Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 201

The most important concept presented in this section is the measurement rela-
tionship between the replica code phase state in the GPS receiver and the satellite
transmit time. This relationship is unambiguous for P(Y) code, but can be ambigu-
ous for C/A code. Every C/A code GPS receiver is vulnerable to this ambiguity prob-
lem and, under weak signal acquisition conditions, the ambiguity will occur. When
the ambiguity does occur in a C/A code GPS receiver, it causes serious range mea-
surement errors, which, in turn, result in severe navigation position errors.

5.7.1 Pseudorange
The definition of pseudorange to SV i , where i is the PRN number is as follows:

[ ]

() () () ()

ρ i ncTnTn = − m (5.27)

R Ti

where:

c = speed of light = 299,792,458 (m/s)

T R ( n ) receive time corresponding to epoch n of the GPS receiver's clock

(seconds)
T Ti ( n )

=

= transmit time based on the SV i clock (seconds)

Figure 5.29 depicts the GPS satellite SV i transmitting its PRN code PRN i start-
ing at the end of the GPS week. Corresponding to each chip of the PRN i code is a lin-
ear SV i clock time. When this signal reaches the GPS receiver, the transmit time,
T Ti ( n ), is the SV i time corresponding to the PRN code state that is being replicated at
receiver epoch n . The pseudorange derived from this measurement corresponds to a

SV i

PRN code at transmit time
i

φ 1 φ 2 φ k φ k+1

SV clock at transmit time
i

T 1 T 2 T k T k+1

End of week

Transmit time (n) = T (n)

Ti

Replica PRN code
at receive time

i

φ 1 φ (n) φ 2 φ k φ k+1

Code
accumulator at
receive time

T 1 T (n) T 2 T k T k+1

Receiver FTF

FTF (n)

GPS receiver

Pseudorange measurement (n)@T(n)

R

Figure 5.29 Relationship of satellite transmit time to pseudorange measurements.