Remote Gait Monitoring System to Facilitate Assessment of People with Multiple Sclerosis

INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 1 Remote Gait Monitoring System to Facilitate Assessment of People with Multiple Sclerosis Joaqu´ ın Ordieres-Mer´ e, Mercedes Grijalvo, Guillermo Mart´ ın- ´ Avila, and Yolanda Aladro Abstract—Gait impairment is among the most common and affecting symptoms of Multiple Sclerosis, occurring in more than 90% of patients as the disease progresses. Conventional clinical tests, such as the Timed 25-foot walk, are not always able to capture the entire richness of gait impairment, especially in everyday settings. To overcome these shortcomings, this research introduces a new remote gait monitoring system based on wearable smart socks embedded with inertial sensors. The system continuously receives high-frequency motion data and therefore enables gait auto-recognition and can improve the classification of MS-associated gait impairment. An end-toend pipeline for data processing was developed, which involves sensor fusion techniques, semantic gait modeling, and machine learning classification. The segmentation and characterization of gait are performed using spectral analysis of accelerometer and gyroscope signals, with Short-Time Fourier Transform based feature extraction to identify the periodicity and quality of gait. In addition, a deep learning approach based on the combination of convolutional neural networks and long-short-term memory networks is used to discriminate walking patterns with high precision that help detect abnormalities related to multiple sclerosis. Experimental validation was carried out on a population of people with MS and healthy controls, with our model achieving an average accuracy of 97.10% and an Area Under the Curve of 0.99 for severe multiple sclerosis classification. The Internet of Wearable Things paradigm introduced here continuous data acquisition and integration with other wearable sensors and offers a non-invasive and scalable solution for continuous gait monitoring. The results highlight the potential of this approach to improve clinical examination, enable early detection of mobility decline, and support individualized rehabilitation planning. Future studies will explore the incorporation of transformerbased AI models to further improve the classification of multiple sclerosis disability. Index Terms—Internet of Wearable Things, Multiple Sclerosis, Remote gait monitoring, Sensor Fusion, Semantic structure. I. INTRODUCTION MULTIPLE sclerosis (MS) is a chronic, inflammatory and neurodegenerative disease of the Central Nervous System, affecting mainly young adults and causing their This paper was submitted 02/19/2025. J. Ordieres-Mer´ e works for the Universidad Polit´ ecnica de Madrid. c / Jos´ e Guti´ errez Abascal 2, 28006 Madrid, SPAIN (e-mail: [email protected]). M. Grijalvo is also associated with the Universidad Polit´ ecnica de Madrid, Madrid 28006, SPAIN (e-mail: [email protected]). G. Mart´ ın- ´ Avila works as neurologist at the Hospital Universitario de Getafe, Carr. Madrid - Toledo, Km 12,500, 28905 Getafe, SPAIN (e-mail: [email protected]). Y. Aladro is the Coordinator of the Multiple Sclerosis Unit at the Hospital Universitario de Getafe, 28905 Getafe, SPAIN (e-mail: [email protected]). She is also professor at Universidad Euopea de Madrid and member of the Research Group IdiPaz (https://www.idipaz.es/) disability. According to the International Federation of MS Atlas in its 3rd code edition, approximately 2,900,000 people with MS (PwMS) live worldwide, including approximately 700,000 in Europe and 55,000 in Spain [1, 2]. Each year, more than 2,000 new cases are diagnosed in Spain. MS often begins between the ages of 20 and 40 years [3, 4]. Gait disturbances are the main cause of disability progression in Multiple Sclerosis (MS), present in more than 90% of patients [5, 6]. The diagnosis and monitoring of progression are based on the Expanded Disability Status Scale (EDSS), and the timed 25-foot walk (T25FW) tests, both with rather low sensitivity and reproducibility, resulting in delayed diagnosis and poor treatment optimization [7]. Although conventional gait parameters provide a valuable snapshot of mobility, this study introduces a novel approach that focuses on the continuous, frequency-based characteristics of gait signals, which we argue are more ecologically valid for remote, long-term monitoring of PwMS in their daily lives. For PwMS, changes from baseline in T25FW over 20% are generally considered clinically significant [8, 9]. These tests have several limitations that make them an incomplete measure of overall gait function. One of its primary drawbacks is that it only evaluates shortdistance walking, providing little insight into endurance and the ability to maintain mobility over longer periods, which is crucial for daily activities. Furthermore, it may not be sensitive enough to detect mild impairments in individuals with earlystage MS, as they can often complete the test within normal time ranges, limiting its usefulness in identifying subtle gait dysfunctions [10]. While these limitations of conventional assessments are well-documented, a growing body of research has demonstrated the potential to enhance these very tests by adding wearable sensors. By doing so, clinicians can obtain objective and quantitative data on patient walking performance during these structured tasks. However, even with the addition of sensors, these tests are performed in a controlled clinical setting, providing only a limited snapshot of a patient’s mobility. They do not capture the variability, fatigue, and compensatory mechanisms that manifest throughout a patient’s day in their natural environment. To truly understand how MS affects mobility on an everyday level, a more ecologically valid assessment is necessary. Another significant limitation of T25FW is its inability to assess fatigue, a major symptom in MS that can severely affect mobility over time. Since the test is very brief, it does not capture the progressive decline in walking ability that may occur with prolonged activity. Similarly, it does not provide a comprehensive analysis of gait, as it does not take into ac-0000–0000/00$00.00 © 2021 IEEE INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 2 count factors such as balance, coordination, and compensatory walking mechanisms that are often present in individuals with MS [11]. The test results can also be influenced by external factors such as surface conditions, the use of assistive devices, and patient motivation, leading to variability in the outcomes. Furthermore, it is subject to ceiling and floor effects, as those with mild MS can perform at near-normal speeds, making it difficult to detect meaningful changes, while those with severe disability who cannot walk cannot complete the test, rendering it ineffective for nonambulatory PwMS [12]. Although the Expanded Disability Status Scale (EDSS) provides a helpful snapshot of neurological impairment in MS, it does not provide a full picture of one’s mobility. To get the full picture, clinicians will rely on a variety of tests. When a patient comes for their follow-up, the doctor performs the EDSS, noting their level of disability. But to truly understand how MS affects your mobility on an everyday level, a further detailed assessment is necessary. The physician may require the patient to perform the 6-Minute Walk Test (6MWT), which measures the distance they can walk in six minutes, assessing their endurance and functional walking capacity. Then, the Timed Up and Go (TUG) test might be used. This simple test aims to evaluate their dynamic balance and coordination, both of which are necessary to perform daily tasks [13]. However, these other assessments, while useful, are not so convenient in a hectic clinical setting. In accordance with the American Thoracic Society (ATS) guidelines, the Six-Minute Walk Test (6MWT) is recommended to be conducted on a 30meter (100 ft) straight course to minimize turns and ensure comparability of results [14–16]. Although shorter walkways (e.g., 25 ft) have been employed in certain studies under spatial constraints, such adaptations can lead to reduced distances due to increased turning frequency and should be interpreted with caution when compared to ATS-standard results [17]. Similarly, the TUG and gait analysis often have to spend considerable amounts of time performing and interpreting, potentially disrupting patient continuity of care. Therefore, while these tests are informative for the evaluation of MS mobility, clinicians must balance their use with careful consideration against the practical needs of their own clinical environment. The use of wearable technology to measure gait dysfunction in PwMS in non-clinical settings is a proposition that is supported by an overwhelming amount of empirical evidence. The reasoning is as follows. MS tends to exhibit gait dysfunction and monitoring the changes is vital in the disease’s management. Conventionally, this has meant face-to-face evaluation by a neurologist, typically specialized hardware in the laboratory. However, these measures over time are not necessarily an accurate reflection of the overall assessment of a patient’s ability to walk on a daily basis, a measure known as ecological validity. From approximately 2018, there has been increasing research that validates wearable sensors, such as those contained in smartwatches, insoles, or small devices worn by the person, as an accurate means of quantifying important gait parameters. Research conducted by Di Flumeri et al. [18] and Tipton et al. [19] has shown that these sensors are capable of precisely recording parameters such as walking speed and cadence, with close correlation with the values recorded using widely recognized laboratory equipment. These tools are more than basic assessment instruments; they can detect subtle changes and differences in gait, as seen by Soltani et al. [20], and can possibly become early markers of disease progression. The focus then turns to how these tools can be applied in practical situations. Research, such as that by Briggs et al. [21], indicates that PwMS typically have the willingness and ability to use these sensors at home, following normal monitoring protocols. This is a significant benefit, allowing for continuous or routine data collection in the context of a patient’s daily environment. The long-term advantages of this change are enormous. The ongoing monitoring process enables early detection of subtle gait changes, hence more timely interventions; this concept is further explored by Sparaco et al. [22] and Salaorni et al. [23]. Secondly, the collected comprehensive data can be used to guide the development of personalized treatment regimens and rehabilitation protocols, with interventions adapted to the individual needs of the patient [24]. Furthermore, remote monitoring can help minimize the need for regular face-to-face clinic appointments, alleviating the burden on both patients and the healthcare system [25]. A set of wearable inertial sensors can provide objective and reliable measures of gait disturbances and constitute potentially useful tools to monitor clinical progression in prospective cohorts of patients, both under laboratory conditions and during daily activities [22]. Wearable devices can detect physical condition, use real-time perception, and compare and analyze a large amount of data for analysis, interpretation, and response and can then select the most appropriate current processing and support [26]. Based on the above, evaluating and quantifying walking in the community for longer periods of time would be a more ecological approach, reflecting better the functional interference of its impairment in the quality of life of PwMS. Therefore, this paper explored how inertial sensors could provide objective and reliable measures of gait disturbances and constitute potentially useful tools for monitoring clinical progression in prospective cohorts of patients, both under laboratory conditions and during daily activities. To achieve this goal, we adopted a new generation of wearable smart socks that provide an extensive inertial measurement unit (IMU) with 12 channels, including pressure sensors for feet. A specific information technology (IT) framework was developed to handle the collected information, as it was relevant for data analysis and for usability when fusing with other sensors (see Fig. 1). Support for the digital usage of technology by patients has previously been evaluated [27, 28]. Within the framework, the identification of the EDSS for PwMS based on such data sets will be further analyzed. II. STATE OF THE ART Currently, wearable devices are more likely to be purchased by individuals who already lead a healthy lifestyle and want to quantify their progress [29]. Most wearable manufacturers (e.g. Fitbit and Nike) stress the potential of their devices to INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 3 Fig. 1. The Sensoria Inc ™smart socks with IMU and three pressure sensors per foot (S0–S2), used as the main wearable platform. become an ’all-in-one’ platform to improve physical performance and positive habit formation [30]. The main vision is that wearable devices with sensors transform care by moving from manual transfer of subjective self-reported information to an integrated, longitudinal, minimally intrusive, and interactive sharing of data based on the ecology of a person in their natural settings [31]. It is mobile health (mHealth) as a key component of connected health and technology-enabled care (TEC) [32]. In (MS), the experience with such devices is limited [22, 26]; but laboratory-based gait assessments detect subtle deficits in gait quality in the early stages, even without subjective functional alterations [23, 33]. Although the metrics obtained in the clinical setting basically provide a static snapshot, they could be useful to predict and detect progression in longitudinal studies. Although preliminary studies such as Stellmann et al. [34], Block et al. [35] have indicated that simple quantification of gait, including stride length and walking time, yields valuable indicators of disease severity in MS, the importance of employing more sophisticated spatial and temporal parameters in assessing changes in motor function is increasingly appreciated. Stride length is a significant parameter that reflects the capacity of PwMS to maintain coordinated movements; notably, shorter stride lengths tend to reflect improvements in disease progression and higher levels of disability. In addition to stride length, research emphasizes the importance of gait velocity, cadence, and variability [36]. Flachenecker et al. [33] show that it is possible with wearable sensors to continuously monitor these parameters, unmasking subtle changes in the pace of walking that can denote a reduction in motor function prior to clinical onset. These devices have proven useful in evaluating different spatiotemporal gait parameters in the laboratory setting and, even more relevant due to their ecological validity, in quantifying ambulation during prolonged monitoring in reallife settings. They have shown clinical utility in Parkinson’s disease, cerebellar disorders, stroke, and other processes. Step symmetry is another key feature that quantifies the degree of coordination of the lower extremities. Step length or timing inconsistencies have been associated with motor dysfunction after MS, as demonstrated by M¨ uller et al. [17] through a study in which they depicted the progression of gait asymmetries with the progression of the disease. In addition, the research by Psarakis et al. [37] emphasizes the role of compensatory gait mechanisms and instability, specifically related to fatigue, which is a prevalent symptom of MS. For example, increased postural sway and decreased ankle dorsiflexion are signs of compromised balance and an increased risk of falling. In addition, Abbadessa et al. [38] explore the usefulness of wearable biosensors in tracking alterations in gait patterns, allowing medical professionals to identify deviations from a patient’s norm and perform interventions on time. In general, although step count and walking time alone are valuable markers of mobility patterns, the addition of parameters such as stride length, gait speed, step symmetry, cadence, and postural stability allows a more sensitive assessment of MS development. These additional gait parameters enhance the validity of remote monitoring, and wearable sensors have emerged as an increasingly effective means of tracking motor function impairment in PwMS. Wearable IMUs for motion sensors are made up of accelerometers and/or gyroscopes that measure linear acceleration and angular velocity and record body movement in the three axes of space. They are shown to be reliable, sensitive and inexpensive assessment tools that have a growing application in gait analysis [39, 40] and other movement disorders [41–43] in the field of neurology. A recent study by Zahn et al. [44] further validates this, demonstrating a high degree of agreement between IMU-derived spatio-temporal parameters and those obtained from gold-standard markerbased motion capture systems during walking in people with MS. These devices have proven useful in evaluating different spatiotemporal gait parameters in the laboratory setting and, even more relevant due to their ecological validity, in quantifying ambulation during prolonged monitoring in real-life settings. They have shown clinical utility in Parkinson’s disease [42, 45], cerebellar disorders [40] or stroke [46], and other processes. The ability of IMUs to estimate position during gait is rooted in the principle of dead reckoning, where acceleration data from the device is double integrated over time to estimate displacement. However, this approach is susceptible to drift errors due to noise accumulation, which requires error correction techniques such as zero-velocity updates (ZUPT) or Kalman filtering [17]. In particular, step-length estimation, a valuable parameter of gait analysis, can be enhanced with step detection algorithms that exploit the periodicity of the accelerometer signals. It enables accurate monitoring of mobility impairment in progressive diseases such as MS. However, orientation estimation is based on sensor fusion algorithms such as Madgwick or Mahony filters, which use a combination of gyroscope and accelerometer data to allow drift-free orientation tracking [47]. Gyroscopes are very sensitive to rotations, but tend to drift in the long term; accelerometers address this issue by offering a gravity reference. Furthermore, the inclusion of magnetometers can be utilized to improve heading estimation, especially where there are negligible external magnetic disturbances[33]. Fundaments of INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 4 the mathematical support for identification of the step-length are included in the Appendix A. Recent advances in transformer-based architectures have substantially enhanced gait analysis by improving the capacity to model complex spatio-temporal dependencies in human movement data. In particular, Le and Pham [48] proposed a spatio-temporal transformer network to estimate critical gait parameters, such as walking speed and gait deviation index, directly from RGB video streams, demonstrating significant improvements over CNN-based baselines while reducing manual feature engineering efforts. Similarly, Dinh et al. [49] introduced a dual input convolutional transformer system that accurately infers gait indices using single view video recordings, validating its utility in clinical environments with limited resources. Cosma et al. [50] developed GaitFormer, a transformer-based model trained with noisy multitask learning on the DenseGait dataset, showing strong generalization and outperforming traditional models even without manual annotation. Complementing this, Nguyen et al. [51] explored the use of transformers in 1D inertial signals for Parkinson’s gait detection, noting both higher classification performance and better stability compared to recurrent models. Beyond recognition, generative transformer architectures like GAITGen [52] have been introduced to synthesize realistic gait sequences conditioned on pathology severity, enriching clinical datasets and improving downstream task performance. Moreover, Basoc et al. [53] explored SetTransformers for dataset-agnostic gait enrollment, demonstrating scalable transformer-based modeling under open set recognition settings. These studies collectively establish transformers as powerful tools for modeling gait patterns in clinical and general domains. Recent years have witnessed a surge in the application of deep learning and IoT for remote gait analysis, particularly in telemedicine contexts. Sarkar [54] presented a hybrid CNN-LSTM architecture for wearable-based gait recognition, achieving robust performance in free-living scenarios. Other works have integrated attention mechanisms with multimodal wearable sensors to enhance gait quality prediction within IoT-driven frameworks [55]. These studies underscore the growing synergy between deep learning models and sensorrich wearables for continuous mobility monitoring. Our framework is also designed to be compatible with cutting-edge machine learning techniques that are pushing the boundaries of gait analysis. Recent advances in transformerbased architectures have substantially enhanced gait analysis by improving the capacity to model complex spatio-temporal dependencies in human movement data. In particular, Le and Pham [48] proposed a spatio-temporal transformer network to estimate critical gait parameters. These studies collectively establish transformers as powerful tools for modeling gait patterns in clinical and general domains. The discussion of these advanced models demonstrates the scalability and forwardlooking nature of our proposed platform. Our work, which focuses on detecting and characterizing real-world gait behavior using spectral analysis and time-frequency representations derived from wearable IMU data, is complementary to these advanced pipelines. The semantic modeling of gait events, independent of disease classification, positions our approach as complementary to transformer-based pipelines. Furthermore, our proposed framework lays the groundwork for future integration of transformer models to enhance gait segmentation and severity estimation, while maintaining interpretability and ecological validity in unconstrained environments. III. METHODS In this article, a top-down approach has been adopted to address the integration of heterogeneous data streams from multi-source wearable devices. It is strongly applicable since it addresses the need for the unification of data on various hierarchical levels of entities of the gathered information. On this basis, an exemplar conceptual framework is demonstrated to comprehensively structure the remote monitoring process. The second phase describes the data collection method that was used, detailing the acquisition and pre-processing of raw sensor data. Data fusion was then performed, with a focus on IMU data and GPS signals to improve motiontracking accuracy. Finally, the proposed analysis pipeline was implemented. It began with the segmentation of gait cycles and was followed by the development of a disease identification algorithm that used the extracted gait features for diagnosis and classification. This section is a bit dense, and to facilitate the understanding of all the involved components, a graphical aid is proposed (see Figure 2). Method IT Framework (Semantics) IoT Data Collection Elaborated Features Data Fusion Analysis Fig. 2. Logical pipeline of our framework. It shows how semantic structuring at the IT layer ensures that low-level sensor data (socks, GPS) can be fused and transformed into clinically meaningful gait features. A. Data collection After an intensive analysis of the available wearable devices, we have selected two instrumented smart socks from Sensoria Inc. (Sensoria Health Inc. Seattle, WA, USA) [56], having as advantage against other providers the integrated information INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 5 from accelerometer, magnetometer, gyroscope as well as the inclusion of three pressure sensors per individual sock. They have made available technical specifications, which allow us to develop our own data capture application running on Android mobile phone [57] grabbing 12 channels of data (three components of the magnetometer vector, three for the acceleration vector, three for gyroscope vector, and three pressure signals) with a frequency between 45Hz and 55Hz. This sampling frequency enables one to accurately describe the walking structure. According to the proposed framework (Fig. 4), the hub layer adds information relevant to position, leg, and software version. Data compression and delivery are then performed to the cloud, where an Influx DB time series database [58] was selected to store the collected data. All these functions have been integrated into an app (developed both for Android and iOS) to facilitate access to the service [59]. Our current dataset includes a modest number of subjects, with 35 PwMS and 12 healthy controls monitored for one day each. This population represents a variety of ages and both sexes, but is not explicitly stratified by the Expanded Disability Status Scale (EDSS) severity categories. The main focus of this study is the methodological development and initial demonstration of discriminative sensitivity in the analysis of gait patterns. The extensive data acquired per participant, which encompasses multiple hours and varied daily activity patterns, substantially enhances the dataset’s effective size and variability. This allows us to robustly evaluate our PSDrelated algorithm’s potential discriminatory power at a preliminary stage. Ongoing work involves active data collection with expanded cohorts and structured clinical stratification to rigorously confirm and further refine the clinical applicability of our gait analysis approach. The collected data can be reviewed using a Grafana dashboard (see Fig. 3), but this is just a view of the raw data. Based on raw data collected at high frequency, the traditional MS assessment looks to estimate a set of gait-based features derived by combining the raw sensor data and the calculated orientation. The orientation is essential to transform the accelerometer data from the sensor frame to the global frame (or a consistent body frame), allowing for integration. Then, for the gait process, the full walking cycle starts when the heel contacts the ground. Key events, including initial contact, toe off, feet adjacent, tibia vertical, mark the phase shifts. For each foot, the full walking cycle starts when the heel contacts the ground. The stance process for each foot is divided into three phases: loading response (LR), midstance (MSt), and terminal stance (TSt). While one foot is in its stance process, the opposite foot is in its swing process, which includes the phases of pre-swing (PSw), initial swing (ISw), mid-swing (MSw), and terminal swing (TSw). Phase labeling, where the phases of LR, MSt, TSt, PSw, and ISw are defined as G0 to G4, and the phases MSw and TSw are combined as G5 [60]. All these elements are presented in Fig. 13, and detailed in Appendix B. The features mentioned above were gait-specific and required the integration of information. However, this article estimated the level of MS disease not by directly reporting these individual parameters but rather by analyzing the harmonic properties of the acceleration, gyroscope, and pressure signal modules to identify characteristic spectral features that correlated with the status of the disability. Nevertheless, since individuals perform various activities in the course of their day-to-day lives, the primary analytical challenge is the segmentation of continuous motion data into walking periods, and thus defining a semantic model of gait events. However, in contrast to the more traditional featureoriented approach, this paper aims to estimate the level of MS disease by analyzing the harmonic properties of the acceleration, gyroscope and pressure signals modules. The proposal is to use a dynamic STFT operator (by combination of sensor signals with Hamming window) in the range of 5Hz to characterize gait behavior. Therefore, the analysis of the accelerometer and gyroscope module allow us to identify the walking process, while the hierarchical analysis of pressures shows the quality of walking. The Hamming window was used because it has been extensively utilized to minimize spectral leakage without losing frequency resolution in the time-frequency plane. Gradual tapering of the window reduces discontinuities at the edge of the window, a very sensitive parameter for accurately delineating gait cycles in the quasi-periodic walking motion signal [61]. The window length was fixed at 7 seconds to compromise between time and frequency resolution based on standard protocols for gait analysis using STFT. This period encompasses several stride cycles (usually 6–10 steps for a nominal gait frequency of 1 Hz), without compromising temporal localization, allowing robust frequency representation. An overlap of 50% was used to enhance continuity between windows and facilitate the detection of transient events, as suggested in research on wearable sensors on human movement [62, 63]. The chosen 0–5 Hz frequency range is based on the physiological bandwidth of human gait. Normal walking frequencies for healthy adults are typically between 0.6 Hz and 2 Hz, with higher-order harmonics up to approximately 3–4 Hz depending on cadence and biomechanical variation [64]. Therefore, the 5 Hz upper limit provides a sufficient buffer to include relevant gait dynamics, including asymmetries and irregularities, especially prevalent in PwMS. STFT analysis confirmed that most of the spectral energy of the gait patterns is indeed concentrated below 2 Hz, as expected clinically and reaffirming our design decision (refer to Fig. 7 and Fig. 11). B. IT Framework As previously discussed, due to the requirements for data sampling and integration with other wearable devices, there is a demand for a more comprehensive conceptualization of wearable data in the complex semantic context of human behavior in their daily activities. To allow enough flexibility, a comprehensive framework is proposed (see Fig. 4). The communication limitations exhibited by the wearable devices forced developers to rely on personal hubs, with different devices connected by the Bluetooth protocol to the smartphone [65, 66]. However, cutting-edge 6G technologies are designed to facilitate cellular IoT connections and services such as long-range low-power communication (LRLPC), INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 6 Fig. 3. Grafana dashboard view of raw gait data showing pressure, acceleration, gyroscope, and magnetometer streams. The highlighted point corresponds to G0 (see Fig. 13). The pressure data clearly illustrates the step structure, while the magnitudes of the acceleration and gyroscope readings (∥Accel∥and ∥Gyroscope∥) also exhibit characteristic behavior for steps. ultra-reliable low-latency communication (URLLC), and innetwork intelligent computing services (INICS). The findings demonstrate that these technologies are well suited to the requirements of the Internet of Wearable Things (IoWT) [66]. It enables the concurrent operation of various wearable devices, reflecting a prevalent trend in the current landscape. Therefore, there are also ongoing requirements concerning multisensor and multicloud architectures that cater to various types of wearable device, all while facilitating the semantic definition of data flows using the appropriate ontology. Furthermore, the need for versatility to perform computations both on the edge and within the cloud infrastructure remains imperative [67]. Consequently, our framework is designed to handle multiple physical layers from different sources. This includes multiple sensors within a single device (e.g., the IMU and pressure sensors in our smart socks) as well as data from multiple wearable devices (e.g., smart socks and a smartwatch), which can all converge at a personal hub. This hub is responsible for preliminary data processing and subsequent submission to the relevant cloud platform, depending on the device manufacturer or the specific data collection application used. In this way, an effective integration of the data can be done, facilitating the end points to obtain all the relevant information [68]. The next pivotal element involves the development of the ontology according to the data source. This necessitates careful attention to establish sufficient connections between entities to adequately define them and facilitate interactions between them. This approach allows for the federation of entities and ontologies, facilitating the creation of an attribute network. The ontological federation and entity federation is the unification of diverse, autonomous datasets and knowledge structures into a single, unified structure that allows seamless interoperability. In numerous complicated systems where data is collected from heterogeneous source, such as IoWT sensors, enterprise databases, biomedical records, or sensors—interentity consistency and semantic coherence are crucial. Ontologies allow for routine description of knowledge by defining concepts, their attributes and interdependencies, allowing for standardized interpretation of data and reasoning [69]. By federating entities and ontologies, an attribute network can be established. This network encapsulates the relationships between different attributes in different domains and forms an interconnected system that supports advanced reasoning, data fusion, and predictive analytics. Each entity within this network possesses a set of attributes, which may be sensor measurements, contextual metadata, historical trends, or derived computational attributes. These attributes are related among entities according to ontologically specified semantic relationships, allowing intelligent data correlation and inference [70]. In practical application scenarios, such a feature network INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 7 Fig. 4. IT framework for integrating heterogeneous wearable data sources across physical, hub, cloud, and semantic layers. This framework’s flexible and scalable design is crucial for enabling the continuous, ecologically valid, and detailed remote monitoring of gait required for a comprehensive assessment of MS. can facilitate context-sensitive analysis and dynamic knowledge discovery. For example, ontological federation of IoT devices, environmental conditions, and structural health issues can enable real-time anomaly detection for smart infrastructure monitoring. Lastly, the ontology federation and entities improve the interoperability, scalability, and semantic density of the data, and the generated attribute network is a graphbased structure that can be compatible with advanced analysis applications [71]. The specific nature of these relationships will depend on the case being analyzed, and as such, they may not be identifiable at the point of initial cloud data injection, but may become apparent in subsequent stages. C. Data fusion IMUs provide high-rate motion tracking using only accelerometers, gyroscopes, and magnetometers, which report real-time estimates of orientation and position. As mentioned in Section II, velocity and position are estimated by integrating acceleration, with contributions from the gyroscope and magnetometer data for orientation. However, this process is prone to drift, significantly degrading the accuracy of the derived positions. The work of Kassas et al. [72] highlights the potential to reduce such errors by incorporating external reference data, such as GPS signals. GPS, by contrast, provides global position tracking, albeit at a much lower sampling rate and subject to errors in urban regions where satellite signals are liable to be obscured. By merging GPS and IMU data, the system leverages the high accuracy of GPS for long-term position estimation and overcomes its low update rate using IMU-derived velocity and orientation estimates. This fusion has been described in the monitoring of mobile mobility for MS and other neurological conditions [73], where the fundamental mathematical tool has been incorporated as an appendix. The integration of GPS and IMU is generally achieved by Kalman filtering or complementary filtering techniques. Kalman filters dynamically change the weighting between IMU and GPS measurements relative to estimated uncertainty for smoother and more precise trajectory estimation. Some literature, for example, Liu et al. [74], illustrates how sensor fusion can be extended to include other data streams, such as barometric measurements, to further improve motion tracking, particularly in settings with poor GPS coverage. The Mahony filter output is the orientation, represented as a quaternion (see 11). Quaternions are preferred over Euler angles (roll, pitch, yaw) to circumvent issues such as gimbal lock and singularities. The filter algorithm proceeds in two primary stages: prediction and update. In the prediction stage, the gyroscope data is integrated to estimate the change in orientation over the sampling interval. The update stage leverages accelerometer and magnetometer data to correct for gyroscope drift. The accelerometer, which measures gravity, provides a reference for pitch and roll. The filter calculates the expected direction of gravity in the IMU’s frame based on the current estimated orientation and compares it to the measured acceleration vector. Similarly, the magnetometer is used and the expected magnetic field vector is compared to the measured vector, providing a heading correction. The error, 𝑒, is computed using the cross-product: 𝑒=(𝑎×𝑔)+(𝑚×𝑏)(1) where 𝑏is the normalized magnetic field vector [𝑏𝑥,0, 𝑏𝑧] (tilt-compensated), and 𝑎and 𝑚are the normalized accelerometer and magnetometer measurements in the sensor frame, respectively. A Proportional-Integral (PI) controller is employed to correct the gyroscope bias. The error, 𝑒, is multiplied by a proportional gain (𝐾𝑝) for immediate correction, and integrated over time and multiplied by an integral gain (𝐾𝑖) to address the accumulated bias. The integral term, 𝑒𝑖𝑛𝑡 , is updated as 𝑒𝑖𝑛𝑡 (𝑡)=𝑒𝑖𝑛𝑡 (𝑡−1) + 𝑒∗Δ𝑡(2) The total correction term is as follows. 𝜔𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 =𝜔+𝐾𝑝∗𝑒+𝐾𝑖∗𝑒𝑖𝑛𝑡 (3) Finally, this corrected angular velocity, 𝜔𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑, is used instead of the raw gyroscope data in the quaternion integration INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 8 step, effectively applying the corrections. The resulting quaternion is normalized to maintain a unit quaternion, representing the refined orientation estimate. The Mahony filter thus acts as a complementary filter, combining short-term gyroscope accuracy with long-term accelerometer and magnetometer stability. Fig. 5. Trajectory comparison showing that sensor fusion eliminates IMU drift and smooths GPS noise. This demonstrates the reliability of our fusion approach for clinical mobility tracking. Kalman filtering provides an alternative, statistically optimal framework for sensor fusion [75]. While some studies utilize Kalman filters for IMU and GPS fusion [76, 77], our system relies on the Mahony filter for attitude estimation, and a separate algorithm for the GPS, as described in the appendix, which provides a robust and accurate estimate of position and orientation. The effects of such fusion can be observed in Fig. 5, showing good agreement on the macroscopic scale. D. Analysis Our approach seeks to replace traditional gait analysis and biomechanical modeling, which are typically conducted in specialized laboratory settings using optical motion capture to monitor segments of body movements, with an unsupervised, non-devoted gait monitoring of the patient’s daily activities. The aim is to reduce invasive effects and still maintain reproducibility with a limited level of supervision, as requested by [78]. To provide a richer context, preprocessing procedures, implementation of fusion techniques, and ontology referencing operations must be considered. The concept of ontology, initially rooted in philosophy, has been adapted in Computer Science as a knowledge artifact that delineates a particular reality and the inherent nature of objects [79]. An ontology can establish a universally accepted lexicon and define (syntactic) guidelines for data representation while also offering a semantic representation of the data. Turcin et al. [80] stated that a domain ontology could be implemented with the process to build a data warehouse architecture to support decisions. Various knowledge domains or disciplines are organized within their respective ontologies, essentially serving as a portrayal of a knowledge realm that contains data, information, and knowledge relevant to that domain. Therefore, the “Ontologie du Systeme Musculo-squelettique des Membres Inferieurs” (OSMMI) [81] has been adopted as the main component of this application, in particular the Gait class and its subclasses. However, because of its generic scope it did not satisfy all the gait requirements, then it is needed to integrate different ontologies. To this end, the Ontology Design Patterns (ODP) will be used for sequence, time interval, and time period, among other relevant concepts, which are modularized and supported by the Modular Ontology Engineering (MOE) methodology [82, 83]. Following this approach, as described in the proposed framework (see Fig. 4), we are ready to move to the modeling layer. The semantic perspective aims to identify walking periods for PwMS by discriminating different types of activity from the collected data. It will be the first step in the value creation process, and on the basis of it, quality of gait can be derived, as well as quality evolution based on time. In this way, gait performance can be determined over time on an individual basis. To address this segmentation, the data is automatically partitioned into windows lasting 7 s each, when the data are available and with an overlap of 50% and the fusion of data between sensors and legs is applied at the signal and feature levels [73]. A Hamming window function is used on each window to minimize data loss between windows and to enhance the signal smoothing of the sensors. To discern the walking process and considering the susceptibility of PwMS to potential harm, pressure data alone were determined to not provide sufficient reliable information. Consequently, a fusion approach was adopted, integrating data from both Acceleration and Gyroscope sensors. An illustrative example of this process is shown in Fig. 6. The adopted algorithm exploits Parseval’s Theorem [84]. Let us denote 𝑥(𝑡)as the magnitude of acceleration or gyroscope readings over time, while by 𝑓the frequency decomposition of 𝑥(𝑡). Since we assume that walking implies an energy consumption over time, let us estimate the energy 𝐸of the 𝑥(𝑡)signal by 𝐸=∫∞ −∞ |𝑥(𝑡)|2𝑑𝑡 =∫∞ −∞ |˜𝑥(𝑓)|2𝑑𝑓 (4) where ˜𝑥(𝑓)=∫∞ −∞ 𝑥(𝑡) · 𝑒−2𝜋 𝑓 𝑡 𝑑𝑡 (5) Therefore, the spectral density of the energy is defined as 𝑆𝑥=|˜𝑥(𝑓)|2(6) For signals extending continuously across time intervals, it is more advantageous to characterize the distribution of signal power across frequencies using the Power Spectral Density (PSD). The power of the signal in a given frequency band [𝑓1, 𝑓2], where 0 ¡ 𝑓1¡𝑓2, can be calculated by integrating over frequency. Since 𝑆𝑥(− 𝑓)=𝑆𝑥(𝑓), an equal amount of power can be attributed to positive and negative frequency bands, which is responsible for the factor of two in ( 7), 𝑃=∫𝑓2 −𝑓1 𝑆𝑥(𝑓)𝑑𝑓 (7) To analyze how the PSD is changing over the time, we have selected a spectrogram tool because it involves time vs. frequency vs. amplitude and since we are using predefined time segments convoluted with the Hamming window, larger INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 9 Fig. 6. Spectrogram analysis of walking sequence, where energy concentration near 1 Hz confirms automatic gait detection. This illustrates how frequency-based analysis outperforms simple step counts. time effects are dismissed. Therefore, values above a threshold in the amplitude of the PSD with frequencies below 2 Hz are a clear mark in time for walking behavior, as depicted in Fig. 6, lower picture. Gait lasting less than five seconds was discarded as the interest is to measure gait power and not just movements involving a few steps but not real walking processes. Based on the concept of Group 3 information in the DataBase Mechanics Morphology Movement (DB3M) [85], various parameters related to physical measurements have been established. These parameters are defined and steps are identified specifically for situations that involve walking. In particular, references to the InfluxDB timestamp are maintained within the database. Using these data with the time windows previously mentioned, the algorithm involving the PSD spectrogram is used to identify gait sequences. It is important to note that, in the context of cyclic activities such as walking, the gyroscope is more sensitive than the accelerometer [86], but contributions from both are needed to increase reliability. Therefore, in this Fig. 7. STFT of a 7-s gait segment. Gyroscope (top) and accelerometer (bottom) signals from right and left legs, showing dominant peak at 1 Hz. proposal, the gyroscope is significantly relevant and its use is combined with signals from the accelerometer module. Human walking frequencies typically fall within the 0.6 Hz to 2 Hz range (equivalent to cycle periods of 1.6 s to 0.5 s) [87]. To accurately capture these frequencies, the NyquistShannon sampling theorem dictates a minimum sampling rate of twice the highest frequency of interest. Consequently, we analyze the frequency band from 0 to 5 Hz, providing a margin above the theoretical minimum of 4 Hz. The proposed method enables the identification of walking segments based on the frequency characteristics of the acquired signals. Automatic gait segmentation was validated in a cohort of 35 PwMS with varying degrees of disease progression and 12 healthy control subjects, the combined group representing a diverse range of demographic and anthropometric characteristics. The duration of monitoring for each participant ranged from several hours to two days. These tests have been conducted within the framework of a protocol validated by the Ethics Committee (CEIm) of the Getafe University Hospital and have received the necessary informed consent from each participant. Complementing the proposed algorithm, the authors implemented a deep learning classifier as an alternative approach, leveraging Artificial Intelligence (AI) to facilitate semantic segmentation of human movement data, specifically focusing on gait patterns in MS individuals. Since there are six features involved (modulus of acceleration, gyroscope and magnetometer as well as pressure sensors), a Convolutional Neural Network (CNN) was selected to elaborate on the integrated perspective, as well as a Long Short Term Memory (LSTM) approach that allows to consider the temporary evolution, with an architecture presented in Table I. The convolutional kernel size of 3 was selected to detect short-term patterns in gait signals, while max-pooling layers of size 2 were used to reduce temporal resolution and prevent overfitting. A three-layer convolutional stack followed by LSTM units enables a hierarchical extraction of gait features, from low-level signal variations to high-level temporal dependencies. INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 16 edition,” Multiple Sclerosis Journal, vol. 26, pp. 1816– 1821, 12 2020. [Online]. Available: https://journals. sagepub.com/doi/full/10.1177/1352458520970841 [2] A. J. Solomon, R. A. Marrie, S. Viswanathan, J. Correale, M. Magyari, N. P. Robertson, D. R. Saylor, W. Kaye, L. Rechtman, E. Bae, R. Shinohara, R. King, J. Laurson-Doube, and A. Helme, “Global barriers to the diagnosis of multiple sclerosis,” Neurology, vol. 101, pp. e624–e635, 8 2023. [Online]. Available: https://n.neurology.org/content/101/6/e624https://n. neurology.org/content/101/6/e624.abstract [3] R. Dobson and G. Giovannoni, “Multiple sclerosis – a review,” European Journal of Neurology, vol. 26, no. 1, p. 27–40, Nov. 2018. [Online]. Available: http://dx.doi.org/10.1111/ene.13819 [4] B. Gbaguidi, F. Guillemin, M. Soudant, M. Debouverie, G. Mathey, and J. Epstein, “Age-period-cohort analysis of the incidence of multiple sclerosis over twenty years in lorraine, france,” Scientific Reports, vol. 12, no. 1, Jan. 2022. [Online]. Available: http://dx.doi.org/10.1038/ s41598-022-04836-5 [5] M. D. Goldman and L. Amezcua, “Progressive multiple sclerosis,” CONTINUUM Lifelong Learning in Neurology, vol. 28, pp. 1083–1103, 8 2022. [Online]. Available: https://journals.lww.com/continuum/fulltext/ 2022/08000/progressive multiple sclerosis.8.aspx [6] H. Karpatkin, B. Siminovich-Blok, J. Rachwani, Z. Langer, and S. Winsor, “Effect of acupuncture on sensorimotor function and mobility in patients with multiple sclerosis: A pilot study,” https://home.liebertpub.com/jicm, vol. 29, pp. 42–49, 1 2023. [Online]. Available: https://www.liebertpub.com/ doi/10.1089/jicm.2022.0610 [7] G. Pardo, S. Coates, and D. T. Okuda, “Outcome measures assisting treatment optimization in multiple sclerosis,” Journal of Neurology, vol. 269, no. 3, p. 1282–1297, Aug. 2021. [Online]. Available: http: //dx.doi.org/10.1007/s00415-021-10674-8 [8] P. Decavel, T. Moulin, and Y. Sagawa, “Gait tests in multiple sclerosis: Reliability and cut-off values,” Gait & Posture, vol. 67, pp. 37–42, 1 2019. [9] B. J. Oliver, K. Walsh, R. Messier, F. Mehta, A. Cabot, E. Klawiter, P. Pagnotta, A. Solomon, and S. E. England, “System-level variation in multiple sclerosis care outcomes: Initial findings from the multiple sclerosis continuous quality improvement research collaborative,” https://home.liebertpub.com/pop, vol. 25, pp. 46–56, 2 2022. [Online]. Available: https://www.liebertpub.com/doi/10.1089/pop.2021.0040 [10] S. E. Bennett, L. E. Bromley, N. M. Fisher, M. R. Tomita, and P. Niewczyk, “Validity and reliability of four clinical gait measures in patients with multiple sclerosis,” International journal of MS care, vol. 19, no. 5, pp. 247– 252, 2017. [11] R. Phan-Ba, P. Calay, P. Grodent, G. Delrue, E. Lommers, V. Delvaux, G. Moonen, and S. Belachew, “Motor fatigue measurement by distance-induced slow down of walking speed in multiple sclerosis,” PLoS One, vol. 7, no. 4, p. e34744, 2012. [12] R. Phan-Ba, A. Pace, P. Calay, P. Grodent, F. Douchamps, R. Hyde, C. Hotermans, V. Delvaux, I. Hansen, G. Moonen et al., “Comparison of the timed 25-foot and the 100-meter walk as performance measures in multiple sclerosis,” Neurorehabilitation and neural repair, vol. 25, no. 7, pp. 672–679, 2011. [13] M. D. Goldman, R. W. Motl, J. Scagnelli, J. H. Pula, J. J. Sosnoff, and D. Cadavid, “Clinically meaningful performance benchmarks in ms: timed 25-foot walk and the real world,” Neurology, vol. 81, no. 21, pp. 1856– 1863, 2013. [14] A. T. Society, “Ats statement: Guidelines for the six-minute walk test,” American Journal of Respiratory and Critical Care Medicine, vol. 166, no. 1, p. 111–117, Jul. 2002. [Online]. Available: http://dx.doi.org/10.1164/ ajrccm.166.1.at1102 [15] D. Brooks, S. Solway, and W. J. Gibbons, “Ats statement on six-minute walk test,” American Journal of Respiratory and Critical Care Medicine, vol. 167, no. 9, p. 1287–1287, May 2003. [Online]. Available: http://dx.doi.org/10.1164/ajrccm.167.9.950 [16] “Erratum. ats statement: Guidelines for the sixminute walk test,” American Journal of Respiratory and Critical Care Medicine, vol. 193, no. 10, p. 1185–1185, May 2016. [Online]. Available: http: //dx.doi.org/10.1164/rccm.19310erratum [17] R. M¨ uller, D. Hamacher, S. Hansen, P. Oschmann, and P. M. Keune, “Wearable inertial sensors are highly sensitive in the detection of gait disturbances and fatigue at early stages of multiple sclerosis,” BMC Neurology, vol. 21, no. 1, Sep. 2021. [Online]. Available: http://dx.doi.org/10.1186/s12883-021-02361-y [18] G. Di Flumeri, P. Aric` o, G. Borghini, N. Sciaraffa, A. Di Florio, and F. Babiloni, “The dry revolution: Evaluation of three different eeg dry electrode types in terms of signal spectral features, mental states classification and usability,” Sensors, vol. 19, no. 6, p. 1365, Mar. 2019. [Online]. Available: http://dx.doi.org/ 10.3390/s19061365 [19] P. W. Tipton, E. R. Stanley, V. Chitu, and Z. K. Wszolek, “Is pre-symptomatic immunosuppression protective in ¡scp¿csf1r¡/scp¿-related leukoencephalopathy?” Movement Disorders, vol. 36, no. 4, p. 852–856, Feb. 2021. [Online]. Available: http://dx.doi.org/10.1002/mds.28515 [20] A. Soltani, K. Aminian, C. Mazza, A. Cereatti, L. Palmerini, T. Bonci, and A. Paraschiv-Ionescu, “Algorithms for walking speed estimation using a lower-backworn inertial sensor: A cross-validation on speed ranges,” IEEE transactions on neural systems and rehabilitation engineering, vol. 29, pp. 1955–1964, 2021. [21] F. B. Briggs, N. R. Thompson, and D. S. Conway, “Prognostic factors of disability in relapsing remitting multiple sclerosis,” Multiple Sclerosis and Related Disorders, vol. 30, p. 9–16, May 2019. [Online]. Available: http://dx.doi.org/10.1016/j.msard.2019.01.045 [22] M. Sparaco, L. Lavorgna, R. Conforti, G. Tedeschi, and S. Bonavita, “The role of wearable devices in multiple INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 17 sclerosis,” Multiple Sclerosis International, vol. 2018, pp. 1–7, 10 2018. [23] F. Salaorni, G. Bonardi, F. Schena, M. Tinazzi, and M. Gandolfi, “Wearable devices for gait and posture monitoring via telemedicine in people with movement disorders and multiple sclerosis: a systematic review,” Expert review of medical devices, pp. 1–20, 12 2023. [Online]. Available: https://pubmed.ncbi.nlm.nih. gov/38124300/ [24] B. Bonnech` ere, “Integrating rehabilomics into the multi-omics approach in the management of multiple sclerosis: The way for precision medicine?” Genes, vol. 14, no. 1, p. 63, Dec. 2022. [Online]. Available: http://dx.doi.org/10.3390/genes14010063 [25] M. A. E.-k. Ahmed, M. F. Zakaria, A. A. E. A. Elaziz, M. M. Fouad, A. M. Elbokl, and M. S. Swelam, “Assessment of the role of telemedicine in the outcome of multiple sclerosis patients,” The Egyptian Journal of Neurology, Psychiatry and Neurosurgery, vol. 59, no. 1, Jul. 2023. [Online]. Available: http: //dx.doi.org/10.1186/s41983-023-00690-y [26] M. L. Frechette, B. M. Meyer, L. J. Tulipani, R. D. Gurchiek, R. S. McGinnis, and J. J. Sosnoff, “Next steps in wearable technology and community ambulation in multiple sclerosis,” Current Neurology and Neuroscience Reports, vol. 19, pp. 1–10, 10 2019. [Online]. Available: https://link.springer.com/article/10. 1007/s11910-019-0997-9 [27] J. Yeung, D. Catolico, N. Fullmer, R. Daniel, R. Lovell, R. Tang, E. M. Pearson, and S. S. Rosenberg, “Evaluating the sensoria smart socks gait monitoring system for rehabilitation outcomes,” PM&R, vol. 11, no. 5, pp. 512– 521, 2019. [28] P. V. Oirschot, M. Heerings, K. Wendrich, B. D. Teuling, F. Dorssers, R. V. Ee, M. B. Martens, and P. J. Jongen, “A two-minute walking test with a smartphone app for persons with multiple sclerosis: Validation study,” JMIR Form Res 2021;5(11):e29128 https://formative.jmir.org/2021/11/e29128, vol. 5, p. e29128, 11 2021. [Online]. Available: https: //formative.jmir.org/2021/11/e29128 [29] S. Paluch and S. Tuzovic, “Persuaded self-tracking with wearable technology: carrot or stick?” Journal of Services Marketing, vol. 33, pp. 436–448, 9 2019. [30] L. Piwek, D. A. Ellis, S. Andrews, and A. Joinson, “The rise of consumer health wearables: Promises and barriers,” PLOS Medicine, vol. 13, p. e1001953, 2 2016. [Online]. Available: https://journals.plos.org/ plosmedicine/article?id=10.1371/journal.pmed.1001953 [31] D. M. Hilty, C. M. Armstrong, D. D. Luxton, M. T. Gentry, and E. A. Krupinski, “A scoping review of sensors, wearables, and remote monitoring for behavioral health: Uses, outcomes, clinical competencies, and research directions,” Journal of Technology in Behavioral Science 2021 6:2, vol. 6, pp. 278–313, 3 2021. [Online]. Available: https://link.springer.com/ article/10.1007/s41347-021-00199-2 [32] A. C. L. Leonardsen, C. Hardeland, A. K. Helgesen, and V. A. Grøndahl, “Patient experiences with technology enabled care across healthcare settingsa systematic review,” BMC Health Services Research, vol. 20, pp. 1–17, 8 2020. [Online]. Available: https://link. springer.com/articles/10.1186/s12913-020-05633-4https: //link.springer.com/article/10.1186/s12913-020-05633-4 [33] F. Flachenecker, H. Gaßner, J. Hannik, D. H. Lee, P. Flachenecker, J. Winkler, B. Eskofier, R. A. Linker, and J. Klucken, “Objective sensor-based gait measures reflect motor impairment in multiple sclerosis patients: Reliability and clinical validation of a wearable sensor device,” Multiple sclerosis and related disorders, vol. 39, p. 101903, 4 2020. [Online]. Available: https://pubmed.ncbi.nlm.nih.gov/31927199/ [34] J. P. Stellmann, A. Neuhaus, N. G¨ otze, S. Briken, C. Lederer, M. Schimpl, C. Heesen, and M. Daumer, “Ecological validity of walking capacity tests in multiple sclerosis,” PLOS ONE, vol. 10, p. e0123822, 4 2015. [Online]. Available: https://journals.plos.org/ plosone/article?id=10.1371/journal.pone.0123822 [35] V. J. Block, R. Bove, C. Zhao, P. Garcha, J. Graves, A. R. Romeo, A. J. Green, D. D. Allen, J. A. Hollenbach, J. E. Olgin, G. M. Marcus, M. J. Pletcher, B. A. C. Cree, and J. M. Gelfand, “Association of continuous assessment of step count by remote monitoring with disability progression among adults with multiple sclerosis,” JAMA Network Open, vol. 2, no. 3, p. e190570, Mar. 2019. [Online]. Available: http://dx.doi.org/10.1001/jamanetworkopen.2019.0570 [36] M. Coca-Tapia, A. Cuesta-G´ omez, F. Molina-Rueda, and M. Carratal´ a-Tejada, “Gait pattern in people with multiple sclerosis: a systematic review,” Diagnostics, vol. 11, no. 4, p. 584, 2021. [37] M. Psarakis, D. A. Greene, M. H. Cole, S. R. Lord, P. Hoang, and M. Brodie, “Wearable technology reveals gait compensations, unstable walking patterns and fatigue in people with multiple sclerosis,” Physiological Measurement, vol. 39, no. 7, p. 075004, Jul. 2018. [Online]. Available: http://dx.doi.org/10.1088/1361-6579/aac0a3 [38] G. Abbadessa, L. Lavorgna, G. Miele, A. Mignone, E. Signoriello, G. Lus, M. Clerico, M. Sparaco, and S. Bonavita, “Assessment of multiple sclerosis disability progression using a wearable biosensor: A pilot study,” Journal of Clinical Medicine, vol. 10, no. 6, p. 1160, Mar. 2021. [Online]. Available: http://dx.doi.org/10.3390/jcm10061160 [39] X. Ferre, E. Villalba-Mora, M.-A. Caballero-Mora, A. Sanchez, W. Aguilera, N. Garcia-Grossocordon, L. Nu˜ nez-Jimenez, L. Rodr´ ıguez-Ma˜ nas, Q. Liu, and F. del Pozo-Guerrero, “Gait speed measurement for elderly patients with risk of frailty,” Mobile Information Systems, vol. 2017, p. 1–11, 2017. [Online]. Available: http://dx.doi.org/10.1155/2017/1310345 [40] M. Wuehr, A. Huppert, F. Schenkel, J. Decker, K. Jahn, and R. Schniepp, “Independent domains of daily mobility in patients with neurological gait disorders,” Journal of neurology, vol. 267, pp. 292–300, 12 2020. [Online]. INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 18 Available: https://pubmed.ncbi.nlm.nih.gov/32533324/ [41] X. Zheng, A. V. Campos, J. Ordieres-Mer´ e, J. Balseiro, S. L. Marcos, and Y. Aladro, “Continuous monitoring of essential tremor using a portable system based on smartwatch,” Frontiers in neurology, vol. 8, 3 2017. [Online]. Available: https://pubmed.ncbi.nlm.nih. gov/28360883/ [42] M. Chirra, L. Marsili, L. Wattley, L. L. Sokol, E. Keeling, S. Maule, G. Sobrero, C. A. Artusi, A. Romagnolo, M. Zibetti, L. Lopiano, A. J. Espay, A. Z. Obeidat, and A. Merola, “Telemedicine in neurological disorders: Opportunities and challenges,” https://home.liebertpub.com/tmj, vol. 25, pp. 541–550, 7 2019. [Online]. Available: https://www.liebertpub.com/ doi/10.1089/tmj.2018.0101 [43] X. Zheng, A. Vieira, S. L. Marcos, Y. Aladro, and J. Ordieres-Mer´ e, “Activity-aware essential tremor evaluation using deep learning method based on acceleration data,” Parkinsonism & related disorders, vol. 58, pp. 17–22, 1 2019. [Online]. Available: https://pubmed.ncbi.nlm.nih.gov/30122598/ [44] A. Zahn, V. Koch, L. Schreff, P. Oschmann, J. Winkler, H. Gaßner, and R. M¨ uller, “Validity of an inertial sensor-based system for the assessment of spatiotemporal parameters in people with multiple sclerosis,” Frontiers in Neurology, vol. Volume 14 - 2023, 2023. [Online]. Available: https://www.frontiersin.org/journals/ neurology/articles/10.3389/fneur.2023.1164001 [45] J. C. Perez-Ibarra, A. A. G. Siqueira, and H. I. Krebs, “Identification of gait events in healthy and parkinson’s disease subjects using inertial sensors: A supervised learning approach,” IEEE Sensors Journal, vol. 20, no. 24, p. 14984–14993, Dec. 2020. [Online]. Available: http://dx.doi.org/10.1109/JSEN.2020.3011627 [46] F.-C. Wang, S.-F. Chen, C.-H. Lin, C.-J. Shih, A.-C. Lin, W. Yuan, Y.-C. Li, and T.-Y. Kuo, “Detection and classification of stroke gaits by deep neural networks employing inertial measurement units,” Sensors, vol. 21, no. 5, p. 1864, Mar. 2021. [Online]. Available: http://dx.doi.org/10.3390/S21051864 [47] S. A. Ludwig, “Investigation of orientation estimation of multiple imus,” Unmanned Systems, vol. 09, no. 04, p. 283–291, Oct. 2020. [Online]. Available: http: //dx.doi.org/10.1142/S2301385021500114 [48] H. Le and H. Pham, “Learning to estimate critical gait parameters from single-view rgb videos with transformerbased attention network,” in 2024 IEEE International Symposium on Biomedical Imaging (ISBI). IEEE, 2024, pp. 1–5. [49] H. Dinh, S. Le, M. Than, M. Ho, N. Vuillerme, and H. Pham, “Quantitative gait analysis from single rgb videos using a dual-input transformer-based network,” arXiv preprint arXiv:2501.01689, 2025. [50] A. Cosma, A. Catruna, and E. Radoi, “Exploring selfsupervised vision transformers for gait recognition in the wild,” Sensors, vol. 23, no. 5, p. 2680, 2023. [51] D. M. D. Nguyen, M. Miah, G.-A. Bilodeau, and W. Bouachir, “Transformers for 1d signals in parkinson’s disease detection from gait,” in 2022 26th international conference on pattern recognition (ICPR). IEEE, 2022, pp. 5089–5095. [52] V. Adeli, S. Mehraban, M. Mirmehdi, A. Whone, B. Filtjens, A. Dadashzadeh, A. Fasano, A. Iaboni, and B. Taati, “Gaitgen: Disentangled motion-pathology impaired gait generative model–bringing motion generation to the clinical domain,” arXiv preprint arXiv:2503.22397, 2025. [53] N. Basoc, A. Cosma, A. Cˇ atrunˇ a, and E. Rˇ adoi, “Database-agnostic gait enrollment using settransformers,” arXiv preprint arXiv:2505.02815, 2025. [54] M. Sarkar, “Integrating machine learning and deep learning techniques for advanced alzheimer’s disease detection through gait analysis,” Journal of Business and Management Studies, vol. 7, no. 1, pp. 140–147, 2025. [55] P. Kalpana, S. Kodati, L. Smitha, N. Sreekanth, A. Smerat, M. A. Ahmad et al., “Explainable ai-driven gait analysis using wearable internet of things (wiot) and human activity recognition.” Journal of Intelligent Systems & Internet of Things, vol. 15, no. 2, 2025. [56] F. Amitrano, M. Macagno, S. Rossotti, D. Vigan` o, M. Cesarelli, and G. D’Addio, “E-textile smart socks for gait analysis: a preliminary validation study,” Gait & Posture, vol. 97, p. 26, 10 2022. [57] J. Ordieres-Mer´ e and R. P. Guillen, “Ms tracking,” 2022. [Online]. Available: https://zenodo.org/records/10079192 [58] S. N. Z. Naqvi, S. Yfantidou, and E. Zim´ anyi, “Time series databases and influxdb,” Studienarbeit, Universit´ e Libre de Bruxelles, vol. 12, pp. 1–44, 2017. [59] A. Farmanesh, “Developing a cross-platform mobile application for health data integration and capture from multi devices using flutter,” Junio 2024, no Publicado. [Online]. Available: https://oa.upm.es/82457/ [60] H. Zhang, X. Liu, J. Li, J. Pan, C. K. Loo, and A. Cangelos, “Research on enhanced gait phase segmentation based on multi-modal spatiotemporal information fusion,” IEEE Internet of Things Journal, 2024. [61] A. V. Oppenheim, Discrete-time signal processing. Pearson Education India, 1999. [62] A. Salarian, H. Russmann, F. J. Vingerhoets, C. Dehollain, Y. Blanc, P. R. Burkhard, and K. Aminian, “Gait assessment in parkinson’s disease: toward an ambulatory system for long-term monitoring,” IEEE transactions on biomedical engineering, vol. 51, no. 8, pp. 1434–1443, 2004. [63] J. Taborri, E. Palermo, S. Rossi, and P. Cappa, “Gait partitioning methods: A systematic review,” Sensors, vol. 16, no. 1, p. 66, 2016. [64] D. A. Winter, Biomechanics and motor control of human gait: normal, elderly and pathological, 1991. [65] I. Natgunanathan, N. Fernando, S. W. Loke, and C. Weerasuriya, “Bluetooth low energy mesh: Applications, considerations and current state-of-theart,” Sensors, vol. 23, no. 4, p. 1826, Feb. 2023. [Online]. Available: http://dx.doi.org/10.3390/s23041826 [66] N.-N. Dao, “Internet of wearable things: Advancements and benefits from 6g technologies,” Future Generation Computer Systems, vol. 138, p. 172–184, Jan. 2023. INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 19 [Online]. Available: http://dx.doi.org/10.1016/j.future. 2022.07.006 [67] J. Wang, C. Shi, M. Xia, F. Zheng, T. Li, Y. Shan, G. Jing, W. Chen, and T. C. Hsia, “Seamless indoor–outdoor footmounted inertial pedestrian positioning system enhanced by smartphone ppp/3-d map/barometer,” IEEE Internet of Things Journal, vol. 11, no. 7, pp. 13 051–13 069, 2024. [68] I. Voigt, H. Inojosa, A. Dillenseger, R. Haase, K. Akg¨ un, and T. Ziemssen, “Digital twins for multiple sclerosis,” Frontiers in Immunology, vol. 12, p. 669811, 5 2021. [69] Y. Huang, “Incorporating domain ontology information into clustering in heterogeneous networks,” WIREs Data Mining and Knowledge Discovery, vol. 11, no. 4, May 2021. [Online]. Available: http://dx.doi.org/10. 1002/widm.1413 [70] M. Zdravkovic and M. Trajanovic, “Integrated product ontologies for inter-organizational networks,” Computer Science and Information Systems, vol. 6, no. 2, p. 29–46, 2009. [Online]. Available: http://dx.doi.org/10. 2298/CSIS0902029Z [71] S. Pouriyeh, M. Allahyari, Q. Liu, G. Cheng, H. R. Arabnia, M. Atzori, F. G. Mohammadi, and K. Kochut, “Ontology summarization: Graph-based methods and beyond,” International Journal of Semantic Computing, vol. 13, no. 02, p. 259–283, Jun. 2019. [Online]. Available: http://dx.doi.org/10.1142/S1793351X19300012 [72] Z. Z. M. Kassas, M. Maaref, J. J. Morales, J. J. Khalife, and K. Shamei, “Robust vehicular localization and map matching in urban environments through imu, gnss, and cellular signals,” IEEE Intelligent Transportation Systems Magazine, vol. 12, no. 3, pp. 36–52, 2020. [73] R. C. King, E. Villeneuve, R. J. White, R. S. Sherratt, W. Holderbaum, and W. S. Harwin, “Application of data fusion techniques and technologies for wearable health monitoring,” Medical Engineering & Physics, vol. 42, pp. 1–12, 4 2017. [74] Y. Liu, T. Cai, H. Yang, C. Liu, J. Song, and M. Yu, “The pedestrian integrated navigation system with micro imu/gps/magnetometer/barometric altimeter,” Gyroscopy and Navigation, vol. 7, no. 1, pp. 29–38, 2016. [75] H. Gu, C. Jin, H. Yuan, and Y. Chen, “Design and implementation of attitude and heading reference system with extended kalman filter based on mems multisensor fusion,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 29, no. Supp01, p. 157–180, Mar. 2021. [Online]. Available: http://dx.doi.org/10.1142/S0218488521400092 [76] W. Pi, P. Yang, D. Duan, C. Chen, X. Cheng, L. Yang, and H. Li, “Malicious user detection for cooperative mobility tracking in autonomous driving,” IEEE Internet of Things Journal, vol. 7, no. 6, pp. 4922–4936, 2020. [77] Y. Yu, R. Chen, L. Chen, X. Zheng, D. Wu, W. Li, and Y. Wu, “A novel 3-d indoor localization algorithm based on ble and multiple sensors,” IEEE Internet of Things Journal, vol. 8, no. 11, pp. 9359–9372, 2021. [78] H. Zhou and H. Hu, “Human motion tracking for rehabilitation—a survey,” Biomedical signal processing and control, vol. 3, no. 1, pp. 1–18, 2008. [79] A. F. Sawsaa and J. Lu, “A generic model of ontology to visualize information science domain (ois),” in Ontologies and Big Data Considerations for Effective Intelligence, J. Lu and Q. Xu, Eds. IGI Global, 2017, pp. 435–442. [Online]. Available: http://services.igi-global.com/resolvedoi/resolve. aspx?doi=10.4018/978-1-5225-2058-0 [80] I. Turcin, V. Ergovic, and M. Lackovic, “Ontology driven decision support system architecture for gait analysis,” IFMBE Proceedings, vol. 38 IFMBE, pp. 78–81, 2013. [Online]. Available: https://link.springer. com/chapter/10.1007/978-3-642-34197-7 20 [81] T.-T. Dao, F. Marin, and M. C. H. B. Tho, “Ontology of the musculo-skeletal system of the lower limbs,” in 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, Aug. 2007. [Online]. Available: http://dx.doi.org/10.1109/IEMBS.2007.4352305 [82] C. G. and Others, “Modular ontology modeling: A tutorial,” Applications and practices in ontology design, extraction, and reasoning, vol. 49, p. 3, 2020. [Online]. Available: https://shorturl.at/BLuRi [83] T. Marthinus and O. Daramola, “On domain ontology for decision support in the treatment of gait-related diseases,” Proceedings - 2021 21st International Conference on Computational Science and Its Applications, ICCSA 2021, pp. 195–203, 2021. [84] M. Hassanzadeh and B. Shahrrava, “Linear version of parseval’s theorem,” IEEE Access, vol. 10, p. 27230–27241, 2022. [Online]. Available: http://dx.doi. org/10.1109/ACCESS.2022.3157736 [85] T. T. Dao, F. Marin, and M. C. H. B. Tho, “Predictive mathematical models based on data mining methods of the pathologies of the lower limbs,” IFMBE Proceedings, vol. 22, pp. 1803–1807, 2008. [Online]. Available: https://link.springer.com/chapter/10. 1007/978-3-540-89208-3 430 [86] G. Qi and B. Huang, “Walking detection using the gyroscope of an unconstrained smartphone,” Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST, vol. 210, pp. 539–548, 2018. [Online]. Available: https://link.springer.com/chapter/10. 1007/978-3-319-66628-0 51 [87] M. Henriksen, H. Lund, R. Moe-Nilssen, H. Bliddal, and B. Danneskiod-Samsøe, “Test–retest reliability of trunk accelerometric gait analysis,” Gait & Posture, vol. 19, pp. 288–297, 6 2004. [88] J. Jung, W. Choi, and S. Lee, “Immediate augmented real-time forefoot weight bearing using visual feedback improves gait symmetry in chronic stroke,” Technology and Health Care, vol. 28, no. 6, pp. 733–741, 2020. [89] M. Grijalvo, J. Ordieres-Mer´ e, J. Villalba-D´ ıez, Y. Aladro-Benito, G. Mart´ ın- ´ Avila, A. SimonHurtado, and C. Vivaracho-Pascual, “Sufficiency for pss tracking gait disorders in multiple sclerosis: A managerial perspective,” Heliyon, vol. 10, no. 9, p. e30001, May 2024. [Online]. Available: INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 20 http://dx.doi.org/10.1016/j.heliyon.2024.e30001 [90] E. Walter, M. Traunfellner, F. Meyer, C. Enzinger, M. Guger, C. Bsteh, P. Altmann, H. Hegen, C. Goger, and V. Mikl, “Cost-effectiveness of the floodlight® ms app in austria. unlocking the mystery of costs and outcomes of a digital health application for patients with multiple sclerosis,” DIGITAL HEALTH, vol. 11, Jan. 2025. [Online]. Available: http://dx.doi.org/10.1177/ 20552076251314550 [91] L. Kremer, L. Schreff, D. Hamacher, P. Oschmann, V. Rothhammer, P. M. Keune, and R. M¨ uller, “Cognitive-motor interference in multiple sclerosis revisited: a dual-task paradigm using wearable inertial sensors and the paced auditory serial addition test,” Frontiers in Neurology, vol. Volume 16 - 2025, 2025. [Online]. Available: https://www.frontiersin.org/journals/ neurology/articles/10.3389/fneur.2025.1546183 [92] D. A. Wajda and J. J. Sosnoff, “Cognitive-motor interference in multiple sclerosis: A systematic review of evidence, correlates, and consequences,” BioMed Research International, vol. 2015, p. 1–8, 2015. [Online]. Available: http://dx.doi.org/10.1155/2015/720856 [93] J. K. Lee and W. C. Jung, “Quaternion-based local frame alignment between an inertial measurement unit and a motion capture system,” Sensors, vol. 18, no. 11, p. 4003, Nov. 2018. [Online]. Available: http://dx.doi.org/10.3390/s18114003 [94] Y. Duan, X. Zhang, and Z. Li, “A new quaternionbased kalman filter for human body motion tracking using the second estimator of the optimal quaternion algorithm and the joint angle constraint method with inertial and magnetic sensors,” Sensors, vol. 20, no. 21, p. 6018, Oct. 2020. [Online]. Available: http://dx.doi.org/10.3390/s20216018 [95] S. Mansoor, U. I. Bhatti, A. I. Bhatti, and S. M. D. Ali, “Improved attitude determination by compensation of gyroscopic drift by use of accelerometers and magnetometers,” Measurement, vol. 131, p. 582–589, Jan. 2019. [Online]. Available: http://dx.doi.org/10.1016/ j.measurement.2018.08.067 [96] C. Virginia Anikwe, H. Friday Nweke, A. Chukwu Ikegwu, C. Adolphus Egwuonwu, F. Uchenna Onu, U. Rita Alo, and Y. Wah Teh, “Mobile and wearable sensors for data-driven health monitoring system: State-of-the-art and future prospect,” Expert Systems with Applications, vol. 202, p. 117362, Sep. 2022. [Online]. Available: http://dx.doi.org/10.1016/j.eswa.2022.117362 Joaqu´ ın Ordieres-Mer´ ereceived the Ph.D. degree in industrial engineering from the Universidad Nacional de Educaci´ on a Distancia (UNED), in 1987. He was a full professor of industrial management with the Universidad de la Rioja, in 1997, and at the Universidad Polit´ ecnica de Madrid, since October 2008. His research interests are related to business analytics. In particular, he focuses on modeling processes from data to improve knowledge and optimize them. He was involved in over 70 research projects, most of them international and competitive. He has published more than 150 research papers, with accumulated cites of over 7700. He participates in ISO TC groups and serves regularly as a Reviewer for different journals, including the Editorial Board Membership in few more, such as MDPI Sensors, the International Journal of Data Mining, Modeling, and Management as well as Frontiers in Built Environment. He also represents his country as a member of some European Union expert committees such as RFCS TGA5. Mercedes Grijalvo received the Ph.D. degree in mechanical engineering and industrial organization from Charles III University of Madrid in 2009. She was an associate professor of industrial management with Charles III University in 2009, and at the Universidad Polit´ ecnica de Madrid since September 2011. She has also been a visiting professor at the Centre de Recherche en Gestion de l’´ Ecole Polytechnique (Paris, France) and Southern Illinois University Carbondale (USA). Finally, in the last years she had served at different leading positions in the board of the department, involving more than 130 members, as well as in different secretaries of different Ph.D. and master programs. Her research interests include innovation and digitalization, both from a business and an educational perspective. She has published as author and/or coauthor more than 50 publications, including articles, books, and book chapters, of which 30 are in scientific publications indexed in JCR and SJR, and 20 in Q1-Q2 journals. She serves regularly as a reviewer in international journals, such as Journal of Business Research and Technological Forecasting and Social Change. Highlight her experience in participating in research projects both in competitive calls from several organizations such as the ones developed with companies. Guillermo Mart´ ın- ´ Avila. was graduated in Medicine from the Universidad Aut´ onoma de Madrid in 2016, in Neurology from the Hospital Universitario de Getafe (Madrid) in 2021. He Is a member of research group in Multiple Sclerosis whose director is Dr. Aladro as Group 79 of IdiPAZ. With this research group, he participates in several clinical studies pending completion among which are the study on biosensors applied in medicine and which includes the School of Industrial Engineers of the Polytechnic University of Madrid. This group initially worked with biosensors in essential tremor and currently in the analysis of gait in PwMS. He is an active collaborating researcher in other projects under development in the MS Unit of the University Hospital of Getafe. INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 21 Yolanda Aladro graduated in Medicine from the Universidad Aut´ onoma de Madrid in 1981, in Neurology from the Hospital San Carlos de Madrid in 1986 and obtained her Ph.D. from the Universidad Europea de Madrid. She has been working as a neurologist since 1986 and in the field of multiple sclerosis and other demyelinating diseases since 1991. She is Coordinator of the Multiple Sclerosis Unit of the University Hospital of Getafe in Madrid, Professor of Neurology at the European University of Madrid, Research Member of the Spanish Multiple Sclerosis Network (REEM), Vice-President of the Medical Advisory Board (MAB) of the Spanish Multiple Sclerosis Association, Member of the MAB of Multiple Sclerosis Spain. She is a member of the Study Group of Demyelinating Diseases (SGDD) of the Spanish Society of Neurology and a coordinator of the SGDD of the Madrid Association of Neurology. She is an expert in multiple sclerosis, to which she has been dedicated for more than 30 years, both in the field of care and research, and heads the Research Group 79, which focuses on clinical research in multiple sclerosis (MS). She has 106 indexed publications, 2263 citations, and an H index of 17 according to the Web of Science. INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 22 APPENDIX A MATHEMATICS OF MOVEMENT. The analysis has been carried out through quaternions objects. They form a non-commutative division algebra over the real numbers. This means that they satisfy the axioms of a ring (addition, subtraction, multiplication) and have multiplicative inverses (except for the zero quaternion). Quaternions provide a robust representation of rotations without singularities or gimbal lock [93, 94]. A quaternion 𝑞is defined as: 𝑞=𝑤+𝑥i+𝑦j+𝑧k(11) where 𝑤is the scalar component and (𝑥, 𝑦, 𝑧)are the vector components. The angular velocity vector 𝝎=(𝜔𝑥, 𝜔𝑦, 𝜔𝑧)is converted into a quaternion representation: 𝜔𝑞=(0, 𝜔𝑥, 𝜔𝑦, 𝜔𝑧)(12) The quaternion derivative is given by: 𝑑𝑞 𝑑𝑡 =1 2𝑞⊗𝜔𝑞(13) where ⊗represents the multiplication of quaternions. Using numerical integration (e.g., Euler method), the quaternion at time 𝑡+Δ𝑡is updated as: 𝑞𝑡+Δ𝑡=𝑞𝑡+1 2𝑞𝑡⊗𝜔𝑞Δ𝑡(14) Gyroscopes suffer from drift over time, requiring correction using accelerometer and magnetometer data [95]. The estimated gravity vector from the quaternion is computed as: 𝑔est =𝑞𝑡⊗ (0,0,0,1) ⊗ 𝑞∗ 𝑡(15) where 𝑞∗ 𝑡is the conjugate of the quaternion. The correction is applied by aligning 𝑔est with the measured gravity vector. The magnetometer provides a heading reference, and the correction is applied via complementary filtering or an Extended Kalman Filter (EKF) [75]. Once orientation is estimated, acceleration data from the IMU can be used to compute velocity and position. The acceleration in the global reference frame is obtained by removing gravity: 𝑎global =𝑞𝑡⊗𝑎sensor ⊗𝑞∗ 𝑡−𝑔(16) where 𝑔=(0,0,9.81)m/s² is the gravitational acceleration. Velocity is computed by integrating acceleration over time: 𝑣𝑡+Δ𝑡=𝑣𝑡+𝑎globalΔ𝑡(17) To mitigate drift, Zero-Velocity Updates (ZUPT) are used when the IMU is detected to be stationary [77]. Position is computed by integrating velocity: 𝑝𝑡+Δ𝑡=𝑝𝑡+𝑣𝑡Δ𝑡+1 2𝑎globalΔ𝑡2(18) The Madgwick filter is unique because it fuses IMU sensors to better estimate orientations over time and minimizes drift error when fuses sensors [47]. Although IMUs provide accuracy in position measurements using dead reckoning when estimating position, they suffer from integration drift, leading to continuous tracking errors. To mitigate position drift, data fusion can help fix it, using GPS fusion with Kalman filtering [76]. The merging of several measurement assets holds great promise for human movement science, such as increased activity recognition and more knowledgeable gait analysis. Wearable and mobile data fusion refers to the integration of multiple sensor modalities to enhance the accuracy, reliability, and scope of real-time monitoring in various applications such as health tracking, motion analysis, and activity recognition. By combining different sensor sources, data fusion mitigates the limitations of individual sensors and provides a more comprehensive understanding of physiological and biomechanical states [67, 96]. APPENDIX B GAIT STRUCTURE. To characterize the gait structure, several relevant features have already been defined and used as reference for the comparative analysis. 1) Temporal Parameters (Timing): •Stance Time: Duration (seconds) of contact between the foot and the ground. •Swing Time: Duration (seconds) the foot is not in contact with the ground. •Stride Time: Duration (seconds) of one complete gait cycle (one step with each foot). •Step Time: Duration (seconds) between the heel strike of one foot and the heel strike of the opposite foot. •Double Support Time: Duration (seconds) when both feet are in contact with the ground. •Cadence: Steps per minute. •Stance/Swing Ratio: Ratio of stance time to swing time. •Stride Time variability: Standar deviation of stride times. •Step Time variability: Standar deviation of step times. 2) Spatial Parameters (Distances): •Step Length: Distance (meters) between successive heel strikes of opposite feet. •Stride Length: Distance (meters) between successive heel strikes of the same foot. •Step Width: Mediolateral distance (meters) between the feet during double support. •Stride Length variability: Standar deviation of Stride Lengths. •Step Length variability: Standar deviation of Step Lengths. 3) Assymetry parameters: •Step Length Asymmetry: Step length is a common gait parameter for quantifying gait asymmetry. •Stance Time Asymmetry. INTERNET OF THINGS JOURNAL, VOL. XX, NO. XX, XXXX 2025 23 G1G2G3G4G5 MSwISwPSwTStMStLR TSw TStMStLRMSw TSwISwPSw G0 Phase Right Foot Left Foot Fig. 13. The figure illustrates a full walking cycle, which begins when a foot’s heel makes contact with the ground (highlighted point in Fig. 6. The cycle is divided into a Stance Process and a Swing Process. The Stance process is when the foot is on the ground and consists of three phases.The Swing process is when the foot is not in contact with the ground and includes four phases. The figure also shows the adopted phase labeling system, where LR, MSt, TSt, PSw, and ISw are defined as G0 to G4, with MSw and TSw combined as G5. The diagram highlights the complementary nature of gait, as one foot is in its stance process while the opposite foot is in its swing process. •Swing Time Asymmetry. 4) Variability and Stability Parameters: •Coefficient of Variation (CV) for any of the above parameters: CV = (Standard Deviation / Mean) * 100%. A higher CV indicates greater variability. Increased variability is a hallmark of MS gait. This can be calculated for stride time, step time, step length, etc. •Harmonic Ratio: A measure of gait smoothness