Positioning Application: How is Spherical Error and Plan Error calculated?

Environment/Versions

SimGEN

SimREPLAYPLUS

SimREPLAY

Answer

The SPHERICAL ERROR as determined by SimGEN is the distance between the simulated vehicle position and the position determined by the receiver under test.

The PLAN ERROR is the component of the spherical error measured in the local horizontal plane.

If the simulated position is given in the ECEF (X,Y,Z) frame by Px,Py,Pz and the receiver position by Rx, Ry, Rz then the spherical error is determined by SimGEN using the following equation. (The result will be a unit of distance)

We could also determine this parameter in the local geographic frame (North, East, Down) in which case if we locate the origin of this frame at the simulated position we get:

Where the difference in N,E,D are calculated by subtracting the reported position values from the receiver values, this gives the error in the receiver position along the North, East and Down axes respectively.

Plan error is defined in the local (North/East) plane so is given by:

From (2) we get:

Substituting this in equation (3) gives:

SimGEN uses equation (1) and equation (4) to determin the spherical and plan error by using the "P" values from the truth data and the "R" values from the data exported from the receiver.