OXTS RT3000 v4 - Using Orientation Measurements; Definitions of Heading, Pitch, and Roll

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Appendix B – Using the orientation measurements
This section has been provided to clarify the definitions of heading, pitch and roll that are output by the RT.
The RT 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 RT 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(y)
-sin(y)
0
cos(q)
0
sin(q)
1
0
0
V
n
=
sin(y)
cos(y)
0
.
0
1
0
.
0
cos(f)
-sin(f)
.
V
b
0 0 1 -sin(q) 0 cos(q) 0 sin(f) cos(f)
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.