GPS Software Receivers - Fundamentals of Global Positioning System Receivers: A Software Approach - page 201

( 75 × 10 − 3

+ 47222 × 200 × 10 − 9 )

ρ 3 = 299792458 ×

10 − 3 10 − 9 ) ρ 4 =

× × − × ×

299792458 ( 75 15232 200

In this equation the fine time is not included. For the actual calculation the fine
time must be included in the above equation. In addition, the ionospheric correc-
tion term from Equation (5.8) or (5.9) and the tropospheric correction term from
Equation (5.19) must also be included. The result obtained from Equation (5.19)
is in meters and it must be divided by the speed of light to change into time.
It should be noted that the ionospheric correction constants are in subframe
4. Using only the information in the first three subframes cannot make iono-
spheric correction.
In the above discussion, the beginning of the C/A code has a time resolution
of 10 milliseconds. The beginning of subframe 1 has a time resolution of 20
milliseconds. The first navigation data point and the difference in milliseconds
have a time resolution of 1 millisecond. These quantities can be used to determine
the beginning of subframe 1 to within 1 millisecond. Thus, the value of the
beginning of the C/A code can be limited up to 5,000 (1 ms). The large values
of the beginnings of the C/A code 9802893, 9803828, 9850115, and 9752661
shown in Figures 9.6a, 9.6b, 9.6c, and 9.6d are not necessary. Instead four new
values can be the remainder of these four values minus multiples of 5,000. The
results are 2893, 3828, 115, and 2661. These new data are listed in Table 9.3.
The only difference between Tables 9.3 and 9.2 is in the sixth column. The
beginnings of subframe 1 can be obtained as

dat = 10 × 5000 × ind + 5000 × difms + bca(ind) ( 9 . 5 )

because dat has a time resolution of 10 ms, difms has a time resolution of 1 ms,
and each millisecond has 5,000 data points. Using this equation the same values
of dat can be obtained and listed in the above table. In the actual software
receiver program, beginnings of the C/A code with values equal to or less than
5,000 are used.
In the above discussion the main task is to find an input data point corre-
sponding to the beginning of subframe 1. The above discussion is only one of
many possible approaches to accomplish this goal.

TABLE 9.3 Coarse Relative Pseudorange (time) with New Beginnings of the C/A
Code

Sat nav 1 sfb 1 inds difms bca(ind) dat diff of dat

a 0 100 196 0 2893 9802893 0

b 7 100 196 7 3828 9838828 35935

c 10 100 197 0 115 9850115 47222

d 17 99 195 7 2661 9787661 − 15232