Global Positioning System Reference
In-Depth Information
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
-1
0
1
z
4
z
3
-1
0
z
2
0
-1
0
1
Figure 7.20 Candidate ambiguities encountered
during the search procedure with decorrelation.
-2
-1
z
1
0
1 2
[28
z
1
={−
2
,
−
1
,
0
,
1
,
2
}
at the first level. The last possibility, using
z
=
(
1
,
0
,
0
)
,
gives no solution. We conclude that five ambiguity sets
z
i
(z
1
,
0
,
0
,
0
)
satisfy the
condition (7.187). In general, several branches can reach the first level. Because
s
n,n
is the largest value in
S
, the number of
z
n
candidates is correspondingly small, thus
lowering the number of branches that originate from level
n
and assuring that not
many branches reach level 1.
The change
=
Lin
—
0.4
——
No
PgE
v
T
Pv
i
can be computed efficiently from (7.187) because all
w
i
sets
become available as part of computing the candidate ambiguity sets. The matrix
S
does not change. The qualifying candidates
z
i
are converted back to
b
i
using the
inverse of (7.181).
If the constant
∆
2
for ambiguity search is chosen improperly, it is possible that the
search procedure may not find any candidate vector or that too many candidate vectors
are obtained. The latter results in time-consuming searches. This dilemma can be
avoided if the constant is set close to the
χ
[28
v
T
Pv
value of the best candidate ambiguity
vector. To do so, the real-valued ambiguities of the float solution are rounded to the
nearest integer, and then substituted into (7.184). The constant is then taken to be
equal to
∆
v
T
Pv
. This approach guarantees obtaining at least one candidate vector,
which consequently is probably the best candidate vector because the decorrelated
ambiguities have such a high precision. One can compute a new constant
∆
2
by adding
or subtracting an increment to one of the nearest integer entries. Using this procedure
results in only a few candidate integer ambiguity vectors and guarantees that at least
two vectors are obtained.
LAMBDA is a general procedure that requires only the covariance submatrix and
the float estimates of the ambiguities. Therefore, the LAMBDA procedure applies
even if other parameters are estimated at the same time, such as station coordi-
nates, tropospheric parameters, and clock errors. LAMBDA readily applies to dual-
frequency observations, or even future situations, when observations from more than
two frequencies become available. Since only the covariance submatrix matters, the
observations can come from any available satellite system such as GPS, GLONASS,
or even Galileo. Even more generally, LAMBDA applies to any least-squares integer
estimation, regardless of what the physical meaning of the integer parameters is.
χ
