Dear Maximilian Nitsch,

I suggest you to see links and attached file on topic.

Article Quaternion-Based Robust Attitude Estimation Using an Adaptiv...

Conference Paper Application of UKF for MEMS IMUs and Fluxgate Sensors Based ...

Article Accurate Attitude Determination Based on Adaptive UKF and RB...

Article An adaptive unscented Kalman filter for quaternion-based ori...

Best regards

Hello Maximilian Nitsch

I think this paper can help https://kodlab.seas.upenn.edu/uploads/Arun/UKFpaper.pdf

Regards

In addition to above references, you may see the paper (attached)

Crassidis, J. L., and Markley, F. L., Unscented Filtering for Spacecraft Attitude Estimation," AIAA Conference Paper 2003

and their book

Markley, F. L., and Crassidis, J. L., Fundamentals of Spacecraft Attitude Determination and Control, Springer 2014

The following book should also be useful:

Farrell, J. A., Aided Navigation, McGraw-Hill 2008, Ch. 10 AHRS

Best wishes

Hari Hablani

IIT Indore, Indore, India

Hello Maximilian Nitsch ,

As far as I know, there is currently no papers that solving or even approaching this problem. That is why I cannot recommend any article where you can directly find the answer to your question. However, this is a question that I have asked myself, and although I have not even gotten to implement it, I have thought about the way I would do it.

The problem lies in the way you define the mean and the covariance matrix of your distribution of unit quaternions, because the Kalman update must be performed in the same space in which such quantities are defined. Since the only quaternions that represent orientations are the unit quaternions, defining the covariance matrix in R4 leads to problems when applying the Kalman filter. I would approach the problem using the following strategy:

1. I would find the expression of the measured quaternion in a chart (this is your measurement).

2. I would predict the measurement on the same chart (the matrices S and R that define the covariance matrix of your measurement prediction, and of the measurement itself respectively, will be expressed in the chart you chose).

3. I would apply the Kalman filter normally in this "euclidean" space (the chart).

To understand the concept of "chart" and how it appears and acquires importance when dealing with unit quaternions in the Kalman filter, I recommend an article that I wrote, and which in my opinion deals with these issues from another more rigorous perspective than the error formulation for the kalman filter:

Article Kalman Filtering for Attitude Estimation with Quaternions an...

The paper is open access. If you read it, you will learn that the strategy you mentioned/proposed in your question (using an alternative representation for the orientation, such as the rotation vector) is closely related to the approach I am suggesting.

I hope you find this information useful, and that it helps you find a satisfactory answer to your question.