451200 Survey Networks Theory, Design and Testing

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451-200 Survey Networks Theory, Design and Testing

• Allison Kealy
• akealy_at_unimelb.edu.au
• Department of Geomatics
• The University of Melbourne Victoria
• 3010

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Introduction

• 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

• 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 measurments
• 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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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 measurment

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Statistical Testing Information

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

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Reliability Indicators

• Reliability is a measure of the susceptibility to
  error
• Global and local values can be computed
• Indicated by either
• Redundancy numbers
• Reliability factors
• Generally only useful for internal comparisons of
  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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Network Testing

• The 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)

• Global and local test values are influenced by
• Blunders or gross errors e.g. reading or
  transcription errors
• Systematic errors, e.g. calibration errors or
  anomalous refraction
• Precision errors, e.g. under or over estimation
  of the repeatability of an instrument or the
  influence of environmental factors

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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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Network Design

• Networks must be designed to suit
• The survey problem
• Specifications for precision and accuracy
• Expectations for reliability
• Limitations on physical access
• Restrictions placed o time and/or cost
• Availability of equipments
• Availability of staff

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Network Design (continued)

• 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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Network Design (continued)

• 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 equipments

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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 s
  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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Steps in Survey 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
• Compute values of observations from coordinates
• Compute standard deviation of measurements

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Steps in Survey Design

• 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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Conclusions

• Any survey work involves a component of network
  design and almost invariably requires testing
• Efficient and appropriate network design is a
  learned skill, supplemented by experience
• Network testing is essential to determine the
  quality of the survey
• http//www.geom.unimelb.edu.au/kealyal/200/Teachin
  g/net_design_test.html

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Survey Network Configurations

• Station coordinates can be fixed, constrained or
  free
• Good approximations for the free stations are
  necessary for convergence
• There must be sufficient measurements to
  geometrically define all the free coordinates

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Survey Network Configurations

• Assuming we have sufficient station coordinates
  and measurements to define the datum, orientation
  and scale, station coordinates are defined by the
  measurements as follows

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Survey Network Configurations

• Strength or weakness of the determination depends
  on the geometry of the relationship between the
  stations and the measurements
• Every station can be tested for the minimum
  numerical requirement to define all the
  coordinates of the station

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Externally Constrained Networks

• Assume survey networks are externally constrained
• Externally constrained networks contain
  sufficient fixed or constrained station
  coordinates to define the datum, orientation and
  scale of the networks
• Datum
• Locates network relative of coordinate system
  origin
• three coordinates fixed, one in each dimension
• Orientation
• Fix the orientation of the network relative to
  the coordinate system
• Use bearings or planimetric coordinate of another
  stations

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Externally Constrained Networks

• Scale
• Use distances to fix the scale of the network
  relative to the coordinate system
• Fix planimetric coordinates of another station
• Minimal Constraints

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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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Testing of Adjustments

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

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