OXTS Survey+ v3, User Manual, Page: 94 / 103

94
Oxford Technical Solutions
Using the orientation measurements
This section has been provided to clarify the definitions of heading, pitch and roll that are
output by the .
The uses quaternions internally to avoid the problems of singularities and to
minimise numerical drift on the attitude integration. Euler angles are used to output the
heading, pitch and roll, and these have singularities at two orientations. The has
rules to avoid problems when operating close to the singularities; if you regenerate the
rotation matrices given below then they will be correct.
The Euler angles output are three consecutive rotations (first heading, then pitch and finally
roll) that transform a vector measured in the navigation co-ordinate frame to the body co-
ordinate frame. The navigation co-ordinate frame is the orientation on the earth at your
current location with axes of north, east and down.
If
V n
is vector
V
measured in the navigation co-ordinate frame and
V b
is the same
vector measured in the body co-ordinate frame the two vectors are related by:
V n C bn

V b
cos(

)
V n
sin(  )
0
sin(

)
cos(  )
0
0
cos(

)
0

0
1
sin(  )
0
sin(

)
1 0
0
cos(  )
1 0

0
cos(

)
0
sin(  )
0
sin(

)
cos(  )

V b
where:

is the heading angle;

is the pitch angle and
 is the roll angle.
Remember – heading, pitch and roll are usually output in degrees, but the functions sin
and
cos
require these values in radians.