GPS Software Receivers - Fundamentals of Global Positioning System Receivers: A Software Approach - page 192

The subframe-finding program matches three consecutive preambles. If all
three are correctly matched, this declares that the beginning of a subframe is
found. The search of three consecutive preambles is arbitrarily chosen. First the
preamble from 360 data points is searched. This data length is one subframe
plus two words, which should have at least one preamble match (there could
be more than one). If multiple matches are found only one of them will be the
preamble. If a match is found, two more preambles 300 data points after the
beginning of the first match are sought. If the search of the two preambles fails,
the first match is not a preamble but some other data with that pattern. If both
preambles are matched, all three preambles are considered as the beginnings of
three consecutive subframes.
The next step is to check the polarity of the last two bits in the HOW. These
two bits should both be negative, thus, the sum of these two bits should be − 2.
However, the sum of these two bits could be either + 2or − 2. If the sum is zero,
there is a mistake and the beginnings of the three subframes must be wrong.
This can be considered as an additional check. If the sum is − 2 the sign of the
HOW word is correct and the subframe number can be found from bits 20 - 22
of the HOW. If the sum is + 2, the polarity of the HOW must be inverted first;
then find the subframe number. From the subframe number one can search for
the beginning of subframes 1, 2, and 3, because they contain the information to
calculate the user position.
9.5 OBTAINING EPHEMERIS DATA FROM SUBFRAME 1
Once the beginning of subframe 1 is found, the following information can be
obtained. The navigation data are in two forms: the binary and the two's com-
plement as discussed in Section 5.12 and Table 5.8. For the convenience of
calculations, most of these data are converted into decimal form:
1. WN: The week number has 10 bits from 61 - 70 in binary form. These data
are converted into decimal form. As discussed in Section 5.12, this number
starts from midnight January 5/morning January 6, 1980 and a rollover of
1,023 weeks must be taken care of. The decoded time must match the data
collection time.
2. T GD : The estimated group delay differential has 8 bits from 197 - 204 in
two's complementary form. These data are converted into decimal form.
3. t oc : the satellite clock corrections have 16 bits from 219 - 234 in binary
form. These data are converted into decimal form.
4. a f 2 : The satellite clock corrections have 8 bits from 241 - 248 in two's
complementary form. These data are converted into decimal form.
5. a f 1 : The satellite clock corrections have 16 bits from 249 - 264 in two's
complementary form. These data are converted into decimal form.
6. a f 0 : The satellite clock corrections have 22 bits from 271 - 292 in two's
complementary form. These data are converted into decimal form.