Global Positioning System Reference
In-Depth Information
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be to abandon the current trial position, i.e., to stop accumulating the ambiguity
function and to begin with the next trial position. This would occur as soon as one
term is below the cutoff criteria, e.g.,
cos
2
π
ϕ
pq
km,L,b
(t)
i
<ε
ϕ
pq
km,L,a
(t)
−
(7.109)
The choice of the cutoff criteria
ε
is critical, not only for accelerating solutions, but
also for assuring that the correct solution is not missed. This early exit strategy is
unforgiving in the sense that once the correct (trial) position is rejected, the scanning
of the remaining trial positions cannot yield the correct solution. The proper choice
for
ε
is largely experimental.
A matter of concern is that the grid of trial positions is close enough to assure that
the true solution is not missed. Of course, a very narrow spacing of the trial positions
increases the computational load, despite the early exit strategy. The optimal spacing
is somewhat related to the wavelength and to the number of satellites. On the other
hand, the ambiguity function technique can be modified in several ways in order to
increase its speed, such as using the double-difference widelanes. In this case, the
trial positions can initially be widely spaced to reflect the wide-lane wavelength of
86 cm. These solutions could serve to identify a smaller physical search space, which
can then be scanned using narrowly spaced trial positions.
The ambiguity function technique offers no opportunity to take the correlation
between the double-difference observables into account. There is no direct accuracy
measure for the final position that maximizes the ambiguity function, such as standard
deviations of the coordinates. The quality of the solution is related to the spacing of
the trial positions. If the trial positions, e.g., havea1cmspacing and a maximum
of the ambiguity function is uniquely identified, then one could speak of centimeter
accurate positioning. In order to arrive at a conventional accuracy measure, one can
take the position that maximizes the ambiguity function and carry out a regular
double-difference least-squares solution. Because the initial positions for this least-
squares solution are already very accurate, a single iteration is sufficient and it should
be possible to fix the integer. The fixed solution would give the desired statistical
information.
The ambiguity function values of all trial positions are ordered by size and normal-
ized (dividing by the number of observations). Often, peaks of lesser value surround
the highest peak and it might be impossible to identify the maximum reliably. This
situation typically happens when the observational strength is lacking. The solution
can be improved by observing longer, selecting a better satellite configuration, using
dual-frequency observations, etc.
The strength of the ambiguity function approach lies in the fact that the correct
solution is obtained even if the data contain cycle slips. Remondi (1984) discusses the
application of the ambiguity function technique to single differences. The geodetic
use of the ambiguity function technique seems to be traceable to very long baseline
interferometry (VLBI) observation processing. Counselman and Gourevitch (1981)
present a very general ambiguity function technique and discuss in detail the patterns
to be expected for various trial solutions.
[26
Lin
—
0.0
——
No
PgE
[26
