NavCom SF-3050 A Computationally Efficient Ambiguity Resolution - Manual (Page 4)

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information content to the deviation one will obtain in
attempting to step to any other narrow or wide-lane
ambiguity value. While the deviation is not always the
same, it is either the fractional complement or a multiple
of the same fraction. Thus to step to N
2
one obtains the
analogous equation:
)
17
9
4
17
9
3 (
17
9
3
2 1 2
φ φ − + =
w
N N (16)
Similarly, the equation to compute the ambiguity value
for the average of the carrier-phase on L
1
and L
2
(which
typically gives the most accurate position) is:
)
17
9
4
17
9
3 (
34
1
4
2 1
φ φ − + =
w A
N N (17)
Obviously there is no noise present in the value for N
w
in
any of the equations above. The noise in the computed
value of the integer ambiguity arises from the
amplification of the multipath corruption of the carrier-
phase measurements in the right-hand term of the above
equations. This noise rarely exceeds one-cycle. Thus, a
search for the narrow-lane ambiguity value which
minimizes the rss residuals, need only test for the two
integer values closest to the value computed in the above
equations.
SCORING THE INTEGER COMBINATIONS
The wide-lane integer combinations with rss residuals less
than a threshold, or if more than ten, the ten combinations
with the smallest rss residuals are subject to the narrow-
lane search and assigned a score. Like a golf score, the
lowest scores are considered the best scores. The score
assigned to each combination is a function of a number of
parameters. The factors considered in assigning a score
include the following: 1) the narrow lane residuals; 2) the
refraction corrected residuals; 3) the L
1
and L
2
position
separation (note that the matrix defined by the left hand
side of equation (9), which is needed to compute the S
matrix, can be used to compute the position updates or
position separation simply by multiplying by the
appropriately scaled search permutations); 4) the distance
from the code solution; 5) the number of the wide-lane
integers in the permutation which selected the larger
(greater than 0.5) fractions; and 6) the number of narrow-
lane integers in the permutation which selected the larger
fractions.
The above factors are used to assign a score to each
permutation which meets a number of criteria. Among the
criteria is that the score be less than a threshold value, and
that threshold value is itself a function of the separation
distance between the base station and the user. If no
permutation is selected as the correct permutation, the
scores are cumulated from epoch to epoch.
The best integer ambiguity permutation is assigned a
differential score. This differential score is the difference
between the second best permutation and the best. If there
is no second best permutation which is acceptable then
the differential score of the best permutation is the
difference between the score threshold and the best
permutation’s score. If the differential score is large
enough the best permutation is accepted as the correct
integer ambiguity set. However, if there are fewer than
seven satellites involved in the ambiguity search, the
entire process is repeated and several repeated selections
of the same integer ambiguity permutation is required for
final acceptance as the correct set of integers.
While the above process is a bit complicated, when seven
or more satellites are available, it often provides the
correct integer ambiguity set in a single epoch.
Identifying the wrong set of integers as the correct set
typically occurs only a few times out of 1000 attempts.
When at least seven satellites are available integer
ambiguity failure is extremely rare.
TEST RESULTS
The RTK ambiguity search process described above has
been incorporated into NavCom’s dual-frequency OEM
GPS receivers. However, in order to more easily evaluate
the ambiguity resolution process, an offline version was
also built. The offline capability allows one to perform
scoring runs in which the ambiguity search process is
repeated over and over. As soon as one set of integer
ambiguity values is declared correct, the search process is
reinitialized (which takes one epoch) and a new search is
performed.
Figures 1 and 2 show the results of processing 10 hours of
short baseline (approximately 10 meters) in a scoring run.
13,659 successful searches were conducted. 84% of the
searches were accomplished in a single epoch.
Figure 3 and 4 show the results of processing
approximately an hour and a half of data collected over a
5 kilometer baseline. 1,772 successful searches were
conducted of which 82% were accomplished in a single
epoch.
The navigation accuracy is shown in a bull’s eye plot in
Figure 5. The standard deviation in north, east and up
were 4, 5 and 11 millimeters respectively.