Quaternion Product Jacobian
Computes the Jacobian of the quaternion product with respect to q1 or q2.
Library
MATLAB Command Line
Click to copy the following command line to the clipboard. Then paste it in the MATLAB Command Window:
qc_open_library('quarc_library/Math Operations/Quaternions')Description
The Quaternion Product Jacobian block computes the Jacobian of the quaternion product, q = q1⊗q2, with respect to either q1 or q2. This Jacobian 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:
The Jacobian with respect to q2 is similar. Hence, the output of the block is a 4x4 matrix where each column is the partial derivative of the quaternion product with respect to the component of q1 corresponding to that column.
Input Ports
q1
The left-hand quaternion in the product.
q2
The right-hand quaternion in the product.
Output Ports
J
The output is the Jacobian of the quaternion product q1⊗q2.
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
Selects the input quaternion with respect to which the derivative is computed. The other input is assumed to be independent.
Targets
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Target Name |
Compatible* |
Model Referencing |
Comments |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
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Yes |
Yes |
Last fully supported in QUARC 2018. |
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Rapid Simulation (RSIM) Target |
Yes |
Yes |
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S-Function Target |
No |
N/A |
Old technology. Use model referencing instead. |
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Normal simulation |
Yes |
Yes |
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