*1.1. Literature Review*

The predominant approach to tracking average velocity and total distance during running is the global positioning system (GPS). Smartphones or even smartwatches comprise a GPS chip, which allows a satellite-based localization of a runner. By tracking the runner's absolute position over a complete run and using a solution to the second geodetic problem [4], the distance of a run can be measured. By incorporating the sampling frequency of the GPS module, a continuous time series of velocity values for the run can be computed. Thus, GPS delivers a time series of velocity, the cumulative distance, and the localization of the running track. From these data, the average velocity and the total distance can be extracted. The drawbacks of GPS are the additional gear (smartwatch, smartphone), the high energy demand, and the restriction to outdoor use.

Integrating sensors directly into running shoes can solve these issues. One type of sensor that can be integrated into a shoe is an inertial measurement unit (IMU). It is a small, lightweight, and inexpensive sensor, which is capable of measuring triaxial accelerations and triaxial angular rates. A shoe setup with integrated IMUs overcomes the described GPS issues: runners only need a running shoe with integrated IMU; IMUs are energy efficient and work both indoors and outdoors. Using IMU data, it is possible to compute a stride length and an average velocity value per stride. The underlying assumption for the velocity computation is that the average velocity of the foot per stride matches the running velocity. By collecting stride velocity values and accumulating the stride length values over time, a distance measure and a continuous velocity recording of a complete run can be provided. The following paragraphs describe the state-of-the-art of four approaches for IMU data processing for calculating these metrics.

In biomechanics, the relationships between stride frequency, stride length, running velocity, and body height was investigated [5]. The results indicated that with increasing running velocity, stride frequency and stride length increase. Thus, increasing running velocity is an interaction of increasing stride length and stride frequency [5]. Stride length itself depends on body height and can be expressed as a relative stride length. From these relationships, a generic model relating running velocity and stride length on the basis of the stride frequency can be deduced. The general idea behind this approach is the inverse correlation between velocity and stride time (the higher the velocity, the shorter the stride time). Thus, in order to estimate the stride length, only the stride time has to be distinguished by segmenting the data into single strides. An average velocity of the stride can then be calculated using the stride length and the measured stride duration.

Recently, Gradl et al. [6] proposed an algorithm that uses quadratic regression to compute the velocity of movements. The velocity was evaluated during running, as well as other movements and showed a relative error of 6.9 ± 5.5%. The proposed algorithm is solely based on foot acceleration. Single strides are segmented from the data stream. Afterwards, the acceleration signal of all axes is integrated prior to the initial ground contact. Finally, the resulting integral value is converted to a velocity value using a quadratic regression model.

Another method to compute velocity and stride length values from IMU signals is to reconstruct the trajectory of the sensor in the course of a stride. This method is heavily used for gait analysis for geriatric patients [7–9] or in inertial navigation scenarios [10,11]. For trajectory reconstruction, sensor fusion techniques must be applied to both the accelerometer and the gyroscope. Several fusion algorithms to cope with this task exist. Bailey et al. [12] and Foxlin et al. [13] used extended Kalman filters to compute the trajectory from the acceleration and angular rate signals, while Rampp et al. [7] applied a linear dedrifting technique. Both algorithms rely on a zero-velocity update during the stance phase for the initialization of the orientation. The literature shows that this approach works well while analyzing walking [7], but it was not evaluated for free running. Bailey et al. [12] applied

their approach to treadmill running and showed a good accuracy of 0.03 ± 0.2 m/s. However, they evaluated neither the velocity nor the stride length in a free running scenario.

Deep learning techniques also show good results in IMU-based classification and regression tasks [14,15]. Hannink et al. [16] showed that deep convolutional neural network regression outperforms traditional stride length estimation in geriatric gait analysis. They trained a network with two convolutional layers, which was fed with the 6D IMU raw data of a stride. The output layer had a single node and provided an estimate of stride length.
