Department of Civil and Environmental Engineering and Geodetic Science

Geodetic and Geoinformation Science Section

GS/CE400.01 Introduction to Surveying

GS601 Introduction to Mapping and Photogrammetry

Friday, 21st September, 2001.

There are lots of things which we call errors. We also use a lot of other terms for this. The fundamental issue is that we can never know the true value of any measured quantity, so we always have some uncertainty associated with the value we adopt

We can use a lot of methods to try to minimize our errors, but we can
never eliminate them. For the purposes of working with errors, we can divide
them into three groups: gross, systematic and random errors. This division
is based on what causes the errors and how we deal with them, rather than
any other aspect of their nature. You will see other classification

schemes, but this one is both comprehensive and useful.

**Gross errors**

are those which we can also call `blunders'. They can be of any size
or nature, and tend to occur through carelessness. Writing down the wrong
value, reading the instrument incorrectly, measuring to the wrong mark;
these are gross errors. They can be caused by people, machinery, weather
conditions and various other things. We deal with gross errors by

careful procedures and relentless checking of our work.

**Systematic errors**

are those which we can model mathematically and therefore correct.
They are caused by the mathematical model of the procedure that we are
using being different to what is going on in the real world. We reduce
and compute with measurements on the basis of models and if the models
are not complete, we will have discrepancies. For example, if we measure
a distance without allowing for the slope of the tape, we will have a systematic
error, which can be eliminated if we use the correct model of the measurement
process. We can eliminate, or at least minimize, systematic errors by careful
work, using the appropriate model for the process in use, and by using
checks that will reveal systematic errors in measurements. Note that checks
that use the same measurement processes may not detect some systematic
errors, so you have to be fairly creative in developing methods for detecting
systematic errors.

**Random errors**

are those which have no apparent cause, but are a consequence of the
measurement process itself. All measurements have to be done to some limit
of precision and we cannot predict the exact measurement we will obtain.
However, random errors have very definite statistical behavior and so can
be dealt with by statistical methods. Random errors are the small differences
between repeated measurements of the same quantity, often of the order
of the finest division in the measuring scale. We can eliminate or minimize
the effects of

random errors by statistical procedures: for example we can adopt the
mean of a set of measurements as the value to be used in later calculations.
With the idea of the ubiquity of errors in all our measurements and everything
we do, we can

now look at one measurement process and see how errors affect it. We
will begin by looking at linear measurements, such as those we make with
tapes and such equipment as EDM.