Application of UKF on quaternions I'm trying to perform a state estimation on quaternions to predict the future orientation of a human head. The only sensor data I can obtain (from the AR headset) is the current orientation of the head, sampled at 200 Hz i.e. I don't have access to any gyroscope or acceloremeter data. After getting the state estimations, I would like to reuse the process/motion model (constant angular velocity) to make predictions further into the future, e.g. 20 ms to 100 ms. 

Since the process model is nonlinear (due to quaternions), one option is to use an Unscented Kalman Filter (UKF). However, as discussed in this paper, quaternions cannot be directly used in the UKF and some conversions need to be made to obtain "quaternion sigma points" (Sec. 3.2 of the paper).

My question is, does it make sense at all to use this kind of method if I only have attitude measurements (quaternions) and no gyro or acceloremeter data? In this case, my state vector would be 7D: four quaternion and three angular velocity components. However, the paper (and most other works I encountered) always have some kind of gyro/acceloremeter measurements which makes me wonder if it's feasible to just have the attitude information and have the filter estimate the angular velocity.
Yes, it's perfectly possible.  All that you'll need is to model how you think the angular velocity components of the state will evolve.  Usually simple brownian (random) motion is enough, at least to start with.  If you know more about how the angular velocities are constrained, then you can include that in the model.

All that it means is there are no outputs from your signal model directly from those elements of the state.

For example, in this answer to another question the state is made up of the $x$ position and the $x$ velocity, but there is no velocity measurement.  

$$
\begin{align*}
\mathbf{x}_{k}  &amp; =\left(\begin{array}[c]{c}x_{k}\\
\dot{x}_{k}\end{array}
\right)  
\end{align*}
$$

All that means is the output matrix $H$ zeros out that part of the state when producing the measurement.