240-design.ppt

451-200 Survey Networks
Theory, Design and Testing
Allison Kealy
akealy@unimelb.edu.au
Department of Geomatics
The University of Melbourne
Victoria
3010

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.

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

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

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

Input Data
 Survey measurments
 Horizontal angles
 Vertical angles
 Distances (slope and horizontal)
 Level differences
 GPS positions and baselines
 Azimuths/bearings
 Measurement precisions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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/2
00/Teaching/net_design_test.html

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

 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 S No
Horizontal angle S S No
Vertical Angle W W S
Slope Distance S S W
Horizontal distance S S No
Height Difference No No Yes

 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 0
Horizontal angle 1 0
Vertical Angle 0 1
Slope Distance 1 0
Horizontal distance 1 0
Height Difference 0 1

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

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

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

Testing of Adjustments
 Factors affecting adjustments
 Mathematical model
 Stochastic model
 Gross errors
 Confidence intervals
 Redundant Measurements

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