GPS C/A Code Signal Structure - Fundamentals of Global Positioning System Receivers: A Software Approach - page 82

TOW is in the HOW in every subframe as discussed in the previous section. The
two LSBs are implied through multiplication of the truncated Z count.
The TOW count has a time unit of 1.5 sec and covers one week of time. Since
one week has 604,800 seconds, the TOW count is from 0 to 403,199 because
604,800/1 . 5 403 , 200. The epoch occurs at approximately midnight Saturday

night/Sunday morning, where midnight is defined as 0000 hours on the UTC
scale, which is nominally referenced to the Greenwich Meridian. Over the years,
the occurrence of the zero-state epoch differs by a few seconds from 0000 hours
on the UTC scale. The 17-bit truncated version of the TOW count covers a whole
week and the time unit is 6 sec (1 . 5sec

=

4), which equals one subframe time.
This truncated TOW is from 0 to 100,799, because 604,800/6 = 100 , 800.
The timeline is shown in Figure 5.8. In Figure 5.8 the Z count is at the end
and start of a week as shown in the upper part of the figure. The TOW count
consists of the 17 MSBs of the actual 19-bit TOW count at the start of the next
subframe as shown in the lower part of the figure. It is important to note that
since the TOW count shows the start of the next subframe its value is 1 rather
than 0 at the end and start of the week. Multiplying the truncated 17-bit TOW
count by 4 converts to the actual 19-bit TOW count as shown in Figure 5.8. This
operation changes the truncated TOW from 0 to 100,799 to from 0 to 403,199,
the full range of the Z count.
The 10 MSBs of the Z count is the week number (WN). It represents the
number of weeks from midnight on the night of January 5, 1980/morning of
January 6, 1980. The total range of WN is from 0 to 1023. At the expiration
of GPS week, the GPS week number will roll over to zero. Users must add
the previous 1,024 weeks into account when converting from GPS time to a
calendar date.

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5.11 PARITY CHECK ALGORITHM ( 3,7 )

In this section the operation of parity bits will be discussed. From Figure 5.9 (in
the following section) one can see that each word has 30 bits and 6 of these are
parity bits. These parity bits are used for parity check and to correct the polarity
of the navigation bits. If the parity check fails, the data should not be used. In
order to check parity, 8 parity bits are used. The additional two bits are the last
two bits (also the last two parity bits) from the previous word.
Let D i represent the data bits in a word received by a receiver where i =

= 25 , 26 ,... ,30representthe
parity bits. The parity encoding equations are listed in Table 5.5, where D 29 and
D 30 are the twentyninth and thirtieth data of the previous word, ⊕ is the modulo-
2 addition and its operation rule is listed in Table 5.2, D 25 through D 30 are the
parity data.
In using Table 5.5, the first 24 calculations must be carried out first. The pur-
pose is to generate a new set of data d i for i

1 , 2 , 3 ,... , 24 represent the source data and i

1 to 24. If D 30 = = 0, then from

the relation in Table 5.2 d i = D i (for i = 1 to 24), which means there is no