More extensive results of postprocessing G12 raw data

FIRST SETUP

Conditions:

• 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 files.
• 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 Precise Ephemeris in EF18 format.
• For the postprocessing software I used the fully functional 30-day trial version of GeoGenius.

Results:

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.

• Triple difference
• Double difference Float
• Double difference Fixed

Some remarks:

• 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 expected.
• 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.

Conclusions

• 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:
  • Not so good location.
  • No planning of observations.
  • 10-15 minute session.
  • NO external antenna.
  • Reference station 30-40 Km away.
  it seems that the computed position in a SINGLE session is within a meter of the real position.
• 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).

SECOND SETUP:

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 results:

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 GeoGenius.