11.- Repeatability

Repeatability is related to the spread of a measure, also referred to as precision. It refers to how close a position solution is to the mean of all the obtained solutions, in a static location scenario.

The difference between accuracy and precision is shown below:

Accuracy vs Precision

Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method. Source: Wikipedia.

Most common precision metrics are defined below:

Measure Formula Confidence region probability
2D 2DRMS 95 %
2D DRMS 65 %
2D CEP , if 50 %
3D 99 % SAS 99 %
3D 90 % SAS 90 %
3D MRSE 61 %
3D SEP 50 %

which are the same expressions than those defined for accuracy, but now the standard deviations are not referred to a reference value but to the mean of the obtained results:

where is the mean of all the coordinates of the obtained positioning solutions, are the East coordinates of the obtained positioning solutions, and is the number of available position fixes. Similar expressions can be defined for the North and Up coordinates:

, where , and

, where .

Example:

2D scatter plot

2D position scatter plot and the circles containing 50 %, 65 % and 95% of position fixes (corresponding to the CEP, DRMS and 2DRMS precision errors, respectively)1.

Indicators of Repeatability

It follows a list of possible repeatability indicators for a software-defined GNSS receiver:

  • Stand-alone receiver’s static positioning precision.
  • Differential GNSS static positioning precision.
  • Average convergence times to sub-metric precision.

References

  1. C. Fernández-Prades, J. Arribas and P. Closas, Turning a Television into a GNSS Receiver, in Proc. of the 26th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2013), Nashville, TN, Sep. 2013, pp. 1492 - 1507. 

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