Table of Contents
Quaternion Rotate Jacobian
Computes the Jacobian of the quaternion rotation of q2 with respect to q1.
Library
QUARC Targets/Math Operations/Quaternions
Description
The Quaternion Rotate Jacobian block computes the Jacobian of the quaternion rotation, q = q1⊗q2⊗q1-1, with respect to q1. If q1 is restricted to be a unit quaternion, then it computes the Jacobian of the quaternion rotation q = q1⊗q2⊗q1*. Select which Jacobian is to be computed via the Derivative with respect to parameter. These Jacobians can be useful for computing extended Kalman filters, for example.
Let q1 = (a1, b1, c1, d1) and q = (a, b, c, d). Then the Jacobian, J, of q with respect to q1 is:
Input Ports
q1
The quaternion containing the angle and axis by which to rotate q2.
q2
The quaternion to rotate. This quaternion is typically a pure vector quaternion (zero scalar part) corresponding to a vector in 3D space.
Output Ports
J
The output is the Jacobian of the quaternion rotation q1⊗q2⊗q1-1 or q1⊗q2⊗q1*.
Data Type Support
This block accepts inputs of type double
. The block output is
of type double
.
Parameters and Dialog Box
Derivative with respect to
If this option is set to general quaternion, q1 then this block does not assume that q1 is a unit quaternion, and computes the Jacobian of q = q1⊗q2⊗q1-1.
If this option is set to unit quaternion, q1 then this block assumes that q1 is a unit quaternion, and computes the Jacobian of q = q1⊗q2⊗q1* instead.
Note that the correct scenario must be chosen because the Jacobian is not the same in the two cases because q1-1≠q1* unless q1 is a unit quaternion.
Targets
Target Name |
Compatible* |
Model Referencing |
Comments |
---|---|---|---|
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
||
Yes |
Yes |
Last fully supported in QUARC 2018. |
|
Rapid Simulation (RSIM) Target |
Yes |
Yes |
|
S-Function Target |
No |
N/A |
Old technology. Use model referencing instead. |
Normal simulation |
Yes |
Yes |
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