Error in Euler angles and quaternions

In summary, the conversation is about comparing Euler angles and quaternions from the speaker's data to those from STK, and determining a suitable metric for measuring discrepancies. They are considering using RMSE or MAD as indicators.
  • #1
jonagad
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TL;DR Summary
Comparing Euler angles and quaternions from my data to STK's. Are RMSE or MAD suitable metrics for measuring discrepancies?
Hi, I got a set of Euler angles and a set of quaternions, and I wanted to compare each set against its corresponding set obtained from STK, and I was wondering what would be a good indicator to measure the error between the Euler angles I got and those from stk , and the same for quaternions, are efficient indicators like the RMSE or the MAD?
 
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  • #2
jonagad said:
TL;DR Summary: Comparing Euler angles and quaternions from my data to STK's. Are RMSE or MAD suitable metrics for measuring discrepancies?

Hi, I got a set of Euler angles and a set of quaternions, and I wanted to compare each set against its corresponding set obtained from STK, and I was wondering what would be a good indicator to measure the error between the Euler angles I got and those from stk , and the same for quaternions, are efficient indicators like the RMSE or the MAD?
For those of us less acronym-savvy, can you please define STK, RMSE and MAD?
 
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FAQ: Error in Euler angles and quaternions

What are Euler angles and quaternions?

Euler angles are a way to represent orientations using three angles, typically referred to as roll, pitch, and yaw. Quaternions are a mathematical representation used to describe rotations in three-dimensional space, consisting of one real part and three imaginary parts. Quaternions are often preferred in computational applications due to their ability to avoid gimbal lock and provide smooth interpolations.

What is gimbal lock and how do quaternions help avoid it?

Gimbal lock occurs when two of the three gimbals align, causing a loss of one degree of rotational freedom. This can happen when using Euler angles for rotation representation. Quaternions avoid gimbal lock because they represent rotations in a four-dimensional space, ensuring that all three degrees of freedom are maintained regardless of the orientation.

How do you convert between Euler angles and quaternions?

Converting between Euler angles and quaternions involves mathematical formulas. To convert Euler angles to a quaternion, you use the sine and cosine of half the angles to compute the quaternion components. Conversely, converting a quaternion to Euler angles involves calculating the angles from the quaternion components using inverse trigonometric functions. Libraries and software often provide built-in functions to handle these conversions.

What are the common sources of error when using Euler angles and quaternions?

Common sources of error include numerical precision issues, especially when dealing with very small or very large values, and the potential for accumulating errors over time. In Euler angles, gimbal lock is a significant issue, while in quaternions, normalization errors can occur if the quaternion is not kept at unit length. Proper handling and regular normalization can mitigate some of these issues.

Why might one choose quaternions over Euler angles for certain applications?

Quaternions are often chosen over Euler angles for applications requiring smooth and continuous rotations, such as in computer graphics, robotics, and aerospace. This is because quaternions avoid gimbal lock, provide more stable numerical results, and allow for easier interpolation between rotations. Euler angles are simpler to understand and use for basic rotations but can introduce complexities and errors in more advanced applications.

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