ERRORS IN MEASUREMENT
It should now be apparent that position fixing simply involves the measurement of angles and distance. However, all measurements, no matter how carefully executed, will contain error, and so the true value of a measurement is never known. It follows from this that if the true value is never known, the true error can never be known and the position of a point known only with a certain level of uncertainty. The sources of error fall into three broad categories, namely:
(1) Natural errors caused by variation in or adverse weather conditions, refraction, unmodelled gravity. effects, etc.
(2) Instrumental errors caused by imperfect construction and adjustment of the surveying instruments used.
(3) Personal errors caused by the inability of the individual to make exact observations due to the limitations of human sight, touch and hearing.
Classification of errors:
(1) Mistakes are sometimes called gross errors, but should not be classified as errors at all. They are blunders, often resulting from fatigue or the inexperience of the surveyor. Typical examples are omitting a whole tape length when measuring distance, sighting the wrong target in a round of angles, reading ‘6’ on a levelling staff as ‘9’ and vice versa. Mistakes are the largest of the errors likely to arise, and therefore great care must be taken to obviate them. However, because they are large they are easy to spot and so deal with.
(2) Systematic errors can be constant or variable throughout an operation and are generally attributable to known circumstances. The value of these errors may often be calculated and applied as a correction to the measured quantity. They can be the result of natural conditions, examples of which are: refraction of light rays, variation in the speed of electromagnetic waves through the atmosphere, expansion or contraction of steel tapes due to temperature variations. In all these cases, corrections can be applied to reduce their effect.
3) Random errors are those variates which remain after all other errors have been removed. They are beyond the control of the observer and result from the human inability of the observer to make exact measurements, for reasons already indicated above.
Basic concept of errors:
The basic concept of errors in the data captured by the surveyor may be likened to target shooting. In the first instance, let us assume that a skilled marksman used a rifle with a bent sight, which resulted in his shooting producing a scatter of shots as at A in Figure That the marksman is skilled (or consistent) is evidenced by the very small scatter, which illustrates excellent precision. However, as the shots are far from the centre, caused by the bent sight (systematic
error), they are completely inaccurate.
Such a situation can arise in practice when a piece ofEDMequipment produces a set of measurements all agreeing to within a few millimetres (high precision) but, due to an operating fault and lack of calibration, the measurements are all incorrect by several centimetres (low accuracy). If the bent sight is now corrected, i.e. systematic errors are minimized, the result is a scatter of shots as at B. In this case, the shots are clustered near the centre of the target and thus high precision, due to the small scatter, can be related directly to accuracy. The scatter is, of course, due to the unavoidable random errors.
If the target was now placed face down, the surveyors’task would be to locate the most probable position of the centre based on an analysis of the position of the shots at B. From this analogy several important facts emerge, as follows.
(1) Scatter is an ‘indicator of precision’. The wider the scatter of a set of results about the mean, the less repeatable the measurements are.
(2) Precision must not be confused with accuracy; the former is a relative grouping without regard to nearness to the truth, whilst the latter denotes absolute nearness to the truth.
(3) Precision may be regarded as an index of accuracy only when all sources of error, other than random errors, have been eliminated.
(4) Accuracy may be defined only by specifying the bounds between which the accidental error of a measured quantity may lie. The reason for defining accuracy thus is that the absolute error of the quantity is generally not known. If it were, it could simply be applied to the measured quantity to give its true value. The error bound is usually specified as symmetrical about zero. Thus the accuracy of measured quantity x is x ± εx where εx is greater than or equal to the true but unknown error of x.
(5) Position fixing by the surveyor, whether it is the coordinate position of points in a control network, or the position of topographic detail, is simply an assessment of the most probable position and, as such, requires a statistical evaluation of its precision.