451617 Fundamentals of Positioning Technologies

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451-617 Fundamentals of Positioning
Technologies Lecture 7 Quality Issues in
Positioning Technologies
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At the end of this lecture students should be
able to

• Discuss what is meant by positioning data
  quality.
• Define the terms that describe the quality of
  measurement data acquired by positioning
  technologies.
• Critically assess the performance of different
  positioning technology.
• Define and give examples of the different types
  of errors in measurement data.
• Evaluate and quantify the impact of errors in
  measurements on derived quantities.

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What do you understand by the term measurement
data quality?
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Measurement Data Quality

• How good is the data
• Uncertainty
• Fitness for use
• What is the context for the measurement?
• How much accuracy is needed?
• What is an appropriate instrument to use for this
  measurement?
• How do I use this instrument correctly?
• What are my potential sources of error?
• How sure will I be of my results? How will I
  know?
• How can I show my level of certainty to others?
• Any other important things such as continuity etc

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What are some of the parameters you would use to
describe the quality of a measurement data set?
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Components of a Measurement

• An estimate of the size of the measured quantity
  (Remember all measurements are estimates.)
• The distance from my home to the market is 4.1
• The units for the measured quantity (Every
  physical measurement has units.)
• The distance from my home to the market is 4.1
  km.
• An estimate of the range of error, or uncertainty
• The distance from my home to the market is 4.1
  (0.2) km.
• A level of certainty or level of confidence
  concerning the range of error (You must know the
  confidence level associated with the error
  estimate for it to have meaning.)
• I am 95 confident that the distance from my
  home to the market is 4.1 (0.2) km.

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Describing Position Data Quality

• Precision
• Accuracy
• Reliability
• .

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What is the difference between accuracy and
precision?
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Accuracy vs Position

• accuracy the nearness of the measurement to the
  absolute truth. To have some idea of accuracy
  you must have a good idea of the truth
• precision the repeatability of a measurement.
  Precision has no bearing on accuracy.

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What do each of these diagram show in terms of
accuracy and precision?
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What are the different types of errors that can
occur in a measurement?
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Types of Errors

• Gross
• Systematic
• Random

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Gross Errors

• Mistakes or blunders. Often factors of 10, 100,
  1000 out. Therefore, relatively easy to spot eg
  look on a scatterplot.
• Gross errors arise from inattention or
  carelessness of the observer (eg students!) in
  handling instrument, reading scales or booking
  results. Therefore gross errors are usually
  caused by people.
• eg, when measuring the length of a line, booking
  down wrong values or transposing digits.
• Gross errors are detected by making repeat,
  independent observations (eg use different
  observer to take the same measurement).
• Gross errors must be eliminated from a data set
  prior to any statistical analysis.

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Gross Errors
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What are some of the sources of gross errors in
the GPS practical?
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Strategies to Minimise Gross Errors

• Develop a careful and conscientious attitude
  towards the work
• Get proper training on the use of measurement
  instruments
• Practice standard, recognized, and repeatable
  work procedures
• Develop and maintain positive and open-minded
  attitudes
• Develop a refined understanding of the problem
  and relevant theory

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Systematic Errors

• Usually caused by defects in equipment. Equipment
  may give constant offset to true measured value
  throughout its lifetime, eg faulty graduation of
  a scale, or may drift giving different erroneous
  measurement with time eg gravity meters.
• The actual systematic error may be small, but
  given certain measurement conditions may
  accumulate.
• eg, Measure a straight line distance along the
  ground with a tape shorter than the total length.
  If the tape is in error e cm and the distance
  measured comprises n tape lengths, the cumulative
  systematic error is n.e cm.

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Systematic Errors
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Systematic Errors

• Systematic errors can be removed by calibrating
  equipment against some known control eg EDMs are
  calibrated over known baselines in a controlled
  thermal and atmospheric environment.
• Alternatively, if a functional relationship for
  the systematic is known , a term can be added
  into the mathematical model to reduce the effect
  to an insignificant magnitude
• Eg e I sec, h is the error in the horizontal
  circle reading of a theodolite having a
  collimation error I at an elevation h. If I has
  been found by testing the theodolite an
  appropriate correction could be applied, or
  alternatively use the principle of reversal (ie
  observe on both faces of the theodolite)
• Systematic errors are not random and are not
  independent. Therefore their presence severely
  inhibits meaningful statistical analysis and
  every effort must be made to remove them prior to
  analysis.

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What are some of the sources of systematic errors
in the GPS practical?
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Random Errors

• Random errors are by definition. For a prolonged
  series of measurements of the same object,
  measurement errors tend to cluster about the mean
  with a symmetric bell-shaped distribution

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Random Errors

• Small errors are more numerous than large errors
• Very large errors do not occur
• Errors are just as likely to be positive as
  negative (ie compensation)
• The true or ideal value of a quantity is the mean
  of an infinite number of similar observations

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Random Errors
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Every measurement has uncertainty associated
with it, so how do the uncertainties in the
measurements affect the certainty of a calculated
result?
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Error Propagation

• We have measured two distances d1 and d2 in a
  straight line. What is the total distance (D) and
  its standard deviation?
• d1 154.26m and has a SD of 0.01m, d2 175.34m
  and has a SD of 0.05m

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Error Propagation
D d1 d2 154.26 175.34 329.60m D (d1
e2) (d2 e2) (154.26 .01) (175.34 .05
)
154.27 175.39
329.66 difference 0.06m
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Error Propagation
The coordinates of a point A are 311.617m E,
447.245m N. Calculate the coordinates of point B
where qAB 37o 11 20 and sAB 57.916m. What
are the coordinates of B. What effect would
there be of an error in the bearing of 1o and in
the distance of 0.5m.
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At the end of this lecture students should be
able to

• Discuss what is meant by positioning data
  quality.
• Define the terms that describe the quality of
  measurement data acquired by positioning
  technologies.
• Critically assess the performance of different
  positioning technology.
• Define and give examples of the different types
  of errors in measurement data.
• Evaluate and quantify the impact of errors in
  measurements on derived quantities.