Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 218

delta pseudorange measurement could be incorporated at a 50-Hz rate with J = 0

and K 1. In either case, the delta range measurement should be modeled by the

navigation process as a change in range over the previous second, not as an average
velocity over the interval.

=

5.7.3 Integrated Doppler
The definition of integrated Doppler is obtained from (5.34). The integrated Dopp-
ler measurement for SV i at FTF( n ) can be converted to units of meters as follows.

[ ]

() () () ()

ID n = N n + Φ n λ m (5.36)

i CAi CAi L

This measurement, when derived from a PLL, is used for ultraprecise differential
interferometric GPS applications, such as static and kinematic surveying or for atti-
tude determination. Note that when the integer cycle count ambiguity is resolved by
the interferometric process, this measurement is equivalent to a pseudorange mea-
surement with more than two orders of magnitude less noise than the transmit time
(pseudorange) measurements obtained from the code loop. The integrated Doppler
noise for a high-quality GPS receiver designed for interferometric applications typi-
cally is about 1 mm (1 sigma) under good signal conditions. A transmit time
(pseudorange) measurement typically will have about 1m of noise (1 sigma). Once
the integer cycle ambiguity is resolved, as long as the PLL does not slip cycles, the
ambiguity remains resolved thereafter. (Further information on differential
interferometric processing and ambiguity resolution is provided in Section 8.4.)
Two GPS receivers that are making transmit time and carrier Doppler phase
measurements on their respective receiver epochs will in general be time skewed
with respect to one another. For ultraprecise differential applications, it is possible
to remove virtually all of the effects of time-variable bias by eliminating this time
skew between GPS receivers (i.e., spatially separated GPS receivers can make syn-
chronous measurements). This is accomplished by precisely aligning the measure-
ments to GPS time epochs instead of to (asynchronous) receiver FTF epochs.
Initially, of course, the measurements must be obtained with respect to the receiver
FTF epochs. After the navigation process determines the time bias between its FTF
epochs and true GPS time, each navigation request for a set of receiver measure-
ments should include the current estimate of the time bias with respect to the FTF (a
very slowly changing value if the reference oscillator is stable). The receiver mea-
surement process then propagates the measurements to the FTF plus the time bias as
nearly perfect (within nanoseconds) of true GPS time. These measurements are typi-
cally on the GPS 1-second time of week epoch. This is important for precision differ-
ential operation since as little as 1 second of time skew between receivers
corresponds to satellite position changes of nearly 4,000m. Of course, the differen-
tial measurements can be propagated to align to the same time epoch if the GPS
receiver's measurements are time skewed, but not with the accuracy that can be
obtained if they are aligned to a common GPS time epoch within each GPS receiver
during the original measurement process. The carrier Doppler measurement must be
corrected for the frequency error in the satellite's atomic standard (i.e., reference
oscillator) before measurement incorporation. This correction is broadcast in the