**5. Conclusions and Future Work**

In this study, we compared four different algorithms with respect to their performance on stride length and mean average velocity per stride calculation for running. We conducted two studies to evaluate the accuracy of the algorithms: one study in a laboratory environment with a motion capture system as the ground truth, in which we acquired 2377 strides of 27 subjects, and one field study in a real-world scenario. We showed that the *Trajectory* algorithm performs best and especially well for velocities up to 5 m/s. The results of the field study showed that this algorithm does not only work on single strides, but also on longer outdoor runs in a real-world scenario. The MAEs for this scenario showed that the trajectory is comparable to GPS measurements, which is the common method for total distance tracking in amateur running. However, the *Trajectory* algorithm is more costly energy wise due to the fact that both the acceleration and the gyroscope have to be acquired with a sampling rate of 200 Hz. When it comes to an energy-efficient use case, the *Acceleration* algorithm is a good choice, as it only needs to sample the accelerometer, and the sampling rate can be decreased to 60 Hz.

We therefore propose the implementation of the *Trajectory* algorithm for use cases with no energy limitations and the implementation of the *Acceleration* algorithm for use cases with energy restrictions.

In future work, we want to address further parameters that can be computed using inertial measurement units and other sensors located in the sole of a running shoe. Using data acquired by sensors on both feet, it is possible to perform bi-lateral analysis by combining the information of both sensors. Thus, the contribution of the individual lower limbs to the running movement can be further evaluated. Using only data from IMUs within the sole of a running shoe and the *Trajectory* algorithm, analysis regarding imbalances in stride length, stride time or orientation of the two feet

can be conducted. Furthermore, other temporal parameters like flight time or stance time could be computed by adding a toe-off detection. Due to inaccuracies with the toe-off detection in running using only one IMU per foot [43], we plan to also incorporate pressure sensors for toe-off detection into the soles of a running shoe.

**Author Contributions:** M.Z. conceived of and designed the experiments; M.Z. and M.U. performed the experiments; M.Z., S.G., and U.J. analyzed the data; B.M.E. contributed reagents/materials/analysis tools; M.Z. wrote the paper.

**Funding:** This work was conducted during the *Servicefactory* research project supported by the German Federal Ministry for Economic Affairs and Energy. Bjoern Eskofier gratefully acknowledges the support of the German Research Foundation (DFG) within the framework of the Heisenberg professorship program (Grant Number ES 434/8-1).

**Acknowledgments:** The authors also thank Christine Martindale for revising the script as a native English speaker. **Conflicts of Interest:** The authors declare no conflict of interest.
