Differential GPS - Understanding GPS: Principles and Applications - page 415

Those ambiguity sets with the smallest variance (usually about 10 in number)
are then ranked in ascending order. Persistence is defined as a minimum of 10
epochs (seconds for the research upon which this discussion is based) and has been
determined experimentally. For a particular ambiguity set to be selected for the
fixed solution, one additional requirement must now be met. The ratio of the resid-
ual calculated for the ambiguity set with the smallest and next smallest variances
must exceed a minimum value. This value has also been determined experimentally
and set to 0.5.
Upon selection of an ambiguity set, the n values of the N vector multiplied by λ

become literally the amount of path length used to adjust the current
smoothed-code DD to create the exact (resolved) DD path length. To complete the
process, the smoothed-code DDs are recomputed using the ambiguity set(s) that
were generated during the search/selection process. The following relationship is
used:

DD = DD − N λ (8.38)

r s

The resolved smoothed-code double differences ( DD r ) are then used to calculate the
fixed baseline solution using (8.30) as modified here:

−1 T

b RQD
fixed

= (8.39)

u u r

The RMS of the difference between the floating and fixed baseline solution is
calculated for the current and subsequent epochs and monitored for consistency.
Should the difference begin to diverge, the fixed baseline solution is discarded and a
new search for integer ambiguities begins. Recall that the receivers, once acquisition
of a given SV is established, keep track of advances or retreats in the receiver-to-sat-
ellite path length. Hence, a valid integer-ambiguity set in one epoch remains equally
valid in the next and subsequent epochs. This being the case, the fixed baseline solu-
tion can be recalculated each epoch by adjusting the current set of smoothed-code
DDs with the resolved ambiguity set ( N ), followed by an updated least squares solu-
tion, or successive application of (8.38) and (8.39). Particularly noteworthy is that
during the entire carrier-cycle ambiguity resolution process, it is unnecessary to gen-
erate the least-squares solution. All calculations remain in the measurement (parity)
space using the least-squares residual vector obtained during the QR factorization.
It is only after the proper consistency among the measurements (DDs) emerges (i.e.,
the emergence of a final resolved integer-ambiguity set) that the fixed baseline solu-
tion is calculated. True, the floating baseline solution is calculated each epoch, but
this is more for monitoring than mathematical necessity. Remaining in the measure-
ment space minimizes computational overhead and speeds the process as a result.
Two separate phenomena work to accelerate the process, which nominally
takes three to four minutes before the carrier-cycle integer ambiguities are deter-
mined with sufficient confidence. First, the GPS constellation is dynamic. Its move-
ment in relationship to the ground and user receiver antennas provides an overall
change in geometry that has a very positive influence when interferometric
techniques are used.
Second, under most conditions, the user platform is also in motion. This move-
ment provides additional, though less significant, changes in geometry. Furthemore,