1 Introduction

According to some business intelligent market research databases, such as Grand View Research,Footnote 1 the number of connected wearable devices worldwide by 2025 is expected to be more than 1.5 billion, being the recognition of human activities one of their most predominant uses.

The recognition of human activities through wearable technology represents a groundbreaking approach with broad implications across several domains. This versatile technology finds invaluable applications in well-being and healthy ageing (Camp et al. 2021; Debes et al. 2016; Kańtoch 2018), enabling individuals to maintain a high quality of life by tracking their movements and activities. Additionally, wearable-based activity recognition approaches plays a pivotal role in physical rehabilitation (Réby et al. 2023; Kim et al. 2021; Meng et al. 2020), offering real-time feedback for tailoring exercise plans to expedite and enhance recovery.

Furthermore, the integration of wearable activity recognition systems into human–machine interaction interfaces is revolutionising the way we engage with technology (Mannini and Sabatini 2010; Huang et al. 2022). Gesture-based controls and motion-sensitive interfaces offer intuitive and seamless interactions with devices, from gaming consoles to virtual reality environments (Dallel et al. 2023), enhancing user experiences and accessibility.

In the realm of sports, this technology serves as a game-changer, providing coaches and athletes with unprecedented insights into performance metrics (Camomilla et al. 2018). From analysing the bio-mechanics of a golf swing (Najafi et al. 2015) to dissecting the intricacies of a gymnast’s routine (Krüger and Edelmann-Nusser 2009), wearable devices empower sports professionals to fine-tune training regimens and optimise athletic potential. In addition, the integration of wearable technologies for activity recognition offers a comprehensive perspective approach on how individuals interact with their environment.

However, the future of wearable technology should focus on give more comprehensive assessment on performance analysis (Mason et al. 2022), rather than focus on data analysis for identifying patterns. Although some efforts have been made to support personalised training (Smyth et al. 2021), there are still challenges to transform the captured data into user models that can offer personalised interaction to the users (Hopfgartner et al. 2020).

Embedded sensors within wearables capture intricate details of motion, allowing for comprehensive analysis by experts and delivering quantitative and qualitative insights. This combined approach, marrying precise measurements with expert judgement, ensures an integral understanding of motor actions, paving the way for tailored interventions and finely tuned training, injure prevention and rehabilitation programmes (Portaz et al. 2023). This approach not only considers the technical aspects of the system but also delves into the intricate taxonomies of psychomotor behaviour (Newell 2020). Understanding these diverse categories of motor behaviour provides a nuanced understanding of how our motor actions are planned, executed, and adapted, enriching the overall comprehension of human activity recognition systems.

Thus, our research aims to classify practitioners of psychomotor activities according to their expertise level in order to provide personalised multisensorial support (e.g. following an approach similar to Santos et al. (2016), where feedback is delivered through visual, auditory and/or tactile channels to provide a personalised response to the user aimed to support the corresponding learning process) when learning psychomotor behaviours.

Additionally, since Physics are intrinsic to the martial arts domain (Santos and Corbí 2019), and following the idea suggested in James et al. (2014), in our research we have explored if changes in the Cartesian coordinate system used by accelerometers can improve the user modelling. This includes the conversion from Cartesian coordinates to spherical or cylindrical coordinates for redefining points in terms of radial distance, inclination, azimuth angles and height, offering a more specialised perspective. We have also explored fusion approaches to represent spatial orientations, as well as rotations of elements in the three-dimensional space with the use of quaternions. In this context, we pose the following research question:

figure a

To approach this research question, we have selected the martial arts domain, where it seems possible to identify beginners and experts in the practice of the art from the inertial signals collected (Corbí and Santos 2018). In fact, previous studies on martial arts show that expert’s inertial signals are clearer, more regular and balanced (Heinz et al. 2006; Kunze et al. 2006). Furthermore, from a practical point of view, martial arts performance involves exercising physical movements in the sports domain, but they have established a detailed system to differentiate beginners and experts while they progress in the practice.

This paper is structured as follows. First, in Sect. 2 we present the background of our research, including taxonomies of psychomotor behaviour. Next, in Sect. 3 we present the materials and methods. Specifically, in Sect. 3.1 we described the datasets built from practitioners performing three different movements of two different martial arts. After that, in Sect. 3.2 we explain the geometrical representations used to define the spatial orientation of the movements carried out. Following, in Sect. 3.3, we present the modelling approaches applied. In Sect. 3.4, we present the experimental setup, and in Sect. 4, the results obtained are presented and followed by a discussion on the findings. Finally, in Sect. 5 some conclusions are outlined.

2 Background

According to Voelcker-Rehage (2008), motor development belongs to adaptive changes in movement behaviour over a person’s lifespan, resulting in a long-term progress (ontogenesis). Motor learning involves lasting enhancements in motor skill proficiency resulting from training and targeted interventions, which are considered short-term changes (microgenesis). Despite this distinction, learning and development are interdependent; the effectiveness of learning motor skills is influenced by developmental status, and learning outcomes also impact development.

In this context, executing skilled motor actions entails achieving a specific objective with the highest level of assurance, like successfully performing a martial art movement (Schmidt and Lee 2014). A proficient motor behaviour involves a structured and harmonised series of deliberate movements involving body, head, and/or limb actions aimed at achieving a specific result. The coordination of various body parts is essential for executing this motion. Sensory and cognitive inputs play a vital role in shaping an individual’s decisions regarding the action and in organising and refining the movements. In addition, motor ability is inherent to an individual, impacting the execution of diverse motor skills. For instance, when executing a punch or kick in martial arts, a practitioner engages in distinct components of the skill, including positioning, release, and follow-through. These actions draw upon underlying motor abilities such as hand-eye coordination, shooting accuracy, agility, and upper body strength (Magill and Anderson 2010).

In skilled motor performance, the goal is to carry out specific limb movements with precise timing and coordination to achieve a desired outcome. Establishing a well-defined ontology for psychomotor planning activities, structured in the form of a tasks hierarchical tree, holds immense significance (Paraschiakos et al. 2020). Such a structured method helps to analyse the relationships between different skills and assess them effectively. This not only enhances our comprehension of psychomotor planning but also serves as a valuable foundation for designing effective training programmes, rehabilitation strategies, and interventions in fields ranging from sports performance to physical therapy.

Our research follows the reverse and analogous process described in Ehatisham-Ul-Haq et al. (2020), evaluating the transition from a fine-grained activity (i.e. walk on your knees, turn and come back in the case of one of the martial arts analysed) to a coarse-grained assessment (expert or beginner) in a basic hierarchical ontology (Fig. 1), and involving a process of increasing generality and abstraction (Olugbade et al. 2022). This process allows a more generalised understanding of the subject matter (expertise level), providing a broader overview of related assessment, enabling to view information in a more encompassing manner, facilitating high-level categorisation and analysis.

Fig. 1
figure 1

Hierarchical ontology diagram for different martial art activities. Fine-grained activities are included in Level 4, as coarse-grained assessment is in Level 3

2.1 Psychomotor learning systems

Psychomotor learning involves the integration of mental and muscular activity with the purpose of learning a motor competence by consolidating it into memory through repetitions (Gagne et al. 1992) and this is done in a gradual manner from a low-performance level (i.e. the learner can hardly recognise the movement) to a high-performance level (i.e. the learner has internalised the movement) (Santos 2016). Nonetheless, supporting personalised learning in this area is still in an early stage of research (Casas-Ortiz et al. 2023) due to the need of modelling more sophisticated or skilled behaviours. The importance of providing personalised support while executing these highly skilled movements relies on the relationship between psychomotor learning performance (Fitts and Posner 1967; Schmidt 1976), motor plasticity (Voelcker-Rehage and Willimczik 2006; Guglielman 2012) and its reinforcement by the fact that psychomotor learning systems can be seen as a closed-loop system (Adams 1971) ready to provide feedback and error detection at latter stage.

Nevertheless, determining the user’s personalised behaviours is mentioned as a current challenge (Qiu et al. 2022) and the way users perform the activities is only explored for authentication purposes (Lateef and Abbas 2022). Even so, some of these reviews acknowledge that users have different motion patterns so the way they perform the activities vary from one user to others (Zhang et al. 2022) (between-users variations) and even for a single user the performance of the activity can vary depending on their physical and mental state (Saha et al. 2022) or because the user motion pattern evolves (Miranda et al. 2022) (within-user variations).

Artificial intelligence algorithms on inertial data collected from wearables can be used to compare learner’s executions with those from experts during the psychomotor learning process, and this can be used either (i) to recognise specific motion learning units, or (ii) to assess the learning performance in a motion unit (Santos 2019). In these two cases, the modelling goal should differ, in particular, while in the latter the kind of movement performed is already known, but not how well the user is executing it. In our research, we focus on the recognition of complex human activities using inertial sensor data. Instead of classifying the activity performed, we focus on modelling the level of user motion performance through the knowledge obtained from the motion features, extracted of the movement performed.

2.2 Martial arts sensor integration

Our study centres on modelling users expertise level in martial arts movements through the information extracted from inertial sensors. The analysis of psychomotor movements in martial arts represents an opportunity for deploying personalised guided intervention during its practice (Santos 2017). Competence levels are clearly standardised in the form of belts, grading the degree of the practitioner’s expertise level (Cox 1993). In particular, practitioners expertise improvement relays on minor details that are revealed when the movement is executed correctly following the Physics involved.

However, up to our knowledge, not many research works to date have focused on analysing martial arts to build personalised psychomotor learning systems. Nonetheless, we have found some works that aim to differentiate between novice and experts from inertial signals, such as Kunze et al. (2006) in Tai-Chi and Heinz et al. (2006) in Kung Fu. In turn, James et al. (2014) used four accelerometers on a practice wooden sword (known as bokken in the Aikid\(\bar{\text {o}}\) jargon), which measured the inertial signals produced in a basic swing (sh\(\bar{\text {o}}\)men) and found a correlation between experience level and sensor output. The analysis of the movement consisted in visualising the time series in a cylindrical coordinate system, which turned out to be a very useful way of movement tracking in a three-dimensional space. In other works, accelerometers and gyroscopes were placed on different parts of the body to assess the acceleration profile of a Judo student during the performance of a ukemi (soft fall) (Glowinski et al. 2016).

These works show the potential and feasibility of modelling the expertise level of martial arts practitioners with inertial data. Thus, in order to provide some insights about how to model the expertise level addressing the research question posed, we have built three specific datasets. These datasets contain inertial information for specific complex movements and from different practitioners. The sensors used to build these datasets (accelerometers, gyroscopes and magnetometers) are embedded into specific micro-electro-mechanical system (MEMS), often referred as inertial measurement unit (IMU).

2.3 Multivariate time series

The depiction of the inertial information gathered by any of the IMUs is in the form of multivariate time series (MTS) and follows a (xyz) three-dimensional Cartesian coordinate plane representation. Due to the circular nature of martial art movements and following (James et al. 2014), who opted to transform Cartesian values into a \((\rho , \phi ,\)z) three-dimensional cylindrical coordinate system, in our research we have explored different options to transform the raw Cartesian information, including transformations to a (r, \(\phi , \theta )\) three-dimensional spherical coordinate system.Footnote 2

Moreover, besides the above coordinate systems transformations, we introduced another innovation for modelling users on psychomotor learning systems deployments, transforming the raw inertial data into a specific group of hyper-complex numbers, the quaternions. Therefore, we can estimate pitch and roll orientation motion fusing accelerometer and gyroscope information in form of quaternions. Although quaternions have been widely used in different disciplines not directly related to the recognition of human activity and mainly linked with multirotor unmanned aerial vehicles, like in Fresk and Nikolakopoulos (2013); Guerrero-Sánchez et al. (2017); Yang et al. (2017); Xing et al. (2019), Sabatini (2005) uses a quaternion-based integration method for gait analysis, applying the spherical Linear intERPolation (SLERP) procedure disclosed in Shoemake (1985). Furthermore, Sabatini (2006); Renaudin and Combettes (2014); Sung et al. (2018); Bergamini et al. (2014) use magnetic data to increase orientation accuracy and mitigate drift issues (Sabatini 2005). Thus, Sabatini (2006) introduces a quaternion-based extended Kalman filter (EKF) to figure out the orientation of rigid bodies, with applications in the analysis of human movements, while Renaudin and Combettes (2014) and Sung et al. (2018) use wearable sensor data, transformed in quaternions, for indoor pedestrian navigation, and for accurate motion estimation respectively. In Bergamini et al. (2014), similar approaches for manual and locomotion tasks are followed.

To recognise human activity or to assess expertise level, inertial MTS data gathered need to be processed prior to perform psychomotor behaviour classification and recognition. Several approaches can be followed to analyse the collected MTS.

At first glance, Bagnall et al. (2016) categorises classification techniques into different groups according the type of discriminatory features used. The complete MTS can be analysed, as Zhou et al. (2006) did for estimating the upper limb motion registered, although a time series feature extraction workflow (i.e. preprocessing, segmentation, feature extraction, dimensionality reduction and classification) is a more efficient and effective process for the recognition of human activity (Avci et al. 2010). In this sense, Barandas et al. (2020) provides a complete library for simplifying the extraction of features in several domains, including temporal, statistical and spectral. In the sport domain, extracting features from inertial data was also the method used by Benson et al. (2018) for classifying running speed conditions.

Alternatively, the use of CNNs for MTS classification have also shown good results, as the outcomes obtained with the use of ResNet (Wang et al. 2016) or AlexNet (Fawaz et al. 2020). Since MTS data have essentially the same topology as images, it is possible to apply the same techniques used for image classification to MTS classification. Thus CNNs, which are effective for classifying images, should also be effective for classifying MTS data. The main drawback of these methods is their high computational complexity.

These CNN methods use convolutional kernels to detect patterns in the input time series data. These kernels are convolved through a sliding dot product operation to generate a feature map. As disclosed in Goodfellow et al. (2016), kernels have some basic parameters: size (length), weights and bias, dilation and padding. The resultant kernel, although smaller, has the same basic structure as the MTS. In this case, each kernel is a vector of weights, with a bias term added to the result of the convolution operation between an input MTS and the weights of the given kernel.

In this sense, Choi et al. (2019) used feed-forward artificial neural network models to classify the inertial time series data estimating the centre of mass–centre of pressure (COM-COP) inclination angle during walking using a wearable magnetic IMU. In addition, the framework proposed in Dempster et al. (2020) achieves state-of-the-art accuracy in MTS classification but with a much lower computational expense than previous methods.

Thus, two different approaches seem of interest for our research problem: on the one hand, feature extraction on the time series, and on the other hand, a CNN-based approach.

3 Materials and methods

We now present the datasets used for the corresponding modelling process. We also set up the methods we have followed for transforming the original raw Cartesian data (baseline), included in the aforementioned datasets, into spherical and cylindrical coordinates systems. Prior to performing any form of classification, we also explored the benefit of reducing the datasets dimensionality by fusing the inertial data with quaternions. Finally, to infer performance level, we use and compare two modelling alternatives, one based on time series features extraction (Barandas et al. 2020) and the other on a convolutional neural network (Dempster et al. 2020).

3.1 Datasets

To explore the research question, whether inertial data can be used to model the users’ expertise level when learning psychomotor skills, and whether the physical characteristics of the movement can be considered in the modelling process, we have built three datasets that collect specific complex movements with different commercial IMUs and in real-world scenarios (i.e. we have collected free-living data on the wild).

The first two datasets gather movements from Aikid\(\bar{\text {o}}\). Aikid\(\bar{\text {o}}\) is a non-aggressive Japanese martial art that consists of entering and turning movements that redirect the momentum of an opponent’s attack, and ends with a throw or joint lock that terminates the technique (Seitz et al. 1991). To determine the expertise level in the Aikid\(\bar{\text {o}}\) datasets, two groups were defined in terms of the corresponding grading belts: expert practitioners (1st ky\(\bar{\text {u}}\) to 6th dan)Footnote 3 and beginners (7th to 2nd ky\(\bar{\text {u}}\)). Note that we considered 1st ky\(\bar{\text {u}}\) Aikid\(\bar{\text {o}}\) practitioners as experts because passing from this level to the 1st dan requires a formal external exam and some practitioners delay their examinations. This entails that they stay in the 1st ky\(\bar{\text {u}}\) level formally (sometimes for years), but in practice, their mastery of this martial art already fits into the 1st dan.

The third dataset gathers some arm movements of American Kenpo Karate, a modern martial art focused on self-defence, that keeps a balance between tradition but applying modern ideas, like the principles of Physics. It uses quick, body-delivered strikes, enhanced by quick posture changes. Kenpo techniques are taught through scripted outlines that define a set of situations (e.g. an opponent attacks you frontally with a punch, while another opponent is grabbing your arms) (Parker 2009). In this case, the expertise level of the practitioners was defined by belt and years practicing the art. In American Kenpo Karate, a white or yellow belt practitioner is considered a beginner, an orange or purple belt practitioner is considered intermediate, a green or brown belt practitioner is considered advanced, and black belt practitioner is considered an expert. After that, there is a rank of ten black belt dans that ranges from instructor to professor, and finally master and grand master. Reaching this level can take several years of training and continuous learning of movements, concepts and effort.

3.1.1 Dataset 1: Aikido–Bokken shomenuchi

This first dataset (D1) gathers one of the Aikid\(\bar{\text {o}}\) movements performed with a wooden sword (bokken). This movement it is used in James et al. (2014) and explored the utility of changing the coordinate system to improve the modelling of the movement taking into account the Physics behind its execution.

It includes 153 participants (\(N = 153\)). Ages are between 18 and 69 years old and corresponds to 13 different performance levels, being the highest 6th dan (assigned to \(-6\) for computational purposes) and the lowest 7th ky\(\bar{\text {u}}\) (assigned to 7). We considered experts from level \(-6\) to level 1 and beginners above. Other biographical and anthropometric data were also gathered, including the years of martial arts experience, weight, height, gender and the arm and forearm length.

To collect the dataset, we used an Axivity AX3 deviceFootnote 4 attached to the tip of the bokken (see right picture on Fig. 2), following a similar approach to the one used in James et al. (2014). Moreover, as in that work, we also video-recorded the data collection to manually label and segment the signal obtained with the device. In particular, the goal of video recording all participants has been no other than to comfortably determine the starting and ending points of each lapse and the overall exercise time, besides easily keeping visual hints of any issues or events worth highlighting.

Fig. 2
figure 2

Three left images represent one straight blade swing (bokken shomenuchi) sequence performed by an Aikid\(\bar{\text {o}}\) practitioner (who authorised the recording and publication of the images). The rightmost image shows the experimental setup comprising an AX3 accelerometer tightly attached to the tip of one of these wooden Japanese swords

The movement included in this dataset consisted in performing repeated straight bokken swings (see Fig. 2), for a few seconds (80 s in our setup). In this sense, the Shomenuchi movements itself is a strike to the top of someone else’s head. Although this movement might seem simple at first sight, it requires a right body positioning and a correct sword grip. What is more, although speed, and thus, cadence, is important, there is no direct correlation between performer’s levels and swing intensity, as shown in Fig. 3, where the learner’s performance represented shows roughly 22 blade swings during 80 s.

In Fig. 3, the linear acceleration intensity is in fractions of g (y-axis) and the duration of the exercise is in seconds (x-axis). In this case, the maximum intensity of almost all of these 22 blade swings registered is around 1 g. During the first 30 s the movements registered show certain level of consistence with similar top intensity. After these 30 s top intensity levels are less regular, which may represent a symptom of possible fatigue in the learner.

Fig. 3
figure 3

Intensity of the linear acceleration as measured in the Aikid\(\bar{\text {o}}\) bokken shomenuchi setup depicted in Fig. 2

3.1.2 Dataset 2: Aikido–Shikko (knee-walking)

To complement the bokken shomenuchi dataset, in Corbí and Santos (2018) we proposed modelling another characteristic movement in Aikid\(\bar{\text {o}}\) called shikko (very similar to a rhythmic knee-walking and schematically depicted in Fig. 4). Shikko movement is difficult to master as it relies on keeping the body centre aligned. It also requires hours of practice and can cause long-term problems on the knees if it is not performed correctly and supervised by an instructor (Homma 2007). However, it is also very useful to develop awareness of one’s own centre of mass, also known as hara in the Aikid\(\bar{\text {o}}\) jargon. The hara is the name given in Aikid\(\bar{\text {o}}\) for the gravity centre of the body and corresponds with just below or directly behind the umbilicusFootnote 5 (and is drawn in the right picture of Fig. 4). A correct control of the hara contributes to keep a stable position that is later needed for other stand-up techniques as it helps to achieve a correct and swift hip movement, which is essential to master the rest of the Aikid\(\bar{\text {o}}\) techniques. Thus, it can (and effectively does) improve the learner’s balance even for movements outside of the shikko practice itself. The rotational movement that is required to turn when knee-walking is particularly good for learning how to properly shift the hips during the practice of Aikid\(\bar{\text {o}}\), encouraging the development of a strong awareness of the body’s centre of mass. Additionally, the shikko movement gathered in this dataset can also be analysed to help understand complex concepts of Physics when an embodied learning approach is used (Corbi et al. 2019).

Fig. 4
figure 4

Left and centre images: schema of the movement and representation of the experimental setup. Right image: approximate location of the hara in a 3D human figure obtained with the origin to centre of mass operator in Wartmann (2001). The hara also represents the origin of the coordinate system of the inertial sensors that we have used to collect the data

This second dataset (D2) includes 185 participants (\(N = 185\)). The ages of the participants are between 19 and 69 years old, and participants were classified into 13 different performance levels (from 6th dan to 7th ky\(\bar{\text {u}}\)). As in D1, the highest was assigned to \(-6\) and the lowest 7, considering experts from level \(-6\) to level 1 and beginners above. Other biographical and anthropometric data (i.e. years of martial arts experience, weight, height, gender and arm and forearm length) were also gathered.

Fig. 5
figure 5

Some snapshots (from two of the authors of this research work) showing some straight (go and return) steps of the shikko exercise and the associated \(180^{\circ }\) turns or ho tenkans (two rightmost pictures in both rows). The practitioners are wearing an attached fanny pack (enclosing a smartphone) around their waist

To collect the data for the D2 dataset, the Aikid\(\bar{\text {o}}\) practitioners were asked to perform two 20 ms lapses (40 ms in total), as shown on the left two pictures in Fig. 4 (and also in Fig. 5), while their movements were recorded with the inertial sensors embedded inside a smartphone attached to the practitioners’ waists using a fanny pack (also known as bum bag), carefully positioned between the skin (at the level of the navel) and the aikidogi (the traditional Japanese garment worn by Aikid\(\bar{\text {o}}\) practitioners). This use of type of smartphones devices have proven to meet the expectations for movement recording, as evinced by Saponas et al. (2008); Kos et al. (2016); del Rosario et al. (2015). In this way, the physical variables acceleration and angular velocity were registered relative to the hara’s coordinate system using, respectively, the accelerometer and gyroscope packed in the smartphone. The information comprised both acceleration and gyroscopic data along the three (xyz) spatial axes; hence, six axes are used.

The overall exercise was also video-recorded as in D1 with a second synchronised smartphone to facilitate manually segmenting and labelling of the movements. For this, the video metadata included precise timestamp information and both smartphones (including their corresponding data streams) were in sync thanks to the application of Network Time Protocol (Mills 2006, 1985) at the system level.

For this D2 dataset we split every shikko performance in any of the phases disclosed in Fig. 4. As a result, we segmented every shikko movement in up to 7 different phases (see Fig. 6). This segmentation was useful for either data augmentation and to identify if we can improve the modelling results for any specific phase using different dataset versions, e.g. in the case of the 3 different turn phases (ho tenkans) included in the shikko movement. Thus, D2 can be analysed in several ways, since it actually includes two different movements: knee-walking in a straight line (going and return) and turning, as represented in Figure  5.

Fig. 6
figure 6

Component x of the accelerometer (left y-axis) and the gyroscope (right y-axis) streams for a complete shikko exercise with four straight walks (2 ’go’s and 2 ’return’s) and three turns or ho tenkans (highlighted in grey and referred to the two right most pictures in Fig. 5)

In Fig. 6 we can observe the x spatial axis component corresponding to the accelerometer (right y-axis, dark line) and the gyroscope (left y-axis, light line) streams for a complete shikko exercise with four straight walks (two go’s and two return’s) and three turns (ho tenkans). Focusing on any of the four straight walks, every knee-walking step is represented by a succession of crests and troughs. Thus, counting each of these peaks, either in the acceleration or the gyro component, the number of steps made by this practitioner can be guesstimated. In any of the turn phases, we are only representing gyro information as an example of how well turns are performed following only x gyro component. In this sense, the last turn is less regular, which may represent a symptom of fatigue.

Regarding the technological setup, the IMU embedded inside the smartphone (model Apple iPhone 8 ®) was set to factory default for gathering inertial data for this dataset.

3.1.3 Dataset 3: American Kenpo Karate (Blocking Set I)

This third dataset (D3) gathers the Blocking set I of American Kenpo Karate,Footnote 6 which is the first defence set learned by an American Kenpo Karate practitioner. This set of movements has been designed to teach the learners to block hits aiming to different parts of the body. It is formed by six defensive arm movements (upward block, inward block, outward extended block, downward block, rear elbow block and push-down block). However, to gather the dataset, we added a start position and removed the last movement, which is complicated for new practitioners. Thus, we capture the six movements that are shown in Fig. 7. In this way, the D3 dataset complements the other two by including differentiated executions within the movement. In addition, it is easy to compare these different executions as well as to teach the set to facilitate the capturing process with different participants on the wild.

Fig. 7
figure 7

An American Kenpo Karate learner (one of the authors of this research work) showing the start position and the 5 blocks conforming the Blocking Set I included in this study (start position, upward block, inward block, outward extended block, downward block and rear elbow block). The right most picture shows the experimental setup consisting in an smartphone attached to the martial artist by means of an runner wristband

The dataset includes 16 participants (\(N = 16\)) and 192 total movements (5 different movements performed twice by each practitioner and static noise to detect absence of motion, with right and left arms: \((6 + 6) \text { times } 16 = 192\)). We evaluated 9 different performance levels, being the highest 18 and the lowest 0 for computational purposes. We considered experts from level 9 and beginners below.

For gathering the inertial information, a smartphone (XiaoMi Mi A2) attached to the practitioners wrist through a running wristband was used, as depicted in the rightmost picture of Fig. 7. For data collection, an ad hoc motion capture software was also developed using Android Studio, whose details and setup are more extensively described in Casas-Ortiz and Santos (2021a, 2021b).

The information obtained from the gyroscope was used to manually label and separate each movement, obtaining the total 192 movements. We only considered the movements performed using the martial artist’s dominant hand for a total of 96 movements (\(192 \text { divided by } 2 = 96\)), as we centred this research on analysing the expertise level. This segmentation was also useful to analyse if we can improve the modelling results for any specific partial movement using different dataset versions. From the technical point of view, the main difference of this dataset (in comparison with the other Aikid\(\bar{\text {o}}\) datasets), is that also comprised information from a magnetometer (for obtaining heading information).

Fig. 8
figure 8

Intensity of the acceleration stream (grey points) from the set of the Kenpo dataset defence technique that appears in Fig. 7, executed by an expert. The black thick line is the Bézier curve approximation (from the experimental points) overlaid with the goal of highlighting each of the 6 sequential gestures

A sample stream of the captured acceleration from a participant’s execution of Blocking Set I is shown in Fig. 8. In the figure, each one of the oscillations represents a movement. The higher the oscillation, the higher the acceleration and the longer the movement. The reason of this is that each movement is usually executed approximately in the same amount of time, and longer movements must thus be quicker to be executed in the same time as shorter movements. In this case, the participant is an expert that is executing the six movements (including the one removed from the dataset).

3.1.4 Summary of datasets

From now on, we will use the following tags to account any of these datasets:

  • D1 (bokken shomenuchi dataset)

  • D2 (shikko dataset)

  • D3 (Blocking Set I dataset)

Data acquisition for all these datasets was made on real-world environments with free-living data and using commercial devices (i.e. a small accelerometerFootnote 7 in D1 and two smartphones in D2 and D3) that embed inertial, and occasionally magnetic and virtual, sensors and are attached to the martial art practitioner (or to an instrument intimately linked to the martial art, as in D1).

Table 1 Summary of the three datasets used in this research
Table 2 Segmentations performed for analysing the datasets

These movements and their associated datasets are summarised in Table 1. The column sensor axis represents the information collected by the sensors in any of the three (xyz) dimensions as an independent variable or predictor. In particular, D1 uses only the three axes of the accelerometer, D2 uses six as it includes a gyroscope in addition to the accelerometer, and D3 uses nine, as it also includes a magnetometer. Graphical depictions of any of the movements are included in Fig. 3 (for D1), Fig. 6 (for D2) and Fig. 8 (for D3).

In Table 2, we depict the segmentations performed within each of the three datasets to explore different modelling approaches from the reference movements captured by the participants. For D1 no further segmentation was done as the movement captured is very short. For D2 dataset, seven different segmented phases were considered: 1st go, 1st turn, 1st return, 2nd turn, 2nd go, 3rd turn and 2nd return, thus resulting in two different movements: four straight walks (2 go’s and 2 return’s) and three turns. In this case, although the ideal number of segmented samples should be 1295 (\(185 \text { times } 7\)), some of the phases were not completely registered because were not properly executed, e.g. 2 turns (ho tenkans) instead of 3, or because were not completely performed, e.g. due knee injuries, resulting in 1193 samples. For D3 dataset, the 16 participants performed the 6 different partial movements corresponding to the aforementioned arm blocks: start, upward block, inward block, outward extended block, downward block and rear elbow block, thus resulting in 96 segmented samples.

Table 3 contains a summary of all the sensors included in each of the devices. For each of these sensors, Table 4 shows details about sensor output resolution and sensitivity. Note that, in the case of sensitivities, comparing for instance BMI120 and ADXL345 accelerometers at minimum output resolution (\(\pm 2\ g\)), we have a sensitivity of \(.06 \ \textrm{m}g\) (or \(1/16384\ g\)) for the Bosch Sensortec GmbH model and \(3.9\ \textrm{m}g\) (or \(1/256\ g\)) for the Analog Devices, Inc. model. This means that every time the least significant bit (LSB) changes, we receive variations of \(.06\ \textrm{m}g\) and \(3.9\ \textrm{m}g\) respectively. And therefore, the sensors used in either D2 and D3 datasets are roughly six times more sensitive than the one used in D1 dataset.

Table 3 Devices and sensors used for capturing the datasets
Table 4 Sensor output resolution and sensitivity

3.2 Coordinate systems and quaternions transformations

For recognising psychomotor behaviours, either related with martial arts, as in Santos (2019); Kunze et al. (2006); Heinz et al. (2006); Glowinski et al. (2016), or in general for any type of activity, as in Ariza-Colpas et al. (2022); Yuan et al. (2018), analyse the inertial data collected following a Cartesian coordinate system, which is the output information processed by the inertial sensors. In our research, besides using the original raw Cartesian system and the transformed cylindrical system, we have also explored the utility of a spherical coordinate system transformation. As disclosed in Sect. 1 and following the same principle stated in James et al. (2014), the reasons are grounded on the helicoidal nature of some martial arts, including Aikid\(\bar{\text {o}}\) and Kenpo. A summary of the different transformations performed is included in Table 5. Note that Cartesian in column coordinates represents the raw original data as output information provided by the sensors (without any transformation), while spherical and cylindrical represent the transformations of the raw Cartesian data into a spherical and cylindrical coordinates system, respectively.

Table 5 Raw data and transformations made with the datasets used in this research. Original raw Cartesian data have been transformed into spherical and cylindrical coordinates systems. Subscript a for accelerometer data, subscript g for gyroscope data and subscript m for magnetometer data

Moreover, in this research, aside these coordinate transformations, quaternion representations were also derived from the collected (xyz) spatial data. As stated in Sect. 2, quaternions have proven to be specifically useful for describing spatial rotations, estimating pitch and roll orientations, encoding axis-angle rotation data, fusing raw data and consequently reducing the complexity of the datasets (Sabatini 2005). In fact, the classification of the skilled movements discussed in Sect. 2 demands to accurately define, either the position and the heading of the centre of mass of the body, as in the D2 dataset (Sect. 3.1.2), or the wrists, as in the D3 dataset (Sect. 3.1.3).

User modelling in the context of intelligent psychomotor learning systems also needs to orchestrate a way to provide certain level of feedback, as defined in the SMDD framework (Santos 2016). Thus, instead of classifying the psychomotor behaviour performed, within a set build with different activities, we need to classify the level of expertise (within a set of different performances of the same activity). In this context, quaternion fusion, besides of providing a more accurate depiction of the movement, also reduces the complexity in the analysis for the personalisation support. Consequently, the process is computationally more affordable, as the classification is implemented with less dimensions, 4 in the case of quaternions versus 6 (in D2) or 9 (in D3) dimensions.

Before introducing the different methods used to derive quaternions, we define them as an extension of complex numbers with three square roots of \(-1 (ijk)\) instead of just i:

$$\begin{aligned} {i}^2 = {j}^2 = {k}^2 = {i} \ {j} \ {k} = -1 \end{aligned}$$

Thus, the first component is a scalar real number s and the other 3 form a vector \(\overrightarrow{v}\) as follows:

$$\begin{aligned} q = q_0 +\textrm{i}q_1 + \textrm{j}q_2 + \textrm{k}q_3 = \langle s, v \rangle \end{aligned}$$

where \(s=q_0\) and \(v=\begin{bmatrix}q_1&\ q_2&\ q_3\end{bmatrix}\). For convenience we will use only unit length quaternions:

$$\begin{aligned} \mid q \mid = \sqrt{q_0^2 +q_1^2 + q_2^2 + q_3^2} = 1 \end{aligned}$$

To fuse inertial data into quaternions, we need, at least, information from a six-axis device (which includes at least inertial information from accelerometer and gyroscope sensors, as in D2 and D3 datasets) being not possible to fuse the information gathered with a three-axis sensor (just an accelerometer sensor, as in D1 dataset). Consequently, we performed quaternion fusion in D2 and D3 datasets but not in D1 datasets, see Table 1 and Table 3.

Quaternion calculation from the original data was based on the framework described in Haslwanter (2020), which provides up to four different methods for fusing sensor data: analytical, Mahony (Mahony et al. 2008), Madgwick (Madgwick et al. 2011) and Kalman, as in Sabatini (2011); Guo and Hong (2019). Analytical method does not take into account magnetometer values, while the Mahony and Madgwick ones use this information for improving the accuracy. The Kalman method requires magnetometer information in order to properly operate. Without this sensor, quaternion fusion is often degraded (as evinced by Fig. 9).

Fig. 9
figure 9

Value of the \(q_3\) component according to several methods for deriving quaternions and using sensor information encoded in Cartesian coordinates. The represented data correspond to D2 dataset, in particular to the first go lap of shikko exercise (performed by a beginner student). In this case, the magnetometer information was missing and was introduced as a constant in the computation for the Kalman method (this translates itself into a roughly degraded outcome)

Using the analytical method, simple quaternion integration is performed calculating orientation and position analytically from angular velocity and linear acceleration without drift compensation, so no magnetometer information is used. In the case of using Madgwick and Mahony methods, magnetometer information is optional. Madgwick method uses gradient descent filter and consequently is computationally more demanding. This method usually represents the most accurate transformation when magnetometer information is used (Ludwig et al. 2018) and includes gyroscope bias drift compensation.

Therefore, for each of the datasets included in this research (see Sects. and 3.1.3), we explore whether we can get better results in assessing the level of experience of martial arts practitioners by transforming and/or fusing the original raw inertial (and occasionally magnetic) data. The reasons for including the analysis of different coordinates system transformations and quaternion fusions are to have a better and more accurate representation of the psychomotor behaviour analysed. While coordinate systems transformations better characterise the nature of the motor skill, the quaternion fusion provides a more accuracy depiction of this. To perform a skilled movement classification, where all registries represents the same movement, we need to refine the inertial information to better represents the movement to classify, which we aim to achieve by performing transformations and fusions.

A summary of the different dataset versions used in this research is included in Table 6, where the baseline (v0) in any of the dataset portrays the original data without any transformation or fusion. In fact, we evaluated up to 33 different datasets, including the three original ones. In this sense, for D1 we only evaluated the raw Cartesian (v0) and both, spherical (v1) and cylindrical (v2) transformations, as quaternion fusion was not possible without gyroscope information. For either D2 and D3 datasets, we evaluated 15 different dataset versions for each of them, from (v0) to (v14). As an example, in the case of D3 dataset, version 7 (v7) corresponds to the original Cartesian D3 dataset transformed into a spherical coordinate system and then fused into quaternions following analytical method, that is, quaternion fusion without magnetometer data. Consequently, while any of the versions (v0), (v1) and (v2) of D3 represent a dataset with \(3+3+3=9\) dimensions (see Table 5), the version (v7) of dataset D3 represents the same, but with only 4 dimensions (see equation 2).

Table 6 Summary of the 33 different versions built for this research, from the original raw Cartesian data gathered from the sensor without any modifications, referred as version 0 (v0) and considered as the baseline version for each of the datasets

3.3 Modelling approaches

We considered all the 33 dataset versions in Table 6, to explore ways to assess expertise level, modelling skilled human motion movements, and to explore ways to offer personalised support to students when learning psychomotor skills (Santos 2019).

As data is collected in form of MTS, the modelling processes need to identify trends and patterns in the inertial data gathered. This requires to analyse the relationship between dependent variables (i.e. the expertise level) and independent variables (i.e. the inertial data registered in each of the corresponding dataset versions obtained (15 for D2 and D3 and just 3 in the case of D1). To model these skilled movements performed by martial art practitioners, exploring the underlying relationships between outcome (expertise level) and predictors (inertial data), we followed two different approaches, as disclosed in Sect. 2.

To identify MTS trends and patterns, we need to extract the most relevant features which best represent the inertial data gathered. One of the two different approaches used in this research for this extraction is similar to the one used in Avci et al. (2010), which conducts the feature extraction in different domains, including time (extracting, for example, MTS mean, variance or standard deviation features) and frequency (extracting MTS spectral centroid or energy features among others). For this approach, we used (Barandas et al. 2020) library, which provides a reliable and rapid method to follow (Avci et al. 2010).

The second approach uses a neural networks based method instead for extracting features and was initially introduced in Jafari et al. (2007); Yang et al. (2008), although in neither case they focused on skilled analysis, performing movement classification but not expertise level assessment. Recent efforts have been made to classify human activity using neural networks, as in Dempster et al. (2020); Fawaz et al. (2020), where the convolutional kernels used in convolutional neural networks are applied to detect patterns in the input MTS (inertial data).

Although the first approach, without using neural networks, is computationally faster, deep learning approaches for classifying human activity have gained relevance (Babangida et al. 2022) and we can find different neural network approaches for human activity recognition, including (Tran et al. 2019; Fu et al. 2020; Wang and Miao 2018; Ferscha and Mattern 2004). However none of them analyse skilled movements and efficiency limitations are still challenging (Zhou et al. 2020), especially when one of the ultimate goals is to provide real-time feedback as required in intelligent psychomotor learning systems (Santos 2016). The reason of using random convolutional kernels in this research for classifying MTS that represent skilled movements is that the random kernels used have less computational requirements and consequently are faster than other neural network methods.

3.3.1 Time series feature extraction

The process included in Avci et al. (2010) for activity recognition follows the stages of pre-processing, segmentation, feature extraction, dimensionality reduction and classification. In the same way, this processing approach has already been discussed as appropriate to model the performance of psychomotor activities from inertial sensor data (Santos 2019). In any case, we will not delve into the first pre-processing stage because in the three datasets used here the raw signals obtained have been partially processed by the sensors themselves through their data processing units.

In order to evaluate how we can use extracted features from MTS, we followed (Barandas et al. 2020) and their Time Series Feature Extraction Library (TSFEL), which provides extraction methods for different features across 3 different domains (temporal, statistical and spectral).Footnote 8 The analysis performed in this research was configured using all these domains. In this sense and according to Barandas et al. (2020), most of the spectral domain features have higher computational complexity than the features included in the other domains (temporal and statistical). We applied this extraction methods to each of the 33 different versions (\(3+15+15\)) obtained from Sect. 3.2 and depicted in Table 6.

After performing the feature extraction stage on each of the versions included in Table 6 for each of the three different datasets, we carried out the dimensionality reduction stage. However, instead of Hartmann et al. (2021), which applied linear discriminant analysis (LDA) for dimensionality reduction, we applied least absolute shrinkage and selection operator (LASSO) linear model with iterative fitting along a regularisation path, as in Liu et al. (2020). We used this method as a general rule in all datasets for its speed and versatility and because it usually produces better results when the dimensionality is high, which is our case after applying TSFEL.

3.3.2 Random convolutional kernel transform

One step forward to the use of typical CNN methods for classifying MTS data is the use of Random Convolutional KErnel Transform (ROCKET) framework, introduced in Dempster et al. (2020). This method may achieve good accuracies, even with basic linear classifiers, while using a fraction of the computational complexity of other CNN methods, like Wang et al. (2016) or Fawaz et al. (2020). In contrast to the convolutional kernels typically used in CNNs, ROCKET generates a large number of random convolutional kernels which, in combination, capture features relevant for MTS classification.

ROCKET computes two features from each convolutional layer. The first feature is calculated using a standard approach called global/average max pooling,Footnote 9 which takes the maximum value from each part of the layer. The second feature is calculated using a unique approach called positive proportion value (ppv), which takes the proportion of positive values from each part of the layer. These two features are then combined to create a more robust feature map.

In our research, for convenience and simplicity we set ROCKET with the default number of random kernels (\(k=10,000\)), having 2k features (20, 000) per time series as output from the transform. Once the transformed feature map is generated we can use it as input data for any classification algorithm. Dempster et al. (2020) suggest to use some common linear algorithms like ridge regression classifier or logistic regression.

In addition for this research, we also tested some CNNs, including ResNet (Wang et al. 2016), InceptionTime (Fawaz et al. 2020), Time Le-Net (Fawaz et al. 2019; Guennec et al. 2016) or Time Warping Invariant Echo State Network (TWIESN) (Lukosevicius et al. 2006). Our outcomes using ROCKET surpassed those obtained with these CNNs, which were also adding high computational complexity to the classification. In this sense, our initial results comparing different CNNs methods versus ROCKET are similar to those already included in Dempster et al. (2020). Finally, while ROCKET execution takes minutes, CNNs may take hours with similar or lesser accuracy results.

3.4 Experimental setup

We have analysed 33 different dataset versions obtained from the 3 original datasets (v0, v1 and v2) as compiled in Table 6 and with the 2 methods disclosed in Sect. 3.3.1 (TSFEL) and Sect. 3.3.2 (ROCKET). In order to evaluate the classification behaviour of the proposed approaches for features extraction, we used some well-known classifiers included in the reputed scikit-learn library,Footnote 10 so we could compare the different proposals. A summary of the classifiers and the parameters used is included in Table 7. The parameters were established after several trials. The input for any of them is the features obtained by either method used: TSFEL and ROCKET.

Table 7 List of classifiers used with TSFEL and ROCKET extracted features

In particular, the random forest (RF) classifier was chosen because it is more robust and easier to train than others. For this classifier, the number of trees was set to 100, and Gini impurity was established as the function to measure the quality of the splits. The logistic regression (LR) classifier was included as suggested while using ROCKET framework, and the algorithm (solver) for optimisation was the limited memory Broyden-Fletcher-Goldfarb-Shanno (lBFGS). The ridge cross-validation (RCV) classifier is also recommended by ROCKET framework for smaller datasets (due to fast cross-validation of the regularisation parameter). For the RCV classifier the values for the regularisation strength (\(\alpha \)) were chosen accordingly for reducing the variance of the estimates. The stochastic gradient descent (SGD) classifier is particularly useful when the number of samples is very large. For SGD the maximum number of iterations taken for the solvers to converge was 1000. Finally, the k-nearest neighbour (kNN) classifier was chosen because is robust to noisy training data and effective when training data is large. The number of neighbours (k) was set to 4 after several trials and due showed good results. For the configuration of these classifiers, we decided to mainly use default values in order to better compare the different types of algorithms and representations, without worrying about differences in the parameters.

Before applying the classifiers, all MTS values were scaled using min-max normalisation with a feature range between 0 and 1. This was done basically because, as disclosed in Sect. 3.2 and in Eq. 3, we use only unit length quaternions, so most of the features obtained are already normalised in this scale.

Thus, applying the classifiers depicted in Table 7 we evaluated the accuracy on modelling users performing skilled movements. We also analysed if we can obtain better results using the baseline version (v0 in Table 6) or using different coordinates systems or quaternions (other versions than v0 in Table 6). For all dataset versions included in Table 6, we performed MTS re-sampling method before applying any of the classifiers in Table 7. This operation was particularly useful while using ROCKET, where all kernel input data sizes were equal, but also when using TSFEL, for avoiding window overlaps.

As disclosed in Sects. 3.1.2 and 3.1.3, besides modelling the complete skilled movements performed by any of the martial artists in each dataset, we also extended our analysis for comparing specific segmented movements as disclosed in Table 2. Thus, in this research, for either D2 and D3 datasets, we analysed both the whole skilled movement and its corresponding segmentations into 7 phases or 6 partial movements, respectively.

We included a basic number of re-shuffling and splitting iterations (2) and the proportion of the dataset included in the test split was (\(30.\%\)). In order to control the randomness of the training and testing indices produced, we used the same seed value for a reproducible output across multiple function calls. A visual overview of the experimental setup, specifically for D2 and D3 datasets, is presented in Fig. 10 and Fig. 11.

Initially, see Fig. 10, we start with basic transformations (2) from the original dataset collected (1). Then, sensor fusion is performed (3), resulting in a total of 15 dataset versions.Footnote 11 Then in Fig. 11, the next step (4) is the homogenisation performed with any of the dataset versions. Since martial artist performances differ in time, the execution of each practitioner is represented by a different number of rows, re sampling each performance we got homogeneousFootnote 12 input data for the next phase (5). As disclosed in Sects. 3.3.1 and 3.3.2, feature extraction (5) is performed with ROCKET and TSFEL. The resultant feature map and feature list (6) are finally used to feed the classifiers disclosed in Table 7.

4 Results and discussions

In this section, we provide a detailed study of the results obtained to assess the level of experience of martial artists when they execute skilled movements. As we have been anticipating, there are important differences when it comes to modelling users psychomotor behaviour depending on the type and form of the motion data collected. Therefore, as we might suppose, the accuracy in the results will differ accordingly depending on the dataset used.

Fig. 10
figure 10

Transformations on a martial art dataset collected with inertial sensors (accelerometer, gyroscope and/or magnetometer) that result in alternative dataset versions for modelling the user expertise. V0 is considered the baseline version from which the initial v1 and v2 (basic transformations) are obtained. Then, for any of these 3 initial versions, a fusion into quaternions is performed

Fig. 11
figure 11

General overview of the experimental setup for D2 and D3 datasets. For any of the 15 different versions obtained during the process depicted in Fig. 11, a phase of time series homogenisation and feature extraction is made prior performing the final classification

Regarding the methods used for extracting the discriminatory features, in the case of TSFEL we obtained better results while using the statistical domain above the others (temporal and spectral). Besides, applying this domain we balanced the computational complexity, the total number of extracted features and the final accuracy obtained. In most of the cases, the resulting feature list, after removing redundancies and noise, usually include only few dimensions, just the most representatives. In the case of using ROCKET, the process is more straightforward, as the only parameter to choose is the number of random kernels. In any case, the features obtained with any of these two methods and for any of the dataset versions can be used directly as input data for any classification algorithm disclosed in Table 7.

In all the result tables disclosed in this section, in column classifier we are including the classifier or classifiers whose highest accuracy is obtained among those included in Table 7. Column samples represents the number of martial artist performances included in any of the different datasets (see Table 1).

4.1 D1 dataset results

In the case of D1 dataset (see Sect. 3.1.1), the results obtained after extracting features with TSFEL (see Sect. 3.3.1) are summarised in Table 8. The results after classifying the feature map obtained using ROCKET (see Sect. 3.3.2) are disclosed in Table 9. Note that for D1 dataset we can only consider 3 different versions (see Table 6), as quaternion fusion was not possible to perform with this dataset because we only have information from one sensor (i.e. the accelerometer). This dataset also did not support either any kind of segmentation (see Table 2).

Table 8 D1—TSFEL statistical domain results. In bold the best result obtained
Table 9 D1—ROCKET results. In bold the best result obtained

The best result for user (martial artist) modelling when performing the bokken shomenuchi movement is obtained while using the dataset version with cylindrical coordinate transformations (v2) and after applying kNN as classifier (see Table 7) in the case of using TSFEL (\(60.89\%\)). In turn, ROCKET best results (\(67.39\%\)) are obtained both while using baseline dataset version (v0) and dataset version with cylindrical coordinate transformations (v2) and after applying different classifiers (LR, RCV and SGD) (see Table 7). Furthermore, for the D1 dataset, even in the worst case version (v1), the lower accuracy result after applying ROCKET (\(65.21\%\)) is better than any result obtained when using TSFEL (see Table 8).

Table 10 D2-TSFEL statistical domain results-summary. In bold the best result obtained

4.2 D2 dataset results

As expected, with D2 dataset (see Sect. 3.1.2) we are improving the accuracy in modelling users (martial artists) from D1, because we have the information from two sensors (accelerometer and gyroscope). The results obtained after using TSFEL are summarised in Table 10, while the results applying ROCKET are available in Table 15. In either case, we are only showing the results obtained with the baseline (v0) version and with basic transformation versions, (v1) and (v2), plus the best result obtained with any of the quaternion fusion versions (see Table 6).

Focusing first on the TSFEL modelling, upper half of the Table 10 (segmented) includes the summarised results obtained while analysing D2 dataset per phases. Version (v6) corresponds to the quaternion fusion following the Kalman method (see Sect. 3.2) with Cartesian coordinates (see Table 6). In the lower half of the Table (complete), we have the results obtained while analysing D2 dataset per martial artist, considering the complete movement, given that in this case, contrary to the previous dataset, it is possible to split the movements into different phases (see Table 2). Version (v4) corresponds to the quaternion fusion following the Madgwick method (see Sect. 3.2) with Cartesian coordinates (see Table 6).

After using TSFEL, the best results for user (martial artist) modelling, when performing the shikko movement, analysed per phases, are obtained while using baseline dataset version (v0), and dataset version with spherical coordinate transformations (v1) and after applying RF as classifier (see Table 7) in both cases. When analysing the complete movement, the best result is obtained while using baseline dataset version (v0) and also after applying RF as classifier (see Table 7). The baseline dataset version (v0) in the complete dataset is the one that obtains the highest accuracy for D2 dataset using RF classifier.

As an example of the use of TSFEL in this dataset, one of the features that is usually included in the resultant feature list, in almost all versions except in versions (v3), (v5) and (v6), is the histogram of the signal, computed as follows:

$$\begin{aligned} n = \sum _{i=1}^{k} m_i \end{aligned}$$

where \(m_i\) represents the histogram in which n is the total number of observations and k the total number of bins (Barandas et al. 2020). For the versions (v4), (v5) and (v6), the most representative feature that is included in all its feature list is the empirical cumulative distribution function (ECDF) along the time axis, which is also included in other versions, and which formula is as follows:

$$\begin{aligned} \frac{1}{n} \sum _{i=1}^{n} I[x_i\leqslant {x}] \end{aligned}$$

where n is the number of data points, I is the indicator function, and \(x_i\) is the ith data point. In this case, the indicator function is used to count the number of data points that are less than or equal to a given value (x). If the result of this comparison is true, then I is equal to 1, and 0 otherwise.

Other features, although present in some of the feature list versions, are less common, including variance, median, mean, root mean square, skewness and kurtosis among others. As a practical example of this, in Table 11 we are representing the most relevant extracted features for the v4 version of the D2 dataset (see Table 6), that were used to feed the classification algorithms. In this case, after using LASSO for dimensionality reduction, we finally picked only 6 features from the total number of features obtained with TSFEL. Initially and for this dataset, for any of the 4 different input variables (\(q_0\), \(q_1\), \(q_2\) and \(q_3\)) TSFEL calculates up to 16 different statistical domain features. TSFEL also calculates several times (10 by default and so called bins) some of this features (e.g. Histogram and ECDF), so each bin correspond to a different feature. Therefore, in Table 11, column bins represents the number of those that are more relevant. For example, in the case of \(q_1\) and Histogram there are up to 3 relevant bins: 0, 1 and 2, where the other 7 bins were not relevant in this case.

Table 11 List of the relevant features for the version v4 of the D2 dataset

Note that, in addition to the above results, for D2 dataset and TSFEL method, we also evaluated movements considering only some stages separately (see Fig. 6), specifically the 2 different going phases (see Table 12), the 2 different return phases (see Table 13), as well as any of the 3 turns analysed jointly (see Table 14). In this case, for the going and return phase analysis, the best results are obtained with the spherical coordinate transformations (v1) and the turn phase, due its circular nature, is better to model using quaternions (v5). In all these 3 analysis (see Table 12, Table 13 and Table 14) the best results are obtained after applying RF as classifier (see Table 7).

Table 12 D2—TSFEL only going movements results—summary. In bold the best result obtained
Table 13 D2—TSFEL only return movements results—summary. In bold the best result obtained
Table 14 D2—TSFEL only turn movements results—summary. In bold the best result obtained

Finally, in the case of using ROCKET with D2 dataset, the best results for user (martial artist) modelling, when performing the shikko movement, analysed per phases, is obtained while using dataset version with spherical coordinate transformations (v1) and after applying RCV as classifier (see Table 7). The best result analysing the complete movement, is obtained while using dataset version with spherical coordinate transformations (v1) and after applying RCV and SGD as classifiers (see Table 7).

Table 15 D2—ROCKET results—summary. In bold the best result obtained

In any case, considering both TSFEL and ROCKET methods for this D2 dataset, the best results in either case, regarding the whole movement or any of the segmented phases, are obtained with the baseline version (v0) in the case of using TSFEL (\(78.57\%\)) or with one of the basic transformations (v1) in the case of using ROCKET (\(82.14\%\)), representing the best efforts obtained for this D2 dataset after applying any of the methods disclosed in Sects. 3.3.1 and 3.3.2. On the other hand, quaternion versions are only useful to model turn phases separately, obtaining in this case a best result of \(76.08\%\) versus the \(65.21\%\) obtained with baseline and basic transformation versions.

Note that sample figures in the TSFEL analysis (1184 in Table 10) differs from those obtained with ROCKET (1193 in Table 15) because in the case of TSFEL, we removed some very short phases to avoid distortions in the extraction of features.

4.3 D3 dataset results

Table 16 D3—TSFEL statistical domain results—summary. In bold the best result obtained
Table 17 D3—ROCKET results—summary. In bold the best result obtained

Reciprocally to Sect. 4.2, in the case of D3 dataset, we have a summary of TSFEL results in Table 16 and the summary of ROCKET results in Table 17. In either case, using TSFEL or ROCKET, in Tables 16 and  17, we are only showing the results obtained with the baseline (v0) version and with basic transformation versions, (v1) and (v2), plus the best result obtained with any of the quaternion fusion versions (see Table 6). In the same way than before, the upper half of the table (segmented) includes the summarised results obtained while analysing D3 dataset per partial movement. In the lower half of the table (complete), we have the results obtained while analysing D3 dataset per martial artist, considering the complete movement.

For this D3 dataset and using TSFEL, the best results (\(80.\%\)) for user (martial artist) modelling, when performing the blocking set I movement, analysed per partial movement (segmented), are obtained while using quaternion fusion (Madgwick) version with Cartesian coordinates (v4) and after applying RF as classifier (see Table 7). The best results for the complete movement are obtained while using many dataset versions, including baseline (v0), basic transformations, (v1) and (v2), and some quaternion fusions.

In the case of using ROCKET in this D3 dataset, the best results (\(80.\%\)) for user (martial artist) modelling, when performing the blocking set I movement, analysed per segmented movements, are obtained while using quaternion fusion (Analytical) version with cylindrical coordinates (v11) and after applying RF and LR as classifiers (see Table 7). Analysing the complete movement, we obtained the best results while using quaternion fusion (Kalman) version with cylindrical coordinates (v14) and after applying RF as classifier (see Table 7). For this D3 dataset, the improvement of using quaternions is notorious, specifically when using ROCKET method and either when analysing the segmented and the complete movement, achieving results that are between 40. and 50.% better than the baseline or the basic transformation versions, see Table 17.

4.4 Results findings and discussion

In Table 18 we include a summary the most representative findings obtained after analysing the results of Sects. 4.1, 4.2 and 4.3.

Table 18 Most relevant result findings—summary

Despite the diverse nature of the different datasets used in this research, following the results introduced in Sects. 4.1, 4.2 and 4.3 we initially may conclude that, especially in the case of using complex datasets, such D2 and D3, we can model users by automatically classifying martial artists between experts and beginners through datasets built with inertial information. As expected, expert martial artists in D2 and D3, tend to fulfil the movements smoothly, showing autonomous behaviour in their performance. In Fig. 12, we have the signals gathered while an expert and a beginner are performing one of the shikko movement phases. As we can appreciate, beginner movements are erratic and less predictable.

Fig. 12
figure 12

Fourth component of the Cartesian-based quaternion (\(q_3\)) for two Aikid\(\bar{\text {o}}\) practitioners (beginner and expert) while performing the first (of the four) straight lap of the shikko-knee-walking exercise

In the same way, and following (Santos 2016), we may conclude that the learning experience in the psychomotor domain is not explained through the conscious knowledge of the discipline but associated with physical skills related to manual tasks and physical movements, acquired through the experience. In the case of D1, the basic swing (sh\(\bar{\text {o}}\)men) movement performed with the bokken, the analysis is not so conclusive. We may explain this because the performance level in this movement is often difficult to appreciate, in addition to the fact that the sensor used in this dataset (see Table 3), only registered 3 dimensions and its sensitivity was also much lower compared with the one gathered in the other datasets (see Table 4). Thus, while in D2 and D3, over \(80.\%\) of the times we achieved to distinguish between beginner or expert practitioner, in D1, although we could not reach \(70.\%\) of accuracy, we could slightly distinguish between beginner or expert too.

In this sense, all datasets used in this research include practitioners from 19 to 69 years old, for the datasets D1 and D2, and from 21 to 65 years old in the case of dataset D3, and consequently the proposed analysis demonstrates how we can infer performance level independently of other physical parameters, such age (Voelcker-Rehage and Willimczik 2006; Voelcker-Rehage 2008). The relevance of this is that our AI-driven analysis mainly considers mastering psychomotor skills as a gradual process where execution improvements comes from the experience, as discussed elsewhere (Santos 2019). Thus, improving belt rank means acquiring more experience, independently of other external factors.

With the proposed analysis, we fulfil the basis for personalising tangible psychomotor learning support, as defined in Santos (2016): sensing the learner’s corporal movement and comparing this against the accurate movement. Thus, once the information collected has been analysed, we can compare beginner movement against the expert movement and decide whether it is appropriate or not to provide the tangible support.

Generally speaking, in the case of D2 dataset, we can assess expertise level with an accuracy of \(78.57\%\), while using TSFEL, and with up to \(82.14\%\), in the case of using ROCKET. In the case of D3 dataset, we reach an accuracy of \(80.\%\) using both methods, TSFEL and ROCKET.

In relation to D2 dataset, as the movement registered was basically rotational, transforms made from raw inertial data (Cartesian) to other coordinate systems (spherical and cylindrical) demonstrated, as expected, an improvement inferring performance level. In this sense, we may distinguish between the two approach methods used, comparing the results obtained with TSFEL and ROCKET. While using ROCKET, the highest accuracy (\(82.14\%\)) is obtained using spherical coordinates during the whole shikko movement. On the contrary, with TSFEL we barely match the highest accuracy obtained with the raw inertial data collected: \(75.\%\) versus \(78.57\%\). However, analysing TSFEL’s results for this shikko movement separately per phases (Table 12, Table 13 and Table 14), we always reach better accuracies with spherical coordinates (goings and returns) or with quaternions (turns). This entails that both methods, TSFEL and ROCKET, work better with transformations (spherical) or fusions (quaternions) than with the baseline version. In addition, the extracting statistical domain features (TSFEL) are more adequate for analysing movement phases and convolutional kernels (ROCKET) are better analysing the whole movement. Using TSFEL in the most rotational shikko movement phase, the turns, we achieved the best accuracy result using quaternions (see Table 14). This is consistent with what was stated above, although we need to take into account that, unfortunately for this D2 dataset, magnetometer data was missing, so quaternion fusion was not as accurate as the one obtained in D3.

Regarding the D3 dataset, both methods, ROCKET or TSFEL, allowed better accuracy results using quaternions, as evinced in Tables 16 and 17. As stated in Sect. 3.1.3, the American Kenpo setup also comprised magnetometer information, which has resulted in a more accurate quaternion derivation. In this case, due we have a small number of practitioners (16), we estimated the analysis to be more realistic in the case of considering any of the six different movements registered separately, as phases for a total number of samples of 96. The results obtained show us the usefulness of using quaternions. In this case, as D3’s movements were not as rotational as the movement included in D2, the results using spherical or cylindrical were similar (ROCKET) or slightly worse (TSFEL) than those obtained in baseline (Cartesian).

Only in the case of using TSFEL, and related with the most representative features obtained after LASSO reduction, in the case of D2, together with some of the different histograms computed from the collected signals, we also found relevant the ECDF computation (Barandas et al. 2020). In the other hand and in the case of D3, the best quaternion accuracy was also with two of the different histograms computed. Thus, in both datasets, D2 and D3, the most relevant TSFEL feature used for distinguish between expert and beginner is the histogram, understood as the relative frequency which is equal to the frequency for an observed data value divided by the total number of data values in the sample.

We also confirmed that the main differences between TSFEL and ROCKET, is the time consumed in their executions: while ROCKET takes minutes, TSFEL extract features in seconds. As expected, although ROCKET is considerable faster than the mentioned CNN methods, its completion time it is not comparable with TSFEL, which is much faster. Thus, as the TSFEL approach is faster than ROCKET, this entails that it might be easy to implement into small devices due its low computer complexity (embedded devices).

Finally, the above is still valid for analysing specific behaviours that are not directly related with expertise level assessment, such fatigue monitoring or emotional level evaluation. As disclosed in Sects. 3.1.1 and 3.1.2, throughout the execution of the movement, we can observe how performance evolves, being able to appreciate certain symptoms of fatigue. Flexibility, as well as Joint Range of Motion (JROM) assessments (Thorpe et al. 2017), are elements that can be analysed, gathering for instance inertial information, to monitor fatigue in sports. Moreover, physical and mental fatigues are related, not only from the point of view of physical performance deterioration, but also via changes in technique execution (Russell et al. 2019). Thus, technical impairments can also be detected analysing inertial information in order to monitor mental fatigue. The foregoing can be directly extrapolated to the analysis of emotional factors and its relationship with psychomotor behaviours (Avalos et al. 2022).

4.5 Limitations and future works

Although D2 is a very detailed and complete dataset to perform our research, the main limitation of this is the lack of information coming from a magnetometer sensor. Having these 3 more coordinates, we could have improved the quaternion fusion as confirmed with D3 dataset, the only dataset used with real magnetometer data. This highlights the need to include enriched inertial data to model in a more precise and accurate way the performances of the practitioners. Furthermore, we can add more devices and thus more sensors to improve the assessment.

In this case, D3 dataset, the number of martial artists included was only 16 and, although we performed some data augmentation, splitting every blocking set I movement into six other different movements, the reduced number or participants was also a limitation of this research. In the same way, it is essential to be able to orchestrate experiences to allow the collection of a greater amount of data. What is exposed in this article, like most of the researches, would be benefited from the inclusion of a greater number of participants.

Despite the intrinsic disclosed limitations derived from the use of other capture devices for the purpose of solving the research question, such as video images (Tee et al. 2022; Ige and Mohd Noor 2022; Qiu et al. 2022; Gupta et al. 2022; Saha et al. 2022; Pereira and Gonçalves 2022; Babangida et al. 2022; Lateef and Abbas 2022), our research could have benefited from a multi modal and multi sensor approach, incorporating video images into the inertial analysis. To resolve this eventuality and to include video images to support inertial analysis, in future researches we will follow similar approaches to those considered with the iBAID (intelligent Basket AID) system (Portaz et al. 2023) where video images are used to support inertial analysis by providing a human-centred approach with the aim of recommending the physical activities and movements to perform when training in basketball, either to improve technique, to recover from an injury or even to stay active when ageing.

The current approach of analysing movement practice individually does have its limitations, particularly in scenarios where collaborative psychomotor efforts are essential. However, in these cases, and as outlined in Echeverria and Santos (2021), there exists a promising avenue for enhancement. By introducing an intermediate level between the existing Level 1 and Level 2 in the suggested hierarchical ontology (as shown in Fig. 1), we can effectively address whether movements are executed individually or within a collaborative scenario. This addition to the hierarchy not only expands the scope of applicability but also ensures a more comprehensive and adaptable approach to movement practice. It holds the potential to significantly enrich the learning experience and outcomes, particularly in contexts where collective coordination is paramount.

Another limitation is the current gender distribution, which shows a clear dominance of male martial artists, depending of the dataset, the percentage of female participants vary from \(12.5\%\) (D3) to \(13.63\%\) (D1) and \(14.59\%\) (D2). In order to fulfil one of the aims of this research, which is to develop psychomotor learning systems that favour gender equality and social inclusion, we should put more efforts into favouring more diverse data collection in the future.

5 Conclusions

This work demonstrates a promising correlation between the inertial sensor data gathered by inertial systems and the modelling of users’ expertise levels during the acquisition of psychomotor skills. The findings suggest that such technology holds potential in providing valuable insights into skill acquisition and proficiency assessment. This novel approach not only enhances our understanding of learning processes but also opens new avenues for personalised and adaptive training methodologies. Further research and refinement in this area have the potential to revolutionise skill acquisition across various domains, benefiting both beginners and experts alike.

As an overview, we have tested whether it was possible to classify martial artists according to their expertise level and by measuring very specific movements or gestures, solving affirmatively the initial research question. These measurements have been carried out just with simple inertial sensors (accelerometers, gyros and magnetometers) attached to a single spot on the practitioner’s body or martial instrument (sword). Two martial arts have been researched as a proof-of-concept: Aikid\(\bar{\text {o}}\) and American Kenpo Karate. The logged data streams have been subsequently transformed and prepared by several means prior to be fed into state-of-the-art classification algorithms. These transformations have comprised coordinate transformations, quaternion fusion, feature extraction and convolutional neural networks, applied to multivariate time series data.

Thus, the method proposed in this research to model users in the frame of psychomotor learning system, uses martial art datasets with transformed and fused inertial raw data, which was collected with magnetic and non-magnetic IMUs and applying different approaches for the classification of the discriminatory features extracted. One of the approaches has been chosen due it represents the current state-of-the-art for time series classification (i.e. TSFEL library), while the other approach used in this research has been specifically conceived for human activity recognition and MTS (i.e. ROCKET framework for CNN).

Results have shown that it is possible to achieve a \(>82\%\) classification success rate. We also demonstrated how transforming raw data into spherical or cylindrical coordinates can improve the accuracy in the classification, overall if the studied movement includes rotational behaviour. The application of quaternions has also shown to be adequate in this setup (above all when magnetometer information is available, as it has been the case of American Kenpo Karate dataset).

Several other final conclusions may be taken into consideration regarding the method used. Thus, while the extraction of features (performed using the TSFEL library) may work better when analysing a unique movement or phase, ROCKET may produce better results when the analysis includes a complete movement or a joint sequence of movements.