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I am working on realising the self-navigation of a vehicle.

I have already written an extended Kalman filter with a state vector using position, velocity, Euler angle, acceleration, and angular velocity. However, I have recently read alternative papers using quaternions as a whole to represent the orientation of the body.

Are there any differences between using quaternions and using acceleration and angular velocity individually in the state vector? If there are, what is the advantage of doing that?

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2 Answers 2

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Quaternions offers 2 advantages. It mitigates the risk of gimbal lock and the math is easier for computers to handle than trig functions. Look for "Advantages of quaternions" in this wikipedia page.

Your question "Are there any differences between using quaternions and using acceleration and angular velocity ..." is confusing. You are using the accelerometer (acceleration) and gyroscope (angular velocity) now. And still will be if you change your math from using (it is assumed) trigonometry functions to using quaternions.

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  • $\begingroup$ Yes I just remembered that there was a gimbal lock issue when solely using Euler angle, and it is lethal to orientation estimate. It's a very basic pre-requisite of robotics. Thx a lot for ur answer. $\endgroup$
    – chen_441
    Mar 29, 2023 at 6:45
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Are there any differences between using quaternions and using acceleration and angular velocity individually in the state vector?

It's not either/or. A "universal" state vector would be $\vec x = \begin{bmatrix}\vec p & \vec v & \vec \theta \end{bmatrix}^T$, where $\vec \theta$ is your choice of any rotation representation, be it Euler angles, quaternions, axis + rotation, or whatever.

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  • $\begingroup$ Yea I found it right a little later after I post this question, they are just interpretations under different settings/models/others. Really thx for ur answer Tim. $\endgroup$
    – chen_441
    Apr 4, 2023 at 12:57

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