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Test of Known Points (Global Test)

Similarly to how we use gross error detection to identify gross errors in observations, we aim to find errors in the basis coordinates. Large adjustment corrections indicate that something is wrong, but not what - it could be due to either the observations or the basis coordinates.

Testing Process

Gross error detection, where we discard observations, is based on a free adjustment where the constraint in the basis network is eliminated. After all detectable errors are corrected or the observation is discarded, we can proceed to testing the basis. The key question now is whether the basis network is consistent with the observations.

To answer this question, a test of known points (global test) is performed:

  • Comparison of the error square sum from free adjustment with the error square sum after constrained adjustment
  • Execution of a statistical F-test to determine if we can detect constraint in the network

Info

If constraint is detected, we must locate where it is. Which points are causing the constraint?

Gemini Terrain releases the basis points one by one. The point that improves the error square sum the most becomes a candidate for release, and a new Global Test is performed with this point free. The process continues until the Global Test is satisfied, meaning we can no longer detect constraint in the network.

Test of Changes

After testing the basis points, we are left with released points that at a given significance level can be claimed to be incorrect.

Warning

A point can be rejected without the new coordinates necessarily being better than the old ones.

Figure: A = Old position, B = New position

We must therefore test whether the new coordinates are preferable. The figure illustrates this clearly:

  1. We imagine that the standard deviation in the direction of the old position is replaced with a confidence interval
  2. If the "true position" should be at point P, we want to use the coordinates of the point that is closest
  3. We must therefore prove with the desired degree of confidence that the new position is actually closer to the "true position" than the old one
  4. Only when this is confirmed do we use the new coordinates

Note

Test of changes runs automatically after the global test is completed. You will be asked whether you want to run test of changes after the global test is finished.