Geoscience Reference
In-Depth Information
As already mentioned, the fundamental GPS observable is the signal travel time between the
satellite and the receiver. However, the receiver clock that measures the time is not perfect and
may introduce an error to the measured pseudorange (even though we limit our discussion here
to pseudoranges, the same applies to the carrier phase measurement that is indirectly related to
the signal transit time, as the phase of the received signal can be related to the phase at the epoch
of transmission in terms of the signal transit time). Thus, in order to determine the most accurate
range, the receiver clock correction must be estimated to bring the receiver clock to synchronization
with the satellite clock, and its effect must be removed from the observed range. The synchroniza-
tion error between satellite and receiver clocks is particularly important given that an error of only
0.1 microsecond in the satellite or receiver clocks results in distance error on the order of 30 m.
Hence, the fourth pseudorange measurement is needed, because the total number of unknowns,
including the receiver clock, is now four. If more than four satellites are observed, a least-squares
solution is employed to derive the optimal solution.
9 . 7 . 1
P
o i n t
v e R s u s
R
e l a t i v e
P
of s i t i of n i n g
There are two primary GPS positioning modes: point positioning (or absolute positioning) and rela-
tive positioning. However, there are several different strategies for GPS data collection and process-
ing, relevant to both positioning modes. In general, GPS can be used in static and kinematic modes,
using both pseudorange and carrier phase data. GPS data can be collected and then postprocessed at
a later time, or processed in real time, depending on the application and the accuracy requirements.
In general, postprocessing in relative mode provides the best accuracy.
9.7.1.1
point (Absolute) positioning
In point, or absolute positioning, a single receiver observes pseudoranges to multiple satellites to
determine the user's location. For the positioning of the moving receiver, the number of unknowns
per epoch equals three receiver coordinates plus a receiver clock correction term. In the static mode
with multiple epochs of observations, there are three receiver coordinates and
n
receiver clock error
terms, each corresponding to a separate epoch of observation
1
to
n.
The satellite geometry and any
unmodeled errors will directly affect the accuracy of the absolute positioning.
9.7.1.2
Relative positioning
The relative positioning technique (also referred to as differencing mode or differential GPS, DGPS)
employs at least two receivers: a reference (base) receiver, whose coordinates must be known, and
the user's receiver, whose coordinates can be determined relative to the reference receiver. Thus,
the major objective of relative positioning is to estimate the 3D baseline vector between the refer-
ence receiver and the unknown location. Using the known coordinates of the reference receiver and
the estimated ∆X, ∆Y, and ∆Z baseline components, the user's receiver coordinates in WGS84 can
be readily computed. Naturally, the user's WGS84 coordinates can be further transformed to any
selected reference system.
An observable in differencing mode is obtained by differencing the simultaneous measure-
ments to the same satellites observed by the reference and the user receivers (between receiver dif-
ferencing), or through “between satellite differencing” and “between epoch differencing.” The most
important advantage of relative positioning is the removal of the systematic error sources (common
to the base station and the user or both satellites and epochs of observation) from the observable,
leading to the increased positioning accuracy. Because for short to medium baselines (up to ~40 to
60 km) the systematic errors in GPS observables due to troposphere, satellite clock, and broadcast
ephemeris errors are of similar magnitude (i.e., they are spatially and temporally correlated), the rel-
ative positioning allows for a removal or at least a significant mitigation of these error sources, when
the observables are differenced. In addition, for baselines longer than 10 km, the ionosphere-free
