86 POSITION-FIXING
Accuracy
Accuracy provides an indication of the quality of mea-
surements and hence a position. In chapter 14 (on
Underwater Survey), accuracy will be discussed in terms
of measurements and the quality of the site-plan. The same
principles apply to any form of measurement and posi-
tion derivation.
The concept of accuracy embodies the idea of ‘abso-
lute position’, implying that there is a correct answer.
The correct answer, however, is never realized because
of intrinsic errors in any measurement or measurement
framework. Schofield (2001) draws an analogy between
survey measurements and target shooting. The centre of
the target represents the absolute position of the point being
measured. The skilled marksperson will produce a scat-
ter of shots on the target. The degree of scatter represents
the precision of measurement; the nearness to the centre
of the target represents the degree of accuracy. Hence it
is possible to have very precise measurements that are totally
inaccurate (figure 11.3). An example of this would be
a series of measurements taken to a point with a tape-
measure to the nearest millimetre but the zero of the
tape starting at 2 cm. Each reading of the tape could be
made very precisely but the value itself would contain
an error and hence be inaccurate. Accuracy is therefore
expressed as bounds within which the measured value
or the absolute position may lie. These bounds are
expressed in statistical terms such as standard deviation
(see below). The essence of achieving accurate survey
data is to minimize errors. There are several definitions
and terms that can be used when describing accuracy.
Errors: Errors come in many shapes and sizes. They
can generally be split into two groups: systematic errors
and random errors. Systematic errors are inherent in
the instrumentation or measurement system as in the
example above. Random errors are less predictable and
include gross errors (e.g. from misreading a tape measure).
The concept of accuracy is the concept of understanding
and quantifying errors.
Standard deviation: This is the measure of variation
of how close all the values are to the average value and
is quoted as a single number. This is an evaluation of
precision.
Measurement accuracy: This is related to the size of
the error in measurement. Distance measurements can
be expressed in terms of a relative error of 1 in 10,000.
For example, this would describe an error of 1 mm over
a distance of 10 m. This is a very useful definition and
is often used when quoting equipment accuracies.
Scale: The area depicted on a map or chart is subject
to scale and represented as a unit of proportion. For
example a scale of 1:1 indicates that 1 unit on paper rep-
resents 1 unit on the ground whereas a scale of 1:50,000
means that 1 unit on paper represents 50,000 units on the
ground (i.e. 1 mm measured on a map would be 50,000
mm or 50 m on the ground).Plotable accuracy: The plotable accuracy is a key
consideration in any survey design. Surveys for the
most part are represented as scaled drawings. When
plotting at a scale of 1:100, 1 mm on paper will represent
100 mm (10 cm) on the ground. The width of a sharp
pencil lead is typically 0.5 mm, equivalent to 50 mm
on the ground at a scale of 1:100. It is therefore a waste
of time and resources measuring to the nearest milli-
metre when it is only possible to plot to an accuracy of
50 mm.Repeatability: This is a measure of consistency. In
other words, can the derived position be relocated using
an independent system or using the same system but on
a separate occasion? Note that a position can be repeat-
able but not necessarily accurate. For example, using a tape-
measure where the zero starts at 2 cm will give repeatable
measurements but they will not be correct. A repeatable
position can be derived despite the presence of system-
atic errors. It is very easy to become obsessed with
accuracy to the detriment of producing a working plan
or drawing. The key is to understand the concept of
accuracy and the accuracy limits that are being
worked to.ABFigure 11.3 A scatter of shots showing precision (A) and
accuracy (B)