Differential GPS - Understanding GPS: Principles and Applications - page 399

tial systems and their associated instruments (e.g., accelerometers and gyros), there
is similar applicability to GPS measurement inconsistencies that manifest them-
selves, in this instance, in the integer wavelength ambiguities inherent in the car-
rier-phase observables. In [27], it has been shown that a similar approach using a
technique that minimizes least square residuals has application to the rapid resolu-
tion of the ambiguities, albeit in a static, nonkinematic environment. This reference
also suggests the use of the wide-lane measurements to reduce computational
overhead, thus speeding up the ambiguity-resolution process.

8.4.1.1 Combining Receiver Measurements
As mentioned in Chapter 3, two distinct measurements are provided by a GPS SPS
receiver: the L1 C/A code pseudorange measurement, also referred to as the code
measurement, and the L1 carrier-phase measurement. Code and carrier-phase mea-
surements are available from each satellite vehicle tracked by the receiver. Dual-fre-
quency GPS receivers, which are capable of recovering the P(Y) code observables,
provide such measurements for both the L1 and L2 frequencies, as well as the C/A
code observables. Unfortunately, these measurements are subject to some detrimen-
tal effects. Inherent in the GPS signal is a variety of errors—errors due to signal
propagation through the ionosphere and troposphere, satellite ephemeris errors and
clock errors, and of course noise. GPS receivers have their own set of prob-
lems—clock instability, signal multipath, and also noise. Fortunately, the term
DGPS implies that we have similar sets of measurements from at least two GPS
receivers separated by some fixed distance called a baseline. By forming linear com-
binations (differences) of like measurements from two receivers, it becomes possible
to eliminate errors that are common to both receivers. Such a combination is
referred to as a single difference (SD). By differencing two SD measurements from
the same satellite vehicle, we form what is called the double difference (DD). The
result is that by using DD processing techniques on the C/A or P(Y) code and car-
rier-phase observables, most of the error sources are removed [15]. One major
exception remains, however, and that is multipath—it can be mitigated but not
eliminated. Note that receiver noise is still present, but its contribution is generally
much less than that of multipath.

8.4.1.2 Carrier-Phase Measurement
Once the receiver locks on to a particular satellite, it not only makes C/A and/or
P(Y) code pseudorange measurements on L1 and L2 (if L2-capable), it also keeps a
running cycle count based on the Doppler frequency shift present on the L1 and L2
carrier frequencies (one cycle represents an advance of 2 radians of carrier phase

or one wavelength). For each epoch, this running cycle count (the value from the
previous epoch plus the advance in phase during the present epoch) is available
from the receiver. More specifically, the advance in carrier phase during an epoch is
determined by integrating the carrier Doppler frequency offset ( f D ) over the interval
of the epoch. Frequency f D is the time rate of change of the carrier phase; hence, inte-
gration over an epoch yields the carrier phase advance (or recession) during the
epoch. Then, at the conclusion of each epoch, a fractional phase measurement is

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