1. 451-200 Survey Networks Theory, Design and Testing
Allison Kealy
Department of Geomatics
The University of Melbourne Victoria
3010

2. Survey Networks: Theory, Design and Testing
Introduction
Survey network adjustment is also known as
Variation of coordinates
Least squares adjustment
Least squares estimation
Survey adjustment
Use routinely for survey computations.
Survey Networks: Theory, Design and Testing

3. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

4. Survey Networks: Theory, Design and Testing
Implementations
Many commercial and proprietary network adjustment packages are available
SkiPro
CompNET
Star*Net
TDVC, DNA
Wide variation in ease of use, sophistication and available features
Survey Networks: Theory, Design and Testing

5. 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
Survey Networks: Theory, Design and Testing

6. Survey Networks: Theory, Design and Testing
Input Data
Survey measurments
Horizontal angles
Vertical angles
Distances (slope and horizontal)
Level differences
GPS positions and baselines
Azimuths/bearings
Measurement precisions
Survey Networks: Theory, Design and Testing

7. 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
Survey Networks: Theory, Design and Testing

8. 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
Survey Networks: Theory, Design and Testing

9. 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
Survey Networks: Theory, Design and Testing

10. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

11. 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
Survey Networks: Theory, Design and Testing

12. 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
Survey Networks: Theory, Design and Testing

13. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

14. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

15. 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
Survey Networks: Theory, Design and Testing

16. 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
Survey Networks: Theory, Design and Testing

17. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

18. 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
Survey Networks: Theory, Design and Testing

19. 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
Survey Networks: Theory, Design and Testing

20. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

21. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

22. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

23. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

24. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

25. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

26. Survey Networks: Theory, Design and Testing
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
Survey Networks: Theory, Design and Testing

27. 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
Survey Networks: Theory, Design and Testing

28. 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:
Measurement type X Y H
Bearing S No
Horizontal angle
Vertical Angle W
Slope Distance
Horizontal distance
Height Difference
Yes
Survey Networks: Theory, Design and Testing

29. 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
Measurement type
Planimetric
height
Bearing 1
Horizontal angle
Vertical Angle
Slope Distance
Horizontal distance
Height Difference
Survey Networks: Theory, Design and Testing

30. 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
Survey Networks: Theory, Design and Testing

31. 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
Survey Networks: Theory, Design and Testing

32. Survey Networks: Theory, Design and Testing
Free Networks
Free or internally constrained
All stations open to adjustment
Based on initial coordinates of stations
Datum, scale and orientation arbitrary
Survey Networks: Theory, Design and Testing

33. Testing of Adjustments
Factors affecting adjustments
Mathematical model
Stochastic model
Gross errors
Confidence intervals
Redundant Measurements
Survey Networks: Theory, Design and Testing