84 MPC User Manual Rev 0D
Appendix B GPS Overview
hairs, the centre of the shaded area is the "location" of the mean estimate, and the radius of the shaded
area is a measure of the uncertainty contained in the estimate.
Figure 81: Accuracy versus Precision1
B.3.1 Single-Point vs. Relative Positioning
In single-point positioning, coordinates of a GPS receiver at an unknown location are sought with
respect to the earth’s reference frame by using the known positions of GPS satellites being tracked.
The position solution generated by the receiver is initially developed in earth-centered coordinates
which can subsequently be converted to any other coordinate system. With as few as four GPS
satellites in view, the absolute position of the receiver in three-dimensional space can be determined.
Only one receiver is needed. With Selectiv e Availability (SA) active, the typical horizontal accuracy
obtainable using single-po int positioning is of the order of 100 m (95% of the time).
In relative positioning, also known as differential positioning, the coordinates of a GPS receiver at an
unknown poin t (the “remote” station) are so ugh t with respect to a GPS receiver at a known point (the
“reference” station). The concept is illustrated in Figure 82 on Page 85. The relative-position
accuracy of two receivers locked on the same satellites and not far removed from each other - up to
tens of kilometers - is extremely high. The largest error contributors in single-point positioning are
those associated with SA and atmos pheric-induced effects. These errors, however, are highly
correlated for adjacent receivers and hence cancel out in relative measurements. Since the position of
the reference station can be determined to a high degree of accuracy using conventional surveying
techniques, any differences between its known position and the position comput ed using GPS
techniques can be attributed to various components of error as well as the receiver’s clock bias. Once
the estimated clock bias is removed, the remaining erro r on each pseudoran ge can be determined. The
reference station sends information about each satellite to the remote station, which in turn can
determine its position much more exactly than would be possible otherw ise.
The advantage of relative positioning is that much greater precision (presently as low as 2 mm,
dependi ng on the m ethod and envi ronmen t) can b e achieve d than by sing le-poin t pos itioni ng. In order
for the observations of the referen ce station to be integrated with those of the remote station, relative
1.Environment Canada, 1993, Guideline for the Application of GPS Positioning, p. 22.
Minister of Supply and Services Canada
High accuracy,
high precision
High accuracy,
low precision Low accuracy,
low precision
Low accuracy,
high precision