Module 2 : Global Positioning System
  Lecture 11 : Satellite geometry and Accuracy measures
Measures for 3-D
Error Type Formula Associated Probability
Mean Radial Spherical Error (MRSE) 61%
Spherical Error Probability (SEP) 50%
It can be shown that                                  
Thus numbers indicating accuracies are meaningful if corresponding accuracy measure is listed. For example, the achievable accuracies with SPS are (Seeber, 2003)

 
Horizontal 2D Standard Deviation Quality Measures
  • Often, horizontal (2D) position, can be expressed as sigma ( σ , standard error ) values.
  • Calculated for a normal distribution of one variable (univariate). For example, σNstd. dev. of all Latitude (or Delta North) values with respect to the average Latitude (or North value).

1σN   68.3% of measured positions within 1σNvalue of average position
2σN   95.4% of measured positions within 2σNvalue of average position
3σN   99.7% of measured positions within 3σNvalue of average position.
4σN   Almost 100% of measured positions within 4σNvalue of average position.

Sigma 2D and Sigma 3D values
Defined for 2D and 3D positions respectively. Standard deviation of the 2D/3D distance values from the average position and given by the following relations

Horizontal confidence error ellipse (GPS Tutor, 1998) :
  • The probability of being within a certain region is described by confidence ellipse (2D) or confidence ellipsoid (3D) and represent an approximation of the true precision measures in all directions
  • Example : 95% horizontal error ellipse means that if the ellipse is centered on the true position, then there is a 95% chance of the estimated position lying within the boundary of the ellipse.
  • The size, shape and orientation of the a posteriori error ellipses depend on the particular satellite geometry and the stochastic modeling strategy that has been adopted.
  • In practice, they will vary slowly with time (with satellite geometry) with step changes being seen mainly at times of satellites entering, or leaving, the configuration (i.e.; rising above, or dropping below the horizon or Elevation Mask settings).
                 Confidence ellipse (GPS Tutor, 1998)
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