21 January 2008 SURVEY Subject Trimble Survey Controller Software: Design of the Backsight Point Configuration Product(s) Trimble® S6 Total Station, Trimble VXTM Spatial Station, 5600 total station Question Does the configuration of the backsight points affect the resection result? Answer Yes. This document explains how to achieve the resection objectives by meeting some additional pre-requisites with the design of the backsight points, beside the general ones mentioned in Trimble Survey Controller Software: Purpose, Advantage, and Objective of Resection Setup.When you design a backsight point configuration, take note of the following:A reliable stationing result is the main pre-requisite for topo measurement and stakeout. The design must guarantee that the grid conditions are well represented by the chosen backsight points. The backsight points should cover and surround the stationing site. This is the area where you want to measure with this station setup. You should not measure any topo points or stakeout points outside this area - if you do this, the errors in orientation (and scale factor) will be extrapolated instead of being interpolated. The backsight points should be well distributed around the horizon. A one-sided accumulation (like the points around BP1) does not improve the result (even though redundancy may show an improvement).  The backsight points should be positioned in the neighborhood. Targets that are far away are not suitable, because you would carry grid conditions from regions far away from the stationing site into this area. Avoid backsight points with distances that are too short. This is not suitable for the calculation of reliable orientation and scale factor parameters as this will lead to extrapolations of errors. Additional backsight points in the middle of the stationing area are useful to recognize constraints in the network. The following examples illustrate the backsight-point design: The colored areas indicate where topo points or stakeout points can be measured when 2, 3, or 4 backsight points are measured:     At least 2 backsight points are necessary to obtain a solution. However, the disadvantages when you use only 2 backsight points are obvious:Only measurements on the line between the 2 points are reliable. If the distance between the 2 points becomes larger, this is not valid implicitly. If you measure outside the colored area, the measurements are not reliable, because the network accuracy and reliability in this area is unknown.This is also valid when the backsight points are of a high accuracy. ExampleThe following example demonstrates the accuracy within and outside the colored area: Assume 4 backsight points. All backsight points may be located on a radius 1 around the center point of all backsight points. This must not be the station point.  Where:Blue circle - backsight pointYellow circle - center points of all backsight pointsYou can now determine:What is the accuracy within the area with radius 1? What is the accuracy outside this area?The answer relates to the station coordinates and for topo points in these areas. These are shown in the following graphic:  Where:The lines in the graph give an indication about the expected accuracy: The red lines represent the station point and the blue lines represent topo points. The three lines (mathematically these curves are of hyperbola type) are for configurations with 2, 3, or 4 backsight points. The units on the horizontal axis are the radial distances. The units on the vertical axis are related to the standard deviation of unit weight. You can now see the following:A point located in the center point of the backsight point will have the highest accuracy (lowest standard deviation) for its coordinates. The amount of the minimum error depends on the number of backsight points and the amount of the standard deviation of the unit weight. Starting from this center point, the standard deviations of the points increase radially. Within the area defined by the backsight points (R=1), there is only a slight rise in the standard deviations, but when measuring outside this area you can recognize a stronger rise. The standard deviation of the station point coordinates increases more than that of the topo point. Therefore, the quality of the topo point does not depend on either the accuracy of the station point or on the azimuth. Conclusions Station points could be located outside the area surrounded by the backsight points. Topo points and stakeout points should be measured inside this area only. With additional backsight points there is only a slight improvement in the accuracy. **NOTE -**These error laws are valid only for error-free backsight points. The problem arising when backsight points have got a lower accuracy will be discussed in Trimble Survey Controller Software: The Influence of Weights in Resections. Related Articles Trimble Survey Controller: Purpose, Advantage And Objective Of Resection SetupTrimble Survey Controller: Advantages Of Redundancy In Station SetupTrimble Survey Controller: Influence Of Centering Accuracy In Station Setup ProgramsTrimble Survey Controller: Problems In Resection Without RedundancyTrimble Survey Controller: Task Of The Stationing ProgramsTrimble Survey Controller: Orientation Parameter In Station SetupTrimble Survey Controller: The Accuracy Of Orientation In Station SetupTrimble Survey Controller: Scale Factor In Station SetupTrimble Survey Controller: The Accuracy Of Scale Factor In Station SetupTrimble Survey Controller: The Influence of Weights in Resections This document is for informational purposes only and is not a legally binding agreement or offer. Trimble makes no warranties and assumes no obligations or liabilities hereunder. If you have questions related to this document, please reply to Global_Services@trimble.com © 2008, Trimble Navigation Limited. All rights reserved. Trimble and the Globe & Triangle logo are trademarks of Trimble Navigation Limited registered in the United States and in other countries. Trimble Survey Controller and VX are trademarks of Trimble Navigation Limited. All other trademarks are the property of their respective owners. |
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