GPS Overview Appendix B
MPC User Manual Rev 0D 93
B.6 Carrier-Phase Algorithms
Carrier-phase alg orithms monitor the actual carrier wave itself. These algorithms are the ones used in
real-time kinematic (RTK) positioning solutio ns - differential systems in which the remote station,
possibly in motion, requires reference-station observation data in real-time. Compared to pseudorange
algorithms, much more accurate position solutions can be achieved: carrier-based algorithms can
achieve accuracies of 1-2 cm (CEP).
Kinematic GPS using carrier-phase observations is usually applied to areas where the relation
between physical elements and data collected in a moving vehicle is desired. For example, carrier-
phase kinematic GPS missions have been performed in aircraft to provide coordinates for aerial
photography, and in road vehicles to tag and have coordinates for highway features. This method can
achieve similar accuracy to that of static carrier-phase, if the ambiguities can be fixed. However,
satellite tracking is much more di fficult, and loss of lock makes reliable ambiguity solutions difficult
to maintain.
A carrier-phase measurement is also referred to as an accumulated delta range (ADR). At the L1
frequency, the wavelength is 19 cm; at L2, it is 24 cm. The instantaneous distance between a GPS
satellite and a receiver can be thought of in terms of a number of wavelengths through which the
signal has propagated. In general, this number has a fractional component and an integer component
(such as 124 567 967.330 cycles), and can be viewed as a pseudorange measurement (in cycles) with
an initially unknown constant integer offset. Tracking loops can compute the fractional component
and the change in the integer component with relative ease; however, the determination of the initial
integer portion is less straig ht-forwar d and, in fact, is term ed the ambiguity.
In contrast to pseudorange algorithms where only corrections are broadcast by the reference station,
carrier-phase algorithms typically “double difference” the actual observations of the reference and
remote station receivers. Double-differenced observations are those formed by subtracting
measurements between identical satellite pairs on two receivers:
ADRdouble differe nce = (ADRrx A,sat i - ADRrx A,sat j) - (ADRrx B,sat i - ADRrx B,sat j)
An ambiguity value is estimated for each double-difference observation. One satellite is common to
every satellite pair; it is called the reference satellite, and it is generally the one with the highest
elevation. In this way, if there are n satellites in view by both receivers, then there will be n-1 satellite
pairs. The difference between receivers A and B removes the correlated noise effects, and the
difference between the different satellites removes each receiver’s clock bias from the solution.
In the RTK system, a floating (or “continuous-valued”) ambiguity solution is continuou sl y generat ed
from a Kalman filter. When possible, fixed-integer ambig uity solutions are also computed because
they are more accu rate, an d pr odu ce mor e rob us t stan dard -dev iation es timates. Each po ssible disc rete
ambiguity value for an observation defines one lane; that is, each lane corresponds to a possible
pseudorange value. There are a large number of possible lane combinations, and a receiver has to
analyze each possibility in order to select the correct one. For single-frequency receivers, there is no
alternative to this brute-force approach. However, one advantage of being able to make both L1 and
L2 measurements is that linear combinations of the measurements made at both frequencies lead to
additional values with either “wider” or “narrower” lanes. Fewer and wider lanes make it easier for
the software to choose the correct lane, having used the floating solution for initialization . Once the
correct wide lane has been selected, the software searches for the correct narrow lane. Thus, the