## 2 Materials and Methods
### Signal Recordings and Pre-Processing  
Signal recordings from 65 participants were grouped into the following datasets:  
1. The learning dataset recorded from a randomly selected 53, i.e., approx. 80% of all the 65 trial participants. Signals that were used as the learning set were recorded as follows: _10 s immobility--2.5 min of a specific motion type--10 s immobility_, the type of gestures performed by test participants were: yaw, roll, pitch, and immobility. The collection of the learning signals therefore consisted of \(53\times 4=212\) recordings. 2. Two types of testing datasets that have not been used for training the classifiers: * \(T\_53\_set\) that was recorded for 53 trial participants for whom the learning data were recorded, * \(T\_12\_set\) that was recorded for the rest of the trial participants, i.e., 12 individuals who did not take part in the recordings of the learning datasets, further, for each of the two testing data sets there were two different testing scenarios applied: * testing scenario \(T\)1 for which the dataset was recorded following the sequence of: _20 s of immobility--40 s of yaw head movement--20 s of immobility--40 s of roll--20 s of immobility--40 s of pitch--20 s of immobility_; thus, two types of the testing datasets were recorded \(T\)1_53_set_ and \(T\)1_12_set_, respectively * testing scenario \(T\)2 for which the datasets were recorded according to the following procedure: head gesture sequences of _roll_, _yaw_ and _pitch_ gestures in random order for time periods lasting from 5 to 20 s and no immobility time gaps between the gestures; thus, two other types of the testing datasets were recorded: \(T\)2_53_set_ and \(T\)2_12_set_ respectively. The signals recorded from the IMU were processed according to the two following procedures:  
1. _With signal parameterization (SP)_: for each of the six recorded IMU signals, i.e., three signals from the accelerometer (\(a_{x}\), \(a_{y}\), \(a_{z}\)) and three signals from the gyroscope (\(\omega_{\alpha}\), \(\omega_{\beta}\), \(\omega_{\gamma}\)), the following features were extracted: (1) average, (2) minimum, (3) maximum, (4) standard deviation, (5) kurtosis, (6) correlation coefficients for pairs of signals from the accelerometer and pairs of signals from the gyroscope, and (7) signal energy. Thus, the total number of parameters derived from the signals was: 6 signals \(\times\) 7 parameters = 42 parameters. Figure 2: Example signal waveforms recorded by: (**a**) acceleration sensors and (**b**) gyroscope sensors. These parameters were calculated for different time window widths, i.e., \(T\in\{0.1,\,0.2,\,0.3,\,0.4,\,0.5,\,0.6,\,0.8,\,1.0,\,2.0\}\) given in seconds. The work focuses on the causal recognition mode of the gestures for which the time windows are determined for current and past samples only. The consecutive windows were shifted by a 0.1 s time step as shown in Figure 3.  
_Time domain representation (TDR)_: current samples of signals recorded from the accelerometer (\(a_{x}\), \(a_{y}\), \(a_{z}\)) and gyroscope (\(\omega_{\alpha}\), \(\omega_{\beta}\), \(\omega_{\gamma\gamma}\)) were used directly as six-element training vectors for the classifiers. In order to eliminate user errors related to an excessively slow start of the selected type of movement, too rapid cessation of motion or incorrect initial movement, the learning datasets comprised 90 s recordings approx. in the middle of the 150 s time recording span. According to the described recording procedure of the learning datasets (collected from 53 individuals), the following datasets were built:  
1. For the procedure with signal parametrization: 900 42-element vectors for each individual. The calculations of these 900 vectors were made for each time window width \(T\in\{0.1,\,0.2,\,0.3,\,0.4,\,0.5,\,0.6,\,0.8,\,1.0,\,2.0\}\), given in seconds, that were shifted with time steps of 0.1 s.
2. For the procedure based on the time domain: 9000 vectors for each individual, with six signal samples representing a \"time capture\" of the given head motion.