Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 217

N CA = integer carrier Doppler phase cycles since some starting point

Φ CA , is initialized to the same
state as the carrier NCO at the beginning of the search process, which is typically
zero. The integer number of carrier Doppler phase cycles, N CA , is ambiguous. Since
only differential measurements are taken from this register, the ambiguity does not
matter. The carrier integer accumulator is usually set to zero when the carrier loop
is first closed following a successful search operation. Note that the marching of
time carrier NCO bias (see Figure 5.2) is not included in the carrier accumulator
because it is simply a bias term to match the carrier at IF. Since only differential
measurements are extracted from the carrier accumulator, this bias term, if
included, would cancel out. The counter rolls over when the Doppler cycle count
exceeds the count capacity or underflows if the Doppler count is in the reverse direc-
tion and drops below the zero count. The differential measurement comes out cor-
rect if the counter capacity is large enough to ensure that this happens no more than
once between any set of differential measurements extracted from the carrier
accumulator.
To extract a carrier Doppler phase measurement, N CAi ( n ),

The fractional part of the carrier accumulator,

Φ CAi ( n ), for SV i corre-
sponding to the carrier accumulator, it must be propagated forward to the nearest
FTF( n ) by the skew time, T S , similar to the technique used in the code tracking loop.

ΦΦ+ =

=

f ∆Φ T

temp CA c CA S

( )

Φ fractional part of Φ cycles (5.34)

CAi temp

( )

N CAi = integer part of Φ cycles

temp

Note that there is no error due to the measurement propagation process for the
carrier Doppler phase measurement because the carrier NCO is running at a con-
stant rate, ∆Φ CA per clock, during the propagation interval.

The precise delta pseudorange is simply the change in phase in the carrier accu-
mulator during a specified time. The formula for extracting the delta pseudorange
from the carrier accumulator is as follows.

[ ]

( ) ( )

NnJ +− NnK − +

CAi CAi

() ()

∆ ρ n = λ m (5.35)

[ ]

i L

( ) ( )

Φ nJ +− Φ nK −

CAi CAi

where:

λ L = wavelength of the L-band carrier frequency

= 0.1903 m/cycle for L1

= 0.2442 m/cycle for L2

As a design example, suppose the navigation measurement incorporation rate is
1 Hz (a very typical rate), then the delta pseudorange measurement should begin
and end with each range measurement. To accommodate this for an FTF period of
20 ms, J

= 0 and K =− 50. Alternatively, if the navigation throughput permits, the