Global Positioning System Reference
In-Depth Information
TABLE 5.6 Comparison of Modulo-2 Addition and
+
1,
−
1 Multiplication
Modulo-2 Addition
Multiplication
Input 1
Input 2
Output
Input 1
Input 2
Output
0
0
0
+
1
+
1
+
1
0
1
1
+
1
−
1
−
1
1
0
1
−
1
+
1
−
1
1
1
0
−
1
−
1
+
1
It appears that in order to use
+
1,
−
1 multiplication to replace the modulo-2
addition the input should be converted as 0
⇒+
1and1
⇒−
1. This operation
can extend to more than two inputs. This designation contradicts the conven-
tional approach from 0
⇒−
1and1
⇒+
1. The following steps can be taken to
check parity:
1. Arbitrarily represent the data
D
i
by 1 and 0 and change 1
⇒−
1and
1.
2. Change the signs of
D
i
(
i
0
⇒+
1 to 24) by multiplying them with
D
30
.These
=
new data are as
d
i
for
i
=
1 to 24.
=
1 to 24 are used to multiply each row of the
H
matrix element by element. The results are 6 rows and each row has 24
elements. Each element can be one of the three values
3. These values of
d
i
for
i
+
1, 0, and
−
1. The
nonzero terms, which are
+
1and
−
1, are multiplied together and the new
1. These new results are multiplied either
by
D
29
or
D
30
according to last six equations in Table 5.5.
4. The final results should equal to [
D
25
D
26
D
27
D
28
D
29
D
30
].
5. The last step is to convert
+
1,
−
1 back to 0 and 1 for further processing.
results should be either
+
1or
−
Subframe matching will be discussed in Section 9.4. A program with subframe
matching and parity check will be listed at the end of Chapter 9.
5.12 NAVIGATION DATA FROM SUBFRAME 1
(
3,7
)
The data contained in the first three subframes are shown in Figure 5.9. The
minimal parameters required to calculate the user position are contained in these
three subframes.
The data used for calculations of locations of the satellites and the user are
discussed below.
1.
Week number (61-70)
: These ten bits are discussed in Section 5.9. Thus
represents the MSB of the Z counts and indicates the number of weeks from
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