Network Least Squares Adjustments Demystified.ppt [Read-Only]

12/29/2014 Network Least Squares Adjustments Demystified By Bruce Carlson and Dean Goodman Carlson Software Course Outline Measurement Errors Adjustments Averaging Traditional Adjustments Least Squares Adjustment Advantages of LSA Creating a Project in SurvNET Sample traverse project in Carlson SurvNET Processing unique datasets Types of Errors Error propagation Traverse networks Traverses with triangulation/resection data GPS Vectors Combination of Traverse/GPS data ALTA Surveys Certifications Relative error ellipses 1

12/29/2014 Surveyors make measurements One aspect of a land surveyor’s job is to make measurements. There are no perfect measurements, all measurements have errors. Errors are inherent in the instrumentation we use. A 5” instrument measures angles to - 5”. An EDM may measures distances to - 0.01’ and 3PPM. Types of Errors There are three classifications of errors: Blunders Systematic Errors Random Errors 2

12/29/2014 Blunders Blunders are mistakes and cannot be adjusted. Blunders MUST be removed from the data set prior to adjustment. Examples of Blunders: Failure to level the instrument. Failure to put the instrument or target over the point. Assigning the wrong point number to a point. Instrumentation out of adjustment. Recording the wrong measurement. Systematic Errors Systematic Errors are predictable errors and should be removed from the dataset prior to adjustment. Examples of systematic errors: Atmospheric corrections – temperature, and pressure. Curvature and Refraction corrections. Wrong prism constant 3

12/29/2014 Random Errors Random errors are errors inherent in the instrumentation used to make the measurement. A theodolite may measure to a - five second precision. An EDM may measure to 0.01 feet plus 3 PPM You can only set your instrument over a point to a - 0.01 feet accuracy. You can only measure from the point to the height of instrument to a - 0.01’ accuracy. Random errors can be adjusted out of the traverse. Error Propagation Random errors propagate throughout the traverse. Errors can accumulate, cancel or decrease. Prior to a least squares adjustments, each measurement is assigned an initial standard error based on the equipment specifications. Error propagation can then be predicted using statistical, mathematical models. 4

12/29/2014 Error Propagation As you traverse further from known control points, the less you know your position. The next slide shows the error ellipses of a traverse with one control point. 5

12/29/2014 Error Propagation Error ellipses increase as you get further from a known point. The next slide shows the error ellipses of the same traverse with two known points, 6

12/29/2014 Error Propagation Additional control points and redundant measurements add strength to the traverse and make the statistics more meaningful. GPS can be used to add additional control. Traverse densification and measurements to points from different locations can add redundancy to the traverse. Triangulation can also be useful in adding redundancy. Adjustments Why do we adjust traverses? All traverses have errors; they do not close exactly on the terminal point. If we do not adjust the traverse, all the error is placed in the last leg of the traverse which is not a valid assumption. Error adjustments are important to future work on a project. Placing all the error in one measurement can prove problematic for both project design and layout. 7

12/29/2014 Averaging Averaging is a type of adjustment. We average SETS of angles measured in both direct and reverse faces: For additional precision (Sm S / N) Standard deviation of the mean equals the standard deviation of the single measurement divided by the square root of the number of measurements. As a check against blunders To help remove instrument errors We average distances and zenith angles measured in both faces and in both directions: For additional precision To help remove instrument errors To mitigate curvature and refraction errors To improve vertical closures. Traditional Adjustments Prior to the advent of high powered computers, when only calculators or hand calculations were used, there were three popular adjustments: Transit Rule Crandall’s Rule Compass Rule Typically angles were balanced prior to adjusting the traverse with these methods. 8

12/29/2014 Crandall’s Rule Crandall’ Rule is a “special case” least squares adjustment. Crandall’s Rule assumes there is NO error in the angles – angles/directions are assigned an infinite weight. Therefore, adjustments are made only to distances. This adjustment was typically used to match bearings with previous surveys but under certain conditions can give unexpected results. The assumption that angles contain no error is not a valid assumption. Transit Rule Transit Rule adjusts both angles and distances but makes the assumption that angles are measured with a higher precision than distances. This assumption may have been valid in the past when using a 10” theodolite for angles while pulling a chain for distances, but it is not valid for today’s measuring equipment. 9

12/29/2014 Compass Rule The Compass Rule assumes both angles and distances are measured with equal precision. Of the traditional adjustments, this assumption is most valid for today’s measuring equipment. The Compass Rule remains a very popular form of adjustment by surveyors but has distinct disadvantages when compared to Least Squares Adjustments. What is Least Squares? Least squares is a statistical method used to compute a best-fit solution for a mathematical model when there are excess measurements of certain variables making up the mathematical model. Least squares requires a mathematical model, a system of equations. It requires redundant measurements of one or more variables (the known variables). Lastly it requires variables that are unknown that are being solved for. The least squares criteria is reached when the sum of the squares of the residuals have been minimized. Least Squares Adjustment applies the least possible amount of correction when adjusting the measurements which arguably makes it the best adjustment. 10

12/29/2014 Advantages of LSA It allows the simultaneous adjustment of a network of traverses. Traditional adjustments can only adjust one traverse at a time. It allows the combined adjustment of traverse data, GPS data and level data – 1D, 2D or 3D adjustments. It allows complete control of the adjustment process. Measurements are weighted based on the equipment used and the number of measurements made. Advantages of LSA It allows processing data of different precision – weights can be applied to individual measurements or groups of measurements. It allows flexible control. The control points can be anywhere in the traverse, you don’t need to start on a known point. Control points do not have to be contiguous and they can be side-shots. It can handle resection data (measurements from an unknown point to known points), triangulation (angleonly measurements) and trilateration (distance-only measurements). 11

12/29/2014 Advantages of LSA Automatic reduction to State Plane Coordinate systems if desired. Extensive data analysis provides more information for evaluation of traverse networks. Enhanced blunder detection tools. Allows flexible field procedures; the data does not have to be in any specific order. Provides tools for ALTA or State survey certifications. Common misconceptions of LSA Least Squares Adjustments are just too complicated. Reports are intuitive and easily understood Flexibility of LSA makes processing of difficult datasets easy. Least Squares Adjustments are only necessary for very precise surveys. LSA can and should be used for any type survey. LSA can be used for simple loop traverses as well as complex traverse networks. 12

12/29/2014 Creating a Project in SurvNET Choose a coordinate system Select data files to be processed Enter pre-processing settings Enter preliminary standard errors Select adjustment and output options Define control points (known points) Process data Analyze report 13

12/29/2014 Coordinate System Select the adjustment model Choose the type coordinate system for your project Local (assumed) NAD83 State Plane NAD27 State Plane UTM User defined 14

12/29/2014 Input Data Files Select the data files to be processed Multiple files of each type can be selected Traverse data files GPS Vector data files Differential/Trig Level files 15

12/29/2014 Preprocessing Select the preprocessing settings Curvature and Refraction corrections Point Substitution feature Measurement tolerances Closure computation 16

12/29/2014 Standard Errors Select preliminary standard errors for measurement weighting Standard errors should reflect the realistic error expectations for the equipment used Distance errors Angle errors Setup errors Control errors Leveling and GPS errors 17

12/29/2014 Adjustment Settings Number of iterations to perform prior to showing convergence error Confidence Interval for statistical analysis ALTA certifications Select connections for relative error ellipse calculations 18

12/29/2014 Output Options Output rounding options Units Output coordinate file Optional coordinate file for ground coordinates Sample Traverse Network Sample Least Squares Adjustment project presented using Carlson SurvNET software See project PARK.PRJ 19

12/29/2014 Processing Unique Datasets Least Squares adjustments can process data that the traditional methods of adjustment cannot Traverses with non-contiguous control points Networks of Traverses Triangulation Total Station Traverse with GPS vectors 20

12/29/2014 Non-contiguous control points See SEP1.PRJ and SEP2.PRJ 21

12/29/2014 Traverse Networks See N DRUIDH.PRJ and DEANPROP.PRJ 22

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12/29/2014 Traverse with Triangulation See NORTHLN6.PRJ 24

12/29/2014 GPS Vectors See “CC&V Control.prj” 25

12/29/2014 Traverse combined with GPS vectors See M07052.PRJ 26

12/29/2014 ALTA and Kentucky Survey Standards ALTA Title Surveys require that the surveyor make the following Certification: The relative positional precision between any two property corners shown on the survey shall be within 0.07 of a foot plus 50 parts per million at a 95% confidence level This certification requires the statistical model produced by a least squares adjustment. 27

12/29/2014 What is Relative Positional Precision? 2011 ALTA Standards 28

12/29/2014 Kentucky Survey Standards The Kentucky Survey Standards as stated in KAR 18:150 are similar to the ALTA standards we just discussed. KAR 18:150 Standards of Practice 29

12/29/2014 KAR 18:150 Standards of Practice KAR 18:150 Standards of Practice 30

12/29/2014 Relative Error Ellipses The determination of the Relative Positional Precision between any two points requires the calculation of the relative error ellipse between the points Relative error ellipses are confidence regions established for the coordinate difference between any two points. This is not the same thing as an error ellipse. Error ellipses are the measure of the positional error of a point. It is defined by an ellipse which is defined by a semi-major axis and semi-minor axis., and the direction of the maximum error. Sample ALTA Survey Project Sample ALTA Survey project presented using Carlson SurvNET See project ALTA.PRJ 31

12/29/2014 Thank you for your attention 32

12/29/2014 2 Surveyors make measurements One aspect of a land surveyor's job is to make measurements. There are no perfect measurements, all measurements have errors. Errors are inherent in the instrumentation we use. A 5" instrument measures angles to - 5". An EDM may measures distances to - 0.01' and 3PPM. Types of Errors There are three classifications of