Global Positioning System Reference
In-Depth Information
t
a/
2
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
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41
42
43
44
45
P
|
t
a/
2
=
w
0
|≤
n (
0
,
1
) dx
=
1
− α
(4.359)
−
t
a/
2
or
t
1
−
a/
2
∞
P
|
t
a/
2
=
w
0
|≥
n (
0
,
1
) dx
+
n(
0
,
1
)dx
= α
(4.360)
−∞
t
a/
2
% of the cases, the observations are rejected and remeasurement or inves-
tigations for error sources are performed, even though the observations are correct
(they do not contain a blunder). From Figure 4.10 it is seen that the probability
In 100
α
β
i
of
a type-II error, i.e., the probability of rejecting the alternative hypothesis (and accept-
ing the zero hypothesis) even though the alternative hypothesis is correct, depends on
the noncentrality factor
[15
∇
i
is not known, the noncentrality
factor is not known either.
As a practical matter one can proceed in the reverse: one
can assume an acceptable probability
δ
i
.
Because the blunder
β
0
for the error of the second kind and compute
the respective noncentrality parameter
Lin
—
1
——
No
PgE
δ
0
. This parameter in turn is used to compute
the lower limit for the blunder, which can still be detected. Figure 4.10 shows that
t
a/
2
P
|
t
a/
2
=
w
a
|≤
n(
δ
i
,
1
) dx
≥ β
0
(4.361)
−
t
a/
2
if
δ
i
≤ δ
0
(4.362)
[15
Figure 4.10
Defining the noncentrality.
