Identifying Identical Points Using Overlapping Error Ellipses

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SUMMARY

This discussion focuses on identifying identical points using overlapping error ellipses generated by least squares software. The user, Scott, encounters a challenge with two points that share identical X and Y coordinates but differ by 500 meters in elevation. The solution proposed involves creating an error ellipse for the difference between the two points to determine if zero is included, which simplifies the process if the uncertainties are uncorrelated. The complexity increases if the uncertainties are correlated, depending on the measurement methods used.

PREREQUISITES
  • Understanding of least squares software for generating coordinates
  • Familiarity with 95% error ellipses in statistical analysis
  • Knowledge of error propagation and correlation in measurements
  • Basic concepts of statistical hypothesis testing
NEXT STEPS
  • Research methods for constructing error ellipses in statistical analysis
  • Learn about error propagation techniques in least squares estimation
  • Explore statistical hypothesis testing to assess point identity
  • Investigate correlation effects on error analysis in measurement data
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and researchers involved in spatial data analysis, particularly those working with error analysis in geospatial measurements.

Scott S
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I'm not very familiar with statistics, so that's my main problem.
I use a least squares software to generate the coordinates of points and their associated 95% error ellipses. If the error ellipses meet a certain pre determined tolerance then I'm done.
However, I have a situation where I have two points which should be identical in Y and X coordinates but are 500 meters apart in elevation.
Of course the error ellipses are slightly different in size and orientation for each point.
Is there (a relatively easy to understand) method to determine if these points are identical based on the error ellipses?
I've done some research and can't find anything which relates to this particular problem.
So, any help or guidance would be greatly appreciated.
Thanks, Scott.
 
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You can make an error ellipse for the difference between the points and see if zero is included. If their individual uncertainties are uncorrelated, this process is quite easy, if not it is more complicated and it will depend on how your measurements are done.
 
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Likes   Reactions: Scott S
Ah! Nice!
Thank you very much.
 

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