (60% confidence level). The larger errors for the long
baselines are the result of only having two sessions (instead of eight as
before). You can have a look at the complete
adjustment report generated by
Ultima Modificación: Mon Apr 8 12:18:34 CEST 2002