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Bernese GPS Software Version 5.0 - Bernese GNSS Software

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9. Combination of Solutions<br />

Step 1:<br />

Step 2:<br />

daily NEQs<br />

CRD<br />

TRP<br />

loop over daily NEQs<br />

CRD<br />

TRP<br />

TRP before<br />

stacking<br />

ADDNEQ2<br />

fix on CRD<br />

weekly<br />

CRD<br />

weekly solution<br />

Stacking CRD Archive<br />

daily solution<br />

Figure 9.13: Back-substitution of weekly coordinates.<br />

However, depending on the size of the network, the number of parameters in the combined<br />

weekly solution may become very large, and memory consumption as well as processing<br />

time may become extensive. A two step pre-elimination and back-substitution procedure<br />

involving several ADDNEQ2 runs may help to solve the situation (see Figure 9.13).<br />

In a first step seven large normal equation files are combined using ADDNEQ2.<br />

Troposphere parameters are pre-eliminated either before stacking or with option<br />

EXCEPT FOR BOUNDARIES and a weekly coordinate file is written. Since troposphere parameters,<br />

although pre-eliminated, are still implicitly contained in the solution the coordinates<br />

obtained are identical to those that would have been computed if troposphere parameters<br />

were not pre-eliminated.<br />

Now, in the second step, ADDNEQ2 is executed again, but this time independently for each<br />

large daily normal equation file. This time troposphere parameters are not pre-eliminated<br />

but estimated and written to file. Coordinates are, however, fixed on the weekly coordinates<br />

estimated in step 1. Except for the missing stacking of troposphere parameters at the<br />

midnight epoch (in case troposphere was not pre-eliminated at the borders in step 1) the<br />

troposphere delay estimates are equal to those that were obtained in a combination of the<br />

large normal equations without pre-elimination.<br />

The main difference resides in the estimated formal accuracies for the troposphere parameters<br />

since the described back-substitution step does not incorporate covariance information<br />

concerning the estimated weekly coordinates.<br />

Note that a similar back-substitution scheme may also be applied for computing epoch<br />

parameters such as kinematic station coordinates or clock parameters. In this case you<br />

may introduce coordinates (of static stations) and troposphere parameters computed with<br />

ADDNEQ2 as fixed into <strong>GPS</strong>EST and recompute the epoch parameters that were preeliminated<br />

in the first <strong>GPS</strong>EST run before saving of the normal equations.<br />

Page 210 AIUB<br />

TRP

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