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INTRODUCTION
Surveying 1A (SVG 105)
ERRORS IN MEASUREMENT
Course Convener: E. Kurwakumire
• Position fixing simply involves the measurement of angles and
distance.
• However, all measurements, no matter how carefully executed, will
contain error
• As a result the true value of a measurement is never known.
• Measurements thus have to fall within some limits of accuracy
• It can also be said that, no measurement (except for counting) can
be free of error.
• For every measuring technique used, a more precise and potentially
more accurate method can be found
• For the purposes of calculating errors, the “true” value is
determined statistically after repeated measurements
• In the simplest case, the “true” value is the mean value of a series
of repeated measurements
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Midlands State University, Dept of Surveying and Geomatics
CLASSIFICATION OF ERRORS
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Mistakes
• There are three major classifications for errors
encountered in surveying measurements:
– Gross Errors (Mistakes/Blunders)
– Systematic Errors
– Random Errors
• Sometimes referred to as Gross Errors. They are blunders and often
result from fatigue or the inexperience of the surveyor.
• Mistakes are the largest of the errors likely to arise in magnitude, and
therefore great care must be taken to obviate them.
• Examples of gross errors include booking 1.684m as 1.864m,omitting a
whole tape length and measuring to or from a wrong point
• Students should be aware that mistakes will occur and must be
discovered and eliminated, preferably by the people who made them.
• All survey measurements are suspect until they have been verified
• Verification may be as simple as repeating the measurement.
• As a rule, every measurement should be immediately checked or
repeated. This immediate repetition enables the surveyor to eliminate
most mistakes and at the same time, improve the precision of the
measurements
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Systematic Errors
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Random Errors
Are defined as those errors whose magnitude and algebraic sign can be
determined
The fact that these errors can be determined allows the surveyor to
eliminate them from the measurements and thus improve the accuracy
Systematic errors can be constant or variable throughout an operation and
are generally attributable to known circumstances. The value of these errors
can 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 crystalsin
EDM equipment.
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• Those errors that remain after all errors have been removed
• They are due to the inability of the observer to make exact
measurements
• Random errors are associated with the skill and vigilance of the
surveyor. Random (also known as accidental) errors are introduced into
each measurement mainly because no human being can perform
perfectly
• Random errors, by their nature, tend to cancel themselves. When
surveyors are skilled and careful in measuring, random errors will be of
little significance except for high precision surveys
• However, random errors resulting from unskilled careless work do cause
problems.
• Random errors follow a normal distribution and obey the laws of
probability є→N (μ, δ2)
• They can be treated using statistical methods
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8/2/2011
The Normal Distribution
The Normal Distribution (2)
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ACCURACY AND PRECISION
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ACCURACY AND PRECISION
• Accuracy:
– The relationship between the value of a
measurement and the true value of the dimension
being measured
– Closeness of measured values to the true value
• Precision:
– Precision describes the degree of refinement with
which the measurement is made
– The degree of closeness of values to each other
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ACCURACY AND PRECISION
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