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, unmodeled 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. Such errors may also be produced by instruments, e.g. maladjustment of the theodolite or level, index error in spring balances, ageing of the crystals in EDM equipment. One form of systematic error is the constant error, which is always there irrespective of the size of the measurement or the observing conditions. Examples of constant errors in tape measurement might be due to a break and join in the tape or tape stretch in the first metre of the tape. In this case the remedy is to ensure that the tape is undamaged and also not to use the first metre of the tape. Examples of constant errors in the repeated observations of a horizontal angle with a theodolite to elevated targets might be miscentring over the station or dislevelment of the theodolite. In this case, the remedy is to ensure that the theodolite is correctly set up.
There is the personal error of the observer who may have a bias against setting a micrometer or in bisecting a target, etc. Such errors can frequently be self-compensating; for instance, a person observing a horizontal angle to a cylindrical target subject to phase, the apparent biased illumination by the sun when shining on one side will be subject to a similar bias on a similar target nearby and so the computed angle between will be substantially correct.
Systematic errors, in the main, conform to mathematical and physical laws; thus it is argued that appropriate corrections can be computed and applied to reduce their effect. It is doubtful, however, whether the effect of systematic errors is ever entirely eliminated, largely due to the inability to obtain an exact measurement of the quantities involved. Typical examples are: the difficulty of obtaining group refractive index throughout the measuring path of EDM distances; and the difficulty of obtaining the temperature of the steel tape, based on air temperature measurements with thermometers. Thus, systematic errors are the most difficult to deal with and therefore they require very careful consideration prior to, during, and after the survey. Careful calibration of all equipment is an essential part of controlling systematic error.
(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. Random errors should be small and there is no procedure that will compensate for or reduce any one single error. The size and sign of any random error is quite unpredictable. Although the behaviour of any one observation is unpredictable the behaviour of a group of random errors is predictable and the larger the group the more predictable is its behaviour. This is the basis of much of the quality assessment of survey products. Random variates are assumed to have a continuous frequency distribution called normal distribution and obey the law of probability. A random variate, x, which is normally distributed with a mean and standard deviation, is written in symbol form asN(µ, σ2). Random errors alone are treated by statistical processes
