Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 108

TLM w ord

MSB LSB

Preamble Reserved Parity

10001011

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

Hand over wor d (HOW)

MSB LSB

Sub-
frame
ID

TOW-count message
(Truncated)

Parity

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

FIGURE 8.3. The first two words of each subframe. These words are referred to as the
telemetry (TLM) word and the hand over word (HOW).

Parity Check Besides 24 bits of data, every 30-bit word contains a 6-bit parity.
The parity is used to check for misinterpreted bits in the navigation data. The par-
ity is computed through the equations in Table 8.1. Here

⊕ denotes the modulo-2

or exclusive OR operation.
D 1 −

D 24 are the 24 data bits in a word, while D 25 −

D 30 are the 6 parity bits
in a word. The two bits denoted D 29 and D 30 are the last two parity bits from
the previous word. When the navigation data are received, a parity check must be
performed to test if the received data are interpreted correctly.

Time of Transmission When the parity check has been performed successfully,
the contents of the navigation data sequence can be decoded. The decoding is fol-
lowing the scheme from, ICD-GPS-200 (1991), which gives details of every word
similar to what is shown in Figure 8.3. The first important issue is to determine
the time when the current subframe was transmitted from the GPS satellite.

TABLE 8.1. Parity encoding equations

= d 1 ⊕ D 30

D 1

= d 2 ⊕ D 30

D 2

= d 3 ⊕ D 30

D 3

.
D 24 = d 24 ⊕ D 30
D 25 = D 29 ⊕ d 1 ⊕ d 2 ⊕ d 3 ⊕ d 5 ⊕ d 6 ⊕ d 10 ⊕ d 11 ⊕ d 12 ⊕ d 13 ⊕ d 14 ⊕ d 17 ⊕ d 18 ⊕ d 20 ⊕ d 23
D 26 =

.

D 30 ⊕

d 24
D 27 = D 29 ⊕ d 1 ⊕ d 3 ⊕ d 4 ⊕ d 5 ⊕ d 7 ⊕ d 8 ⊕ d 12 ⊕ d 13 ⊕ d 14 ⊕ d 15 ⊕ d 16 ⊕ d 19 ⊕ d 20 ⊕ d 22
D 28 = D 30 ⊕ d 2 ⊕ d 4 ⊕ d 5 ⊕ d 6 ⊕ d 8 ⊕ d 9 ⊕ d 13 ⊕ d 14 ⊕ d 15 ⊕ d 16 ⊕ d 17 ⊕ d 20 ⊕ d 21 ⊕ d 23
D 29 = D 30 ⊕ d 1 ⊕ d 3 ⊕ d 5 ⊕ d 6 ⊕ d 7 ⊕ d 9 ⊕ d 10 ⊕ d 14 ⊕ d 15 ⊕ d 16 ⊕ d 17 ⊕ d 18 ⊕ d 21 ⊕ d 22 ⊕ d 24
D 30 = D 29 ⊕ d 3 ⊕ d 5 ⊕ d 6 ⊕ d 8 ⊕ d 9 ⊕ d 10 ⊕ d 11 ⊕ d 13 ⊕ d 15 ⊕ d 19 ⊕ d 22 ⊕ d 23 ⊕ d 24

d 2 ⊕ d 3 ⊕ d 4 ⊕ d 6 ⊕ d 7 ⊕ d 11 ⊕ d 12 ⊕ d 13 ⊕ d 14 ⊕ d 15 ⊕ d 18 ⊕ d 19 ⊕ d 21 ⊕