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**Contents:**

Activities where an athlete is performing skating style sub-techniques, skiing without poles, running with poles, bare running or performing any other activity that could produce motion patterns similar to the definitions are not considered valid in this context. Additional motion components may be included to provide a more specific description of the sub-techniques.

Specific examples are components related to ski gliding and the diagonal synchronicity between arms and legs to also classify running and amble gait.

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Non-cyclic activities like downhill tucking, standing still and non-repetitive motion are not standard classical XC skiing sub-techniques and will be covered by the noTech class. However, these activities are included here in order to fully span the classification sample space.

Assumption 1. The athlete performs classical XC skiing, and the variables x motionComp , representing the chosen measures from Definition 1, are independent. Proposition 1.

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Under Assumption 1, the motion components from Definition 1 are sufficient measures for a unique decision function description of the classical XC sub-techniques in Definition 2. The outline proof is given by proposing the following logical compositions, derived from the definition 2, as decision functions:.

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The non-technique set is defined by:. An example flowchart of the decision functions from Equation 3 to 9. With the exception for armCorr the tolerances are omitted in the diagram in order to reduce the notation. Remark 2. First, this means that there may exist different motion component measures that can be used in the sub-technique decision functions. Second, since Definition 2 only holds qualitative information, other decision function definitions may be proposed, i. Remark 3. All sub-techniques belong to either of these classes and are further refined by the leg motion components.

Remark 4. The decision functions l j and the specific set of tolerance parameters in proof of Proposition 1 may be used as a detailed measurable definition of the classical XC sub-techniques.

A drawback of such an approach is that this would require models and sensor systems that specifically estimate the proposed motion components. This can however be handled by standards, specifying motion components and decision functions dependent on the sensor setup. Remark 5. In Definition 2, DK is defined independent of which leg generates the kick, such that the DK cycle is constrained by the arm cycle time. The quantification of the motion components in Definition 1 relies on measurements from sensor systems either in the environment or being attached to the athlete or the equipment.

In this work, IMU sensors were attached to the arms and skis of the athlete to provide acceleration and angular rate information that were used to estimate the motion components. Assumption 2. Sensor calibration.

All sensor information is time synchronous and aligned to a common athlete body coordinate frame, defined in Figure 1. To simplify calibration and maximize the signal to noise ratio, gyroscope sensors were used as comparison signals A. Here A left and A right are the angular rates around the lateral axis from the left and right arms respectively. Note that more elaborated approaches utilizing all the channels of the accelerometers and gyroscopes may be considered.

As for arm synchronization, the angular rate around the arm's lateral axis was used as a basis for estimating arm motion. From the sum of squared values in Equation 11 , the variance of the arm motion components can be calculated:. For the independent leg motion estimation, the difference in relative angles of the legs is used as a basis. These signals are derived from the angular rate around the lateral and vertical body axes.

The angular rate raw data are band-pass filtered, integrated with bias removal and finally differentiated accordingly:. The independent leg motion is then estimated similar to Equation 13 given by:. Several methods may be applied to quantify the athlete's kick rotation. In this presentation, the signal strength of the rotation around the vertical axis is compared with the rotation around the lateral axis. This was chosen such that the tolerance parameter was less influenced by the individual differences in athlete capabilities.

This is handled by the leg motion restrictions, preventing rotational kick classification in cases of insignificant motion. Typically angular rate measurements provide a good signal to noise estimation of orientation, but at the cost of estimator drift due to bias and numerical issues during the integration step, i. Due to the gravitational field, the accelerometer data may be used to generate absolute estimates of angles around the longitudinal and lateral axis, under the assumption of relative low dynamic environment.

However, the main requirement in the following section HRB estimator is the availability of absolute estimates, i. However, neither of these sensor systems were available in this work, thus only absolute roll and pitch estimates are provided. These can be estimated through knowledge of the gravity components, see for example the textbook by Farrell and Barth , and calculated according to the following relationship:. The use of the absolute angular estimates of the skis in this work is limited to the low pass components f f.

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HRB can be identified by using the ski orientation or the kick direction as estimators. The kick direction may be identified by acceleration measurements from the skies but this has not yet been explored and is left for further work. For example in Andersson et al. In our presentation reliable estimates of the absolute yaw were not available as there was no magnetometer in the applied IMU sensors. Absolute ski roll and pitch are however estimated by using the gravitational acceleration component as a reference.

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Note that these estimates differ from the relative angular estimates presented in Equation 15 , which were based on the angular rate measurements from the IMU. It is common to combine the two estimates in an attitude observer, as discussed in section 2. For simplicity this is not considered as it will not gain any principal advantages for the presented low frequency estimator. However, in cases with absolute yaw measurements available and estimators utilizing high frequency components, such observers should be considered. The HRB estimator used in this study was defined by:. Under the assumptions that the roll angles are relatively small and that the athlete keeps the skis in parallel and legs straight with stiff ankle and knee, then the roll angle will measure the distance between the skis:.

Turning and skating downhill will produce negative estimates. The study was pre-approved by the Norwegian Centre for Research Data, conducted in accordance with the Declaration of Helsinki and assured by the responsible institution, the Norwegian University of Science and Technology.

All participants were fully informed of all test protocols and procedures before they provided their written consent to participate. The skiers were instructed to initially ski at a low intensity using their preferred sub-technique, then at competition speed i.

The track represents a typical racing track, and it was chosen to stimulate the athlete to use their full repertoire of sub-techniques. To compare the algorithm results with reference data, two men and two women were randomly selected. These skiers are referred to as subjects 1 to 4 throughout the text. All test subjects had competed at national and international levels, and the use of sub-technique in the LIT session was labeled and manually synced to the motion data based on a video, captured by a skier following the test subject.

The labeling was done independent of the definitions in this paper. The sub-technique cycles were defined to start and stop when the subject's left arm was extended all the way behind the body Rindal et al. Time behind the fastest lap relative to the distance from the start of the lap.

lingnertiofracar.cf The fastest lap 5 is used as a reference and all data are projected onto this lap through linearly scaled distance measures. The specific sub-techniques and the elevation are displayed along the distance to show the elevation effects. Positional sub-technique distribution. Comparing the sub-technique distribution of the low-intensity LIT validated lap 2 with the fastest high-intensity HIT lap 5. The plot highlights the sub-technique distribution with dependence on the track turns.

Converting from data samples to cycles: Within each cycle, the sub-technique with the highest sum of algorithm classification samples was chosen to represent the algorithm classification result. Note that this will have some low pass filtering properties, letting the majority of samples represent the cycle. Tucking: The TCK class appears between cycles and is not considered a sub-technique cycle in this paper. It is therefore labeled as noTech. These mapping rules were based on discussions between XC skiing experts and algorithm developers.

Discussions like these are practical examples of why it is necessary to work toward a common framework for motion components and the unique sub-technique definitions. Further discussion of the rules is provided in section 4. This work builds upon data presented in Solli et al. The sensor system sampling frequency, Hz, was down sampled to 20 Hz and all data channels were synchronized in time, before the classification.