GPS Software Receivers - Fundamentals of Global Positioning System Receivers: A Software Approach - page 200

TABLE 9.2 Coarse Relative Pseudorange (time)

Sat nav 1 ∗ sfb 1 ∗∗ ind difms bca(ind) ∗∗∗ dat diffofdat

a 0 100 196 0 9802893 9802893 0

b 7 100 196 7 9803828 9838828 35935

c 10 100 197 0 9850115 9850115 47222

d 17 99 195 7 9752661 9787661 − 15232

∗ Obtained from tracking program and adjusted to a value less than 20.
∗∗ Obtained from subframe 1 matching program.
∗∗∗ Obtained from tracking program.

case. The values in the second and third columns are obtained from the track-
ing and subframe matching programs. The ind and difms are calculated from
Equations (9.1) and (9.2). The values of bca(ind) are also obtained from the
tracking program. The final values of dat can be found from Equation (9.3). The
last column is the relative time difference with respect to satellite a, which can
be found by subtracting 9802893 from the dat values. In order to obtain time
resolution better than 200 ns, the fine time obtained from the tracking program
must be used. This time is calculated every 10 ms and used to determine the
beginning of the C/A code. For simplicity, the fine time associated with index
(196, 196, 197, 195) will be used to find the fine pseudorange (time). This oper-
ation is just to add the fine time to the difference time. For better results the fine
time value can be obtained from manipulating more data points such as a least
squares data fitting.
One can use the relative times 0, 35935, 47222, and − 15232 to calculate the
pseudoranges. In this calculation, some of the pseudoranges will be negative. A
constant might be added to the relative times to make them positive; however,
this is not necessary but only a convenient step. Since the time delay from the
satellites to the user is in the range of 67 to 86 ms as shown in Section 3.3, a
value between these two numbers is a reasonable choice. Although the discussion
is about pseudorange, the actual units are in time which can be changed into
distance by multiplying the speed of light. The pseudoranges ρ can be found as

ρ = c(const + diff of dat + finetime) ( 9 . 4 )

where c = 299792458 m/s is speed of light; const is an arbitrarily chosen con-
stant to make all the pseudoranges positive; the relative transit time ( diff of dat )
is listed in the last column of Table 9.1; and the fine time is obtained from the
tracking program.
Let us choose the const

= 75 ms. For the above example, the four pseudor-
anges (pr) can be calculated as

10 − 3 )

ρ 1 =

× ×

299792458 ( 75

10 − 3 10 − 9 ) ρ 2 = 299792458 × ( 75 × + 35935 × 200 ×