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. Survey Networks: Theory, Design and Testing

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 http://www.geom.unimelb.edu.au/kealyal/200/Teaching/net_design_test.html Survey Networks: Theory, Design and Testing

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

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

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

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

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

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

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