Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 109

GPS time seconds

0 12345678910 112131415161718

Z-count

0123456789 0 1 2

Truncated
Z-count

0 1 2 3

FIGURE 8.4. The relation between GPS time, Z-count, and the truncated Z-count in the
HOW of the navigation data.

The second word of every subframe is the so-called HOW that includes a trun-
cated version of the TOW. This number is referred to as the Z-count. The Z-
count is the number of seconds passed since the last GPS week rollover in units
of 1.5 s. The rollover happens at midnight between Saturday and Sunday. The
maximum value of the Z-count is 403,199 as one week contains 604,800 s and
604,800 s/1.5 = 403,200 s. The Z-count value in the HOW is a truncated version
containing only the 17 most significant bits (MSB). This truncation makes the
Z-count increase in 6-s steps corresponding to the time between transmission of
two consecutive navigation subframes. Figure 8.4 shows the relation between the
three time measures: GPS time, Z-count, and truncated Z-count.

TABLE 8.2. Decoding scheme for GPS ephemeris parameters in the navigation data.
n ∗ means that the current n bits should be decoded using the two's-complement.

Parameter No. of bits Scale factor (LSB) Unit

IODE 8

16 ∗ 2 − 5

C rs m

16 ∗ 2 − 43

n semicircle/s

32 ∗ 2 − 31 µ 0 semicircle

16 ∗ 2 − 29

C uc radian

2 − 33 e 32 dimensionless

16 ∗ 2 − 29 C us radian

√ a

2 − 19 m 1 / 2 32

2 4 t oe 16 s

16 ∗ 2 − 29 C ic radian

32 ∗ 2 − 31 0 semicircle

16 ∗ 2 − 29

C is radian

32 ∗ 2 − 31 i 0 semicircle

16 ∗ 2 − 5

C rc m

32 ∗ 2 − 31

ω semicircle

˙

24 ∗ 2 − 43

semicircle/s

i

14 ∗ 2 − 43

semicircle/s