Civil Engineering Reference
In-Depth Information
GPS receiver with a horizontal accuracy of 1 cm
+
1 ppm. The circle of uncer-
tainty would mean that if we drew a circle with a radius of 1 cm around our point
and made 100 measurements, 95 of the measurements would be inside the circle.
However, we can never really know with certainty than any particular point will be
an exact distance from the center of our circle. We can see from this example that
evaluating the accuracy of points measured with GPS is fundamentally different
than it would be if the points were measured in a conventional traverse survey
where angles and distances were measured with a total station.
The same GPS circle of uncertainty will apply equally to a house lot where
the corners are 100 feet apart and a large parcel where the corners are 3,000 feet
apart. In the case of a house lot, an accuracy of 1 cm might not be acceptable, but
in the case of the large parcel it might. This is because surveyors need to be able
to locate property corners with a specific accuracy. For example, if our standard
is 1 in 10,000, and the boundary distance of our house lot is 100 feet, we must
locate the corner within 0.01 feet (1 foot in 10,000 feet is 0.01 feet in 100 feet).
If the GPS receiver accuracy is 1 cm this translates to 0.03 feet. The GPS will
therefore not be accurate enough for establishing the lot corner. On the other hand
if our boundary line is 3,000 feet long, based on our 1 in 10,000 requirement our
linear tolerance is now 0.30 feet. Because the GPS accuracy of 0.03 feet has not
changed, we can expect 95 % of our points to be within 0.03 feet so our accuracy
is 10 times better than required. Looked at another way, using the GPS receiver,
the points would need to be at least 330 feet apart to meet our standard. Of course,
it is possible for regulatory agencies to have different positional tolerances for
GPS and linear techniques.
When considering the purchase or use of GPS receivers it is important to com-
pare positional accuracies at the same certainty level. Manufactures may specify
certainty levels of 68.3 % rather than 95 %. In our previous example using a circle
of uncertainty with a radius of 1 cm, if we used the manufacturer's probability,
only 68 of the points measured would be in the circle, so we would have consider-
ably less confidence in the measurement than in the case of 95 % probability. In
addition to the circle of uncertainty, GPS manufacturers also specify an additional
ppm (parts per million) figure. This simply means that the stated error must be
increased for each part per million of baseline length—the distance between the
receiver and base station. The ppm adjustment is usually quite small, 1 ppm being
about 0.01 feet in two miles.
In our first example, we used significant digits such as 0.1 and 0.01 as an indi-
cation of uncertainty, and it is true that the number of decimal places shown is an
indication of uncertainty. However, it is important to understand that this rule can
lead to undesirable results in surveying. For example, a surveyor may locate the
middle of a shallow stream which is 20 feet wide by standing in the middle of the
stream with a prism pole. The data collector will record a location to the nearest
hundredth of a foot even though the person holding the pole may not be able to
tell where the middle of the stream is within a foot or more. Although the location
of the prism pole is accurate within 0.01 feet, the location of the stream is only
accurate to a foot. In the end, we are really only concerned with the location of the
