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.
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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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1. What is the difference between Euler angles and quaternions?

Euler angles and quaternions are two mathematical representations used to describe the orientation of an object in 3D space. Euler angles use three angles (usually denoted as roll, pitch, and yaw) to describe the rotations around the x, y, and z axes, respectively. Quaternions, on the other hand, use four numbers (a scalar and three imaginary components) to represent the same rotations. While Euler angles are more intuitive and easier to visualize, quaternions are more computationally efficient and do not suffer from gimbal lock, a problem that can occur with Euler angles.

2. What is gimbal lock and how does it affect Euler angles?

Gimbal lock is a phenomenon that occurs when using Euler angles to represent rotations. It happens when two of the axes align, causing the third axis to lose its freedom of movement. This can lead to unexpected and unintuitive behavior in the rotation of an object. It is important to note that quaternions do not suffer from gimbal lock.

3. How do I convert between Euler angles and quaternions?

There are various formulas and algorithms for converting between Euler angles and quaternions. One common method is to first convert the Euler angles to a rotation matrix, and then use the elements of the matrix to calculate the corresponding quaternion. Conversely, to convert from quaternions to Euler angles, the quaternion is first converted to a rotation matrix, and then the angles are extracted from the matrix.

4. Which representation should I use for my application?

The choice between Euler angles and quaternions depends on the specific needs of your application. If you require a more intuitive representation for visualization purposes, Euler angles may be a better choice. However, if your application involves a lot of complex rotations and requires efficient calculations, quaternions may be a better option.

5. How do I handle errors in Euler angles and quaternions?

Errors can occur in both Euler angles and quaternions due to various factors such as numerical precision, conversion methods, and interpolation techniques. To handle these errors, it is important to use appropriate mathematical techniques and algorithms, as well as proper error handling and validation in your code. It is also helpful to have a good understanding of the limitations and potential sources of error in both representations.

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