Appendices
Copyright © 2015 Coda Octopus Products Ltd
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F180R MOTION Sensor User and Reference Guide
Note how the Kalman filter also solves for any errors in the GNSS antenna mount offset and
orientation. This mitigates any errors introduced when measuring the antenna offsets during
the system setup.
The position solution presented by an integrated GPS and INS system such as the F180R
System Inertial Attitude and Positioning System benefits from the following attributes:
Robust navigation solution
Low noise level
Low drift rate
High data rate
6.3
Rotation Convention
This Appendix has been provided to clarify the definitions of Heading, Pitch and Roll that are
output by the F180R System.
The F180R System 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 F180R System 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 Vn is vector V measured in the navigation co-ordinate frame and Vb is the same vector
measured in the body co-ordinate frame the two vectors are related by:
where:
ψ is the heading angle;
θ is the pitch angle;
φ is the roll angle.
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