Carrier and Code Tracking - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 103

Transmitted
code

Received
code

Frame 1 Frame 71 Frame 72

0 1 70 71

Time [ms]

FIGURE 7.21. The delay between the time of transmission at the satellite and time of
reception at the receiver.

7.8 Pseudorange Computations

Precise estimation of the pseudorange from a satellite to the receiver is crucial for
a modern C/A code GPS receiver. The relationship between the standard devia-
tion of the observations and that of the coordinates of the receiver position (see
page 131) is

e n u

σ pos = σ + σ + σ = PDOP σ 0 , (7.31)

where σ 0 is the standard de-

viation of unit weight. PDOP is the position dilution of precision, which depends
on the geometry of the satellite constellation. Optimal accuracy of the position is
obtained when the standard deviation of unit weight is as small as possible.
A pseudorange measurement is computed as the travel time from the satellite
to the receiver multiplied by the speed of light in vacuum. The receiver has to
estimate exactly when the start of a frame arrives at the receiver. This is done by
adding the code phase to the time when the frame entered the receiver.
In Figure 7.21, the satellite transmits the start of the C/A code at t

σ pos is the standard deviation of the receiver position,

0ms.This
signal is received by the receiver approximately 70 ms after it is transmitted from
the satellite. A range from the satellite to the receiver of 21,000 km corresponds to
a travel time of 70 ms. As described before, the receiver is using block processing.
That is, to calculate an accurate pseudorange and hereby an accurate position, the
exact start of the C/A code in frame 71 in Figure 7.21 has to be found.
Figure 7.22 shows the first 700 samples of frame 71 in detail. The receiver has
a time tag for the start of the frame. The problem is then to determine exactly
where the start of the code is in the frame of data. In Figure 7.22, the start of the
C/A code is at sample number 605, which is the correct code start in the simulated
data used in this section.
Since the sampling frequency of the reference data set is at 38

=

. 192 MHz, each

sample corresponds to

c

p =

192 MHz =

7 . 86 m .

.

38