AMBIGUITY RESOLUTION AND WAVEFRONT GEOMETRY |
Imagine t
he carrier phase wavefronts from satellites 1 and 2, as illustrated
in
Figure 1 below in a 2-D representation. The grid has a mesh which is
wide (
19cm wavelength
on L1). (In
reality these wavefronts can be considered to be the result
of
between-receiver differencing of data to each of the satellites in
turn.)
Figure 1. Wavefront grid formed from two satellites.
The two sets of parallel lines (in 3-D they are
surfaces) can be combined
into lines of double-differenced ambiguities
(each line is the intersection
of two wavefronts, and represents a constant
double-differenced integer
ambiguity value), as illustrated in Figure 2
below.
Figure 2. Constant double-differenced "lines-of-ambiguities" involving two satellites.
In
the case of (m+1) satellites, the geometric lattice is formed by
the
intersection of m sets of "lines-of-ambiguities". In next
the
figure, pairs of candidate ambiguities n*12 and
n*23
are located at the intersection of the resulting lattice
formed from two
sets of "lines-of-ambiguities".
However, there is no redundant information to allow for the unambiguous selection of the correct pair of ambiguities (corresponding to one intersection point of the "lines-of-ambiguities"). The observations from a fourth satellite would permit another set of parallel "lines-of-ambiguities" to be overlain on Figure below. There may be one intersection that satisfies all geometric conditions, or more likely the case, several which are "close" intersections. As data is accumulated and the satellite geometry changes (due to the motion of the satellites), each set of "lines-of-ambiguities" (involving a pair of satellites) rotates by a different amount. Hence the total lattice pattern changes in a manner similar to interference fringe lines, and the one correct ambiguity set may become steadily more obvious (it is the only intersection point about which all the grids rotate).
Figure 3. Two sets of constant double-differenced "lines-of-ambiguities" involving three satellites.
Hence what is required is either:
a significant
change
in satellite-receiver geometry over an observation session
so that
the intersection point representing the correct resolved integer
ambiguity
values becomes obvious. This is generally the situation
for
conventional static GPS surveying with long observation
sessions.
good geometry
at a
single epoch, or over a very short time period (a matter
of
minutes), when there is close to orthogonal intersection of the
"lines-of-ambiguities"
and sufficient redundancy so that there is
only one candidate intersection
point within the grid. This is the
requirement for modern GPS
surveying
techniques.
Geometric issues in relation to ambiguity search procedures is discussed further in section 8.3.1.
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© Chris Rizos, SNAP-UNSW, 1999