8 / 15
where
W
+
T
= 1
.
(9)
The average number of frames required for making the right decision
in the “Search” mode is
w
s
=
1
p
cs
(1
−
F
)
,
(10)
where a value
w
s
should be as small as possible.
Table 2 shows values
w
s
when
p
r
= 0
,
1
,
n
= 16
,
b
= 145
and at
different values
ε
s
.
Table 2
Values
w
s
in the “Search” mode for
p
r
= 0
.
1
p
r
n ε
s
b
p
cs
p
fs
F
T
W w
s
0.1 16 0 145 0.185 1.53
∙
10
−
5
0.002 0.988 0.011 5.408
0.1 16 1 145 0.514 0.0002 0.036 0.930 0.069 2.017
0.1 16 2 145 0.789 0.002 0.261 0.690 0.309 1.716
0.1 16 3 145 0.931 0.010 0.787 0.200 0.799 5.059
0.1 16 4 145 0.982 0.038 0.996 0.003 0.996 297.625
0.1 16 5 145 0.996 0.105
1 1.02
∙
10
−
7
1 9796884
0.1 16 6 145 0.999 0.227
1 1.11
∙
10
−
16
1 9.01
∙
10
15
From these data it follows that for
ε
s
= 0
the value
T
is maximum, but
w
s
is also of great importance. Therefore, it is required to select a set
ST
consisting of some values
T
close to the maximum value, in this case it is
ST
=
{
0
.
988; 0
.
930
}
when
ε
s
=
{
0
,
1
}
, and then to select the value
ε
s
for
which
w
s
is minimal. In the above example
ε
s
= 1
is selected, for which
T
= 0
.
930
and
w
s
= 2
.
017
.
The criterion for the selection of the parameter
ε
s
in the “Search”
mode is:
ε
s
= arg max
ε
s
{
T
(
ε
s
) = max (
T
)
, w
s
(
ε
s
) = min (
w
s
)
}
.
(11)
In Table 3. values
w
s
with
p
r
= 10
−
2
and
p
r
= 10
−
3
are given
additionally to illustrate the dependencies of the parameters.
The results of the experiments with telemetry data in the IRIG-106
format are shown in Table 4. The experiments were performed for
p
r
= 0
.
1
and for different probability values of bit missing
p
d
=
{
0
,
10
−
4
,
10
−
3
,
10
−
2
}
.
The synchronization code of the IRIG-106 standard with the 16-bit length
was used.
124 ISSN 0236-3933. HERALD of the BMSTU. Series Instrument Engineering. 2015. No. 2