451200 Geomatics Science 2

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451-200 Geomatics Science 2

• Lecture 2
• Survey Network Design and Adjustment

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At the end of todays lecture students should

• Understand the goals of survey network design.
• Appreciate the benefits of survey network design.
• Know what are the variables that influence the
  survey network design.
• Know what software is available for survey
  network design.
• Understand the goals of survey network
  adjustment.
• Know what parameters are used to describe the
  adjustment output and how to interpret them.
• Know what software is available for survey
  network adjustment.

 
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Your boss gives you a survey project requiring
the determination of coordinates for a number of
points. whats the first thing you do?
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Survey network design
Whats the direction to the moon?
Straight up for six hours then turn left
Coordinates of windmill 321679.1968
.0002m 1245920.0347 0.0005m Over Surveyed?
Under surveyed?
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What do you think describes a good survey network
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Goals of survey network design

• Perform each survey in a cost effective way.
• If a survey can be performed with fewer points on
  the ground, while still meeting accuracy
  requirements, wouldn't it be beneficial? Further,
  if you could select locations on the ground that
  were easy to gain access to and make observations
  from, wouldn't that be beneficial?
• Determination of the field procedures and
  equipment needed to achieve accuracy
  requirements.
• This could be something as simple as using a more
  accurate total station, or perhaps changing your
  field procedures a bit to achieve better accuracy
  (for example, making terrestrial measurements
  during the cooler times of day, better
  instrument/target setups, making additional
  measurements, and so on).

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Goals of survey network design

• Determination of whether you should take on the
  project.
• Based on the accuracy requirements, you may
  decide that given the nature of your equipment
  and/or crew, you may not be able to meet the
  requirements and therefore should pass on the
  survey.
• Quick completion of the design.
• The network design process should require
  significantly less time than the survey itself
  otherwise, the design process may not be worth
  the effort. For medium-sized projects, a day or
  two of "what-if" analysis may be all that is
  required.

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Benefits of survey network design

• The purpose of network design is to estimate the
  confidence of your future survey, before you
  enter the field.
• The measure of confidence is a function of your
  network design.
• Network design allows you to experiment with
  different variables so as to meet or exceed the
  stated survey accuracy requirements.

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What are the factors the will affect the design
of a survey network?
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Survey network design variables

• The number and physical location of survey points
• The number and types of observations to be
  measured
• The observation standard deviations (standard
  errors) you expect to achieve in the field
• Altering any one of these variables will change
  the estimated confidence of your survey. Network
  design allows you to perform "what-if" analysis
  on these variables so that you can estimate how
  you will do in the field.

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Survey network design

• Network design allows you to achieve the first
  three goals above by providing you with estimates
  of the accuracy that will be achieved given the
  input observation types, their standard
  deviations and station locations in the survey.
  After an initial design, you may discover that
  the accuracy estimated will not meet the survey
  requirements. Using an iterative process of
  changing out the variables mentioned above, you
  may find a way to satisfy the accuracy
  requirements.
• Before bidding on a new project, you might
  initially set up an elaborate design with many
  different observation types built in. After
  running the design and satisfying the confidence
  requirements, you might then scale back the
  network with fewer stations and observations.
  After running the design again, you may happily
  discover that you are still within the accuracy
  requirements of the project, but now the project
  will cost less to perform.

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Survey network design

• Next, you might consider using only GPS for the
  project. However, after running your proposed
  network through the design process you might
  discover that a problem has emerged that cannot
  be fixed through GPS alone. In fact, you may need
  to add terrestrial observations for some portion
  of the project in order to stay within accuracy
  requirements. This might occur in an area in
  which you have poor satellite visibility or in an
  area in which the points you need to establish
  are only a few hundred meters apart. Perhaps only
  the terrestrial equipment can give you the
  accuracy you need in these areas.
• After the design is completed, you will have
  created a blueprint (of sorts) for the field
  crew. That blueprint will tell them roughly where
  to locate the stations, the types of observations
  to measure at each station, and the level of
  accuracy needed for those observations. You could
  conceivably use GPS in one section of the
  project, a 10-second total station in another
  section, and a 1- to 2-second total station in
  yet another section or the project. Through the
  use of network design, you can determine how the
  survey should proceed.

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Survey network design

• Of course, the most important element to design
  is achieving "in the field" what you designed in
  the office. If you are unable to measure angles
  to /- 5 seconds or measure distances to /-
  0.004 meters (like you specified in your design),
  then your project will probably not meet the
  expectations derived from design. Bottom line
  Don't be overly optimistic about what you can
  achieve in the field.

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Survey network design

• Network design is part experience and part
  science
• Experience comes from practiced knowledge of
  network types, error propagation and geometry
• Scientific analysis comes from the interpretation
  of error ellipses and other indicators of network
  quality

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Steps in survey network design

• Using available information lay out possible
  positions of stations
• Check line of sights
• Do field recce and adjust positions of stations
• Determine approximate coordinates
• Perform least square adjustment, to compute
  observational redundancy numbers, standard
  deviations of coordinates and error ellipses
• Inspect the solution for weak areas based on
  redundancy numbers and ellipse shapes
• Evaluate cost of survey
• Write specification

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Effects of survey network design
1km
17 distance measured sd (2mm2ppm of D) BD
1000m
1.5km
17 horizontal angles measured ss 5
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Name S-Maj A .004 C
.007 E .004 F .003 G
.003
Name S-Maj A .017 C
.022 E .017 F .013 G
.016
Name S-Maj A .003 C
.006 E .003 F .003 G
.003
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Name S-Maj A .007 B
.006 E .006 F .004 G
.003
Name S-Maj A .031 B
.026 E .029 F .024 G
.017
Name S-Maj A .006 B
.005 E .005 F .004 G
.003
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Name S-Maj A .004 C
.007 E .004 F .003 G
.003
Name S-Maj A .069 C
.156 E .114 F .077 G
.106
Name S-Maj A .004 C
.006 E .004 F .003 G
.003
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So what do we get from the survey network design
process?

• What quality observations you need, eg 1 or 3.
  This tells you what type of instruments and
  techniques to adopt.
• How many times you need to repeat each
  measurement.
• What shape your network should be and what lines
  to observe.

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Class example
 
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Survey network design

• Basic network types comprise
• Level networks
• Resection
• Intersection
• Control traverse
• Control networks
• The choice of type is primarily based on the
  survey problem, specifications for
  precision/accuracy and available equipment

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Level network

• Measurement data is level differences only
• All horizontal angles must be fixed
• At least one station height must be fixed to set
  the vertical datum
• Level differences are typically set proportional
  to the square root of the run length

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Resection

• Measurement data is horizontal angles only
• All coordinates of the resection targets must be
  held fixed
• The height of the instrument station must be held
  fixed
• Horizontal angle precisions are set from the
  standard deviations of the means of the multiple
  rounds of observations

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Control Traverse

• Measurement data is horizontal and vertical
  angles, distances and perhaps level differences
• At least one known control station and one
  reference object are needed
• Precision data may be estimated from experience
  or adopted from instrument specifications

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Control Networks

• All measurement data types
• At least one control station and one reference
  object needed
• Precision data may be estimated from experience,
  adopted from the instrument specifications or
  computed
• High numerical and geometric redundancies leading
  to very high reliabilities

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Survey network adjustment

• Survey network adjustment is also known as
• Variation of coordinates
• Least squares adjustment
• Least squares estimation
• Survey adjustment
• Use routinely for survey computations.

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Advantages of network adjustment

• Networks adjustment is widely adopted due to
• Consistent treatment of redundant measurements
• Rigorous processing of measurement variability
• Ability to statistically test and analyse the
  results

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Implementations

• Many commercial and proprietary network
  adjustment packages are available
• SkiPro
• CompNET
• StarNet
• TDVC, DNA
• Wide variation in ease of use, sophistication and
  available features

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Non-Network Adjustment

• Coordinate geometry computations
• Also known as COGO packages
• Simple 2D or 3D geometry computations for
  radiations, intersections etc
• Traverse adjustment
• Known as Bowditch or traverse rules
• Valid method of distributing errors
• Not statistically rigorous

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Input data

• Survey measurements
• Horizontal angles
• Vertical angles
• Distances (slope and horizontal)
• Level differences
• GPS positions and baselines
• Azimuths/bearings
• Measurement precisions

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Input data (continued)

• Fixed and adjustable coordinate indicators
• Known coordinates of unknown stations
• Approximate coordinates of unknown stations
• Auxiliary data such as
• Coordinate system and datum
• Atmospheric refraction
• Default values for precisions etc

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Algorithm functional model

• Describe the geometric relationship between
  measurements and stations
• Very well understood for conventional
  measurements
• GPS knowledge well established
• Sets the response of station positions to
  different measurement types

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Algorithm stochastic model

• Models the statistical properties of the
  measurements
• Assumes a Gaussian or normal distribution
  function of random error
• Effectively a weighting of the importance of
  different measurements based on precision data
• Precision levels are often not well estimated

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Testing of adjustments

• Factors affecting adjustments
• Mathematical model
• Stochastic model
• Gross errors
• Confidence intervals
• Redundant Measurements

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Network analysis

• Analysis of the results of survey networks is
  essential
• Assessment of station coordinate precisions
  against specifications is often first priority
• Networks may also be tested for accuracy if
  suitable independent checks are available
• Testing of networks for gross errors and other
  factors is mandatory

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Results output

• Adjusted coordinates for all stations
• Precision of all coordinates
• Error ellipses for all stations
• Adjusted measurements
• Measurement residuals
• Differences between the measured and adjusted
  values for any measurement

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Network testing

• Global and local statistical tests are conducted
• An estimate of the variance factor is used as a
  global test of the entire survey network
• Individual measurements are locally tested
  against the student t distribution
• Both test distributions are independent of the
  number of redundancies in the network
• The confidence of the testing improves with
  higher redundancy numbers

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Network testing (continued)

• An initial global test is required to determine
  the likelihood of errors in individual
  measurements
• Local errors are tested, de-activating the
  measurements with the worst t statistic and
  re-processing the adjustment
• Measurements are deactivated until all local
  tests are acceptable or the point of diminishing
  returns is reached
• If the global test still fails then systematic or
  precision errors are investigated

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Statistical testing information

• Unit weight precision
• Also known as variance factor, sigma zero (s0)
• Squared quantity known as estimate of the
  variance factor or unit weight variance
• Indicates overall or global quality of the
  solution
• Should be close to 1
• t statistics for each measurement
• Indicates local quality of individual measurements

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Reasons for variance factor to fail

• Typing error in input
• Have you left out some observations
• Are enough parameters held fixed
• Gross error in observations
• Screening of observations
• Use t statistic
• Use residual analysis
• Model error
• Use residual analysis
• Poor estimate of quality
• If s0 is too small input s too large
• If s0 is too large input s too small
• Error in the least squares program

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Reliability indicators

• Reliability is a measure of the susceptibility to
  error
• Internal and external values can be computed
• Indicated by either
• Redundancy numbers
• Reliability factors
• Generally only useful for internal comparisons of
  measurements

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Externally constrained networks

• Externally constrained networks contain
  sufficient fixed or constrained station
  coordinates to define the datum, orientation and
  scale of the network.
• The first external constraint is the network
  datum. Any externally constrained network must
  have at least three coordinates fixed or
  constrained, one in each dimension. This minimum
  information determines the location of the
  network relative to the coordinate origin.
  Typically, the three coordinates are of a single
  station, but this is not mandatory.
• The second external constraint is the orientation
  of the network. Orientation may be supplied by
  measurements such as base lines, which implicitly
  fix the orientation of the network relative to
  the coordinate system. Alternatively, a
  planimetric coordinate of another station must be
  explicitly fixed or constrained. The choice of
  the station and coordinate should be governed by
  the geometry of the network.
• The third external constraint is the scale of the
  network. Scale may be supplied by measurements
  such as base lines or distances, which implicitly
  fix the scale of the network relative to the
  coordinate system. Alternatively, another
  planimetric coordinate of another station must be
  fixed or constrained. The choice of the station
  and coordinate should again be governed by the
  geometry of the network. Typically, this leads to
  the situation where the planimetric coordinates
  of two stations are fixed or constrained, which
  effectively fixes the orientation and length of
  one line in the network.

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Externally constrained networks

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Minimally constrained networks

• The information given in the third column of the
  table is the minimal constraints in each case.
  This is the minimum number of coordinates which
  must be fixed or constrained to satisfy the
  requirements. The minimal constraint concept is
  useful for networks which must be free of any
  distortion which might be imposed by multiple
  external constraints.
• The provision of additional fixed or constrained
  coordinates will improve the definition of the
  datum, orientation and scale as appropriate. This
  will lead to a more precise and reliable network,
  but may introduce distortions if the fixed or
  constrained coordinates are not accurate.

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Free networks

• Free or internally constrained
• All stations open to adjustment
• Based on initial coordinates of stations
• Datum, scale and orientation arbitrary

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Class example
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At the end of todays lecture students should

• Understand the goals of survey network design.
• Appreciate the benefits of survey network design.
• Know what are the variables that influence the
  survey network design.
• Know what software is available for survey
  network design.
• Understand the goals of survey network
  adjustment.
• Know what parameters are used to describe the
  adjustment output and how to interpret them.
• Know what software is available for survey
  network adjustment.