*Limitations*

The magnitude of error compensation does scale with respect to total fixation duration and amount of stationary motion phases. However, the solution does not reduce the effect during dynamic motion phases, since it does not directly estimate and correct the dc-bias term of the raw gyroscope signal. This is due to various other noise effects that are present in the raw gyroscope signal. Main noise terms among other that influence the in-run dc-bias estimation are ac-noise, oscillating head motion, output rate limitations and possible desynchronization between timestamps of both systems.

When estimating in-run dc-bias the presence of these noise terms can lead to a wrong estimation. Since the dc-bias is subtracted from the raw gyroscope signal at every time step, it effects the complete measurement from that point forward and might result in a worse heading estimate. However, if a sufficient amount of sensor data has been gathered, a low-pass filtered dc-bias estimation might be used to reduce the drift at a smaller scale since the data are only captured during near stationary motion phases and therefore restrain heavy amplitude changes.

The proposed solution can be affected by very slow motion acceleration triggering the visual fixation detection plugin and falsely labeling a static phases. This effect however only appears if the resulting angular rate of the head motion is smaller than the angular rate constraint derived from the dispersion and time threshold of the fixation detection plugin and stays below the median angular rate threshold that is sampled throughout the trial. In this work the angular rate constraint from the fixation detection plugin that might lead to a wrong classification during fixation and simulatanious head motion is 0.95 ◦ *s* for a 220 ms measurement window. This angular rate results in the maximum dispersion of 0.21◦. This would result in a fixation detection which would in turn trigger the zero rotation update mechanism for one cycle. After this the dispersion threshold is exceeded, setting the trigger to false which in turn resets the online fixation detection sliding window.

#### **8. Future Work**

Future research will focus on adaptive gyroscope noise parameter estimation based on the proposed visual fixation trigger for head motion detection. The gyroscope noise parameter estimation can be used to reduce the heading errors even further and without the visual fixation trigger being active. While a sufficient amount of samples is gathered during visual fixations an adapted noise parameter can be estimated and used to identify no motion phases just as the visual fixation trigger. A second instance of the filter running in parallel could be used to compute orientation that includes the estimated gyroscope noise and compare it to the first instance of the filter in real-time. Based on the deviation between both solutions, the estimated bias could be used or discarded from that point on which in turn will lead to improved heading accuracy. Advanced parameter specification of the

proposed fusion method will be explored by a broader set of experiments, including experiments in real use cases, multiple age varying paticipants as well as the influence of gyroscope noise parameter estimation on the proposed method.

**Author Contributions:** Conceptualization, L.W.; methodology, L.W.; software, L.W.; validation, L.W., and M.G.; formal analysis, L.W..; investigation, L.W. and M.G.; resources, M.G.; data curation, L.W.; writing–original draft preparation, L.W..; writing–review and editing, L.W. and M.G.; visualization, L.W.; supervision, M.G.; project administration, M.G.; funding acquisition, M.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Federal Ministry of Education and Research of Germany gran<sup>t</sup> number 13FH011IX6. We acknowledge support by the Open Access Publication Fund of the Westfälische Hochschule, University of Applied Sciences.

**Conflicts of Interest:** The authors declare no conflict of interest.
