Walking is a central activity of daily life, and restrictions of this ability lead to a reduction in the quality of life (1, 2). Therefore, gait analysis is an important tool in different medical and therapeutic fields (3, 4). The measurement of various gait characteristics can either facilitate diagnosis or be used to track the progress of rehabilitation. Gait can be measured by spatial (e.g., step or stride length) and temporal (e.g., stride time, cadence) parameters, relative durations of gait phases, and kinematic and kinetic gait variables (5). These parameters are used to quantify gait deviation in both clinical practice and research, and their use varies with the medical field, the research question, and the analysis options. While gait assessment in clinical practice is mostly based on visual observation by medical experts (6), it is desirable to support expert knowledge and time by objective measurements. This is also important because relevant gait changes are often too subtle to be detected by the naked eye (7).

Traditionally, sensor-based gait assessment is performed with stationary systems like marker-based optical motion tracking, instrumented treadmills, or pressure-sensitive walkways (6, 8). Besides being expensive, one major drawback of those systems is that they are limited to a small capture space or require the subject to walk on a treadmill (4, 9–12). Furthermore, the use of walking aids is often not possible or restricted in combination with such systems.

A promising, more ambulatory, and less restrictive alternative is inertial gait analysis, i.e., gait analysis with inertial sensor technology. Lightweight and battery-powered inertial measurement units (IMUs) are used, which transmit the data wirelessly.

The transition from expensive stationary systems to small wearable sensors opens up possibilities that go beyond replacing the measurement technology used for gait assessment in a clinical setting. Integrating objective long-term gait monitoring in day-to-day life—as illustrated in Figure 1—could provide more powerful tools for clinicians to help patients in rehabilitation but also to gain further insights into disease progression. Furthermore, non-obtrusive wearable plug-and-play systems facilitate applications in neuroprosthetics (13) or exoskeletons and can be used to provide biofeedback (14). In the last years, wireless battery-powered IMUs have become smaller, lighter, more accurate, and at the same time cheaper and more energy-efficient, and it is to be expected that this development is going to continue. For those new trends, it is important to develop methods that can provide a wide variety of gait parameters that are useful to medical experts. At the same time, the methods need to be robust so that the system can be used by patients in unsupervised settings, outdoors as well as indoors.

It has been shown by previous contributions (15–17) that major gait parameters can be determined with two IMUs that are placed on the feet or the shoes, as illustrated in Figure 1. This includes stride length, gait phase durations (e.g., stance and swing percentage), and also the cadence and walking speed.

Our aim is to propose methods for gait assessment that meet the requirements for day-to-day life monitoring in unsupervised settings and that are validated on a broad group of subjects including patients with various gait pathologies. The proposed methods do not assume any fixed orientation of the sensor with respect to the foot and do not require the subject to perform dedicated calibration movements. Furthermore, magnetometers are not used since the magnetic field is known to be severely disturbed in indoor environments (18). This makes the use of inertial gait analysis easy and practical in clinical settings and facilitates future applications of ubiquitous gait analysis in home environments.

The remainder of the article is structured as follows. In section 2, we briefly review existing methods for IMU-based spatiotemporal gait parameter estimation. In section 3, we describe the proposed methods, which we then validate in section 4 using experimental data of 98 orthopedic and neurological patients, as well as 39 healthy subjects walking at different speeds. The results are discussed in section 5, and section 6 provides conclusions.

Several methods have been proposed that employ inertial sensors to obtain spatiotemporal gait parameters. In the following, we present a brief overview of the current state of the art and summarize the different hardware setups that are used, which parameters are calculated, and how the methods were validated. Table 1 categorizes 23 publications that provide a range of examples for the variety of existing approaches in the estimation of spatiotemporal gait parameters with inertial sensors.

There are different hardware setups, based on the number of inertial sensors and their placement. The chosen setup has an impact on which and how many parameters can be derived from the measured data. The most commonly used setup consists of two IMUs. As shown in Table 1, sensors are typically placed on the feet or shoes and sometimes on the shank. This setup is occasionally extended by adding a third sensor on the pelvis or lumbar spine (34, 35). Note that it has even been shown that temporal gait events can be obtained from a single IMU at the pelvis (38), but the potential for extracting further spatial parameters is limited. Full (lower) body motion tracking opens up additional possibilities, as demonstrated with 7 IMUs on the lower body and pelvis in (37) and with 8–15 IMUs in (36). Another, less common, option consists of combining inertial sensors with further measurement devices, e.g., a camera on one foot and LEDs on the other foot to facilitate the direct measurement of relative positions (39).

Some methods require that a known orientation of the sensor axes with respect to the anatomical foot axes has to be ensured by precise placement. Many methods in the literature are based on such assumptions, including (13, 15–17, 22, 23, 25, 26, 30–33). In practice, however, ensuring a precise placement is a challenge, especially in non-supervised application scenarios and during activities of daily life. Alternatives are to develop methods that are agnostic to the sensor-to-segment orientation—e.g., by only relying on signal norms—or to determine this orientation in a process commonly called anatomical calibration (40). For setups with more sensors, there are recently developed methods that facilitate automatic anatomical calibration by exploiting kinematic constraints of the respective joints without requiring the subject to perform precise calibration movements (41, 42). For those setups, the linking of the sensors to the body segments poses another challenge to a plug-and-play approach, which can be solved by automatic pairing methods (43).

The calculation of spatiotemporal gait parameters is usually implemented in a two-stage approach. In a first step, gait events and corresponding gait phases are detected. In a second step, spatial parameters are calculated.

Existing methods vary in the set of gait events or phases that are detected. In many cases, the focus is only on the separation between stance and swing (cf. Table 1), although sometimes additional events, such as mid-swing (33), are also detected. It is also common to detect four events that occur during the gait cycle and are only defined by the ipsilateral (same) foot. Those events are initial contact, full contact, heel rise, and toe-off, although the terminology varies. Despite being common practice in gait analysis (5, 44), employing bilateral information, i.e., combining information from both feet to define the gait phase, is far less common in IMU-based gait analysis. One example is (36) in which single and double limb support durations are calculated.

There are various approaches for detection of gait events using inertial sensors. It has been shown that exploiting features of the angular rate signal in the sagittal plane is sufficient to achieve reliable gait event detection (16, 22, 25, 30, 32). Many other methods use both accelerometers and gyroscopes and detect characteristic signal features in the inertial sensor data, including (13, 15, 17, 19–21, 23, 31, 33). Sometimes automatic adaption mechanisms are used to adjust thresholds based on the subject's walking style (19–21, 33). An alternative to the signal-based methods is to rely on a kinematic model to detect gait events (36, 37). Machine learning methods, often based on hidden Markov models (26, 35), are also used for event detection [cf. (45)].

In addition to the detection of gait events, spatial parameters such as stride length and walking speed are often calculated. Those parameters are obtained by either signal integration, human gait models, or by machine learning methods (46). By far the most common approach is numerical strapdown integration of the accelerations (16, 17, 22, 27, 28, 31, 32, 37). The cyclic nature of gait and the fact that there is frequent ground contact are exploited to correct for drift that is due to double integration. It has been shown that Fourier-based integration is an alternative to numerical integration (34), that spatial parameters can be obtained from kinematic models (27, 36), and that convolutional neural networks can also be used to estimate spatial parameters (23).

Most publications focus on common spatiotemporal parameters such as stride length, walking speed, and cadence. Other than those spatiotemporal parameters, there is a multitude of spatiotemporal gait parameters that are relevant in a clinical context for various pathologies (6). Examples that can be estimated using inertial sensors include step width (37), swing width (31, 37), incline (22), and foot clearance (47).

Some publications (13, 19–21, 25, 33) focus on real-time detection of events, e.g., to trigger functional electrical stimulation (FES). While the approaches used are usually similar to the ones used in offline gait analysis, this typically implies a focus on minimizing the detection delay rather than the accuracy of the reported values.

As shown in Table 1, evaluation is often performed with marker-based optical motion capture as ground truth. Systems based on the detection of pressure, such as pressure-sensitive walkways, instrumented treadmills, and pressure insoles, are a common alternative. In some cases, no validation with respect to a gold standard is performed. Instead, the settings of a (calibrated) treadmill are used for walking speed and incline (22), a manually counted number of steps is combined with the detection of irregularities (21), validation is performed by visual inspection of the results (19), or the focus is only on test-retest reliability (36).

Even though it has been shown that the accuracy of gait analysis methods decreases when applied to non-healthy subjects (45), the evaluation of inertial gait analysis methods is often only based on healthy subjects. When data obtained from non-healthy subjects is part of the evaluation, the number of subjects is often small, for example five transfemoral amputees (20), 10 stroke patients (33), 10 hemiparetic patients and 10 Huntington's disease patients (35), or 10 patients with Parkinson's disease (31).

To the best of our knowledge, few publications (15–17, 23, 29, 32) exist which propose methods for IMU-based spatiotemporal gait parameter estimation and validate the methods on a larger set of subjects with gait pathologies. In the following, we briefly summarize those publications.

In (15), sensors are placed on the forefoot in a known orientation, and four different unilateral gait events are detected based on features of the angular velocity in the sagittal plane, the norm of the accelerometer signal, and the derivative of angular velocity norm. Using pressure insoles as reference, the method is validated on 10 healthy and 32 orthopedic subjects.

The commercial Gait Up system is evaluated in (29) with 25 subacute stroke patients as subjects and marker-based optical motion capture as reference.

Gait events and stride length are calculated in (16) based on shank-mounted IMUs. Events are detected based on the angular rate in the sagittal plane, and stride length is obtained via double integration of the accelerations. The latter relies on the proprietary orientation estimation algorithm provided by the sensor manufacturer. Experimental evaluation is performed using the GAITRite pressure-sensitive walkway as reference on 10 healthy elderly and 30 non-healthy subjects.

In (32), the same method is validated on a much larger group of subjects, consisting of 236 community-living older adults, including 31 mild cognitive impaired subjects and 125 Parkinson's disease patients.

In (17), IMUs are placed laterally on the shoe in a fixed orientation, stance, and swing durations are calculated based on characteristic signal features, and the stride length is obtained via double integration. The method is evaluated using a large data set of 101 geriatric inpatients, with reference data obtained from a GAITRite pressure-sensitive walkway.

Using the same gait event detection method and the same data set for evaluation as (17), Hannink et al. (23) estimates stride length, stride width, mediolateral change in foot angle, heel contact times, and toe contact times using deep convolutional neural networks.

In summary, the main shortcoming of existing approaches for the vision of plug-and-play ambulatory gait analysis is that most methods—especially those with broad validation—require a precise attachment of the sensor to the subject's foot. Some methods only focus on gait events and do not provide spatial parameters, and some methods rely on proprietary algorithms of the sensor manufacturers. Furthermore, very few of the proposed methods are validated on a large group of subjects with diverse gait pathologies.

In the following section, we propose a set of methods that combine the valuable achievements of existing methods with additional features that overcome the remaining limitations.

In the following, we propose a set of methods to determine gait parameters from two IMUs attached to the foot. The proposed methods are based on the following assumptions and requirements: An IMU is attached to each foot (or shoe) in an arbitrary orientation. This implies that the proposed method does not make any assumption about the orientation of the sensor coordinate system, which means it does not require any specific sensor axis to be aligned with an anatomical or functional axis of the foot. In order to avoid artifacts caused by toe or ankle motions, and also to not limit the subject's freedom of movement, we propose to attach the IMU on the instep, i.e., the dorsal side of the midfoot. We obtain the accelerometer and gyroscope readings of both IMUs at a fixed sampling rate (typically in the range 50–1,000 Hz). We assume that data for several steps is processed at once, which allows us to employ non-causal signal processing to increase the accuracy compared to sample-by-sample real-time capable methods. This processing can either be performed in batches while the subject is walking, e.g., for use in biofeedback applications, or after the recording is completed. During the recording, the subject walks either on a treadmill or an indoor or outdoor ground.

The set of methods that we propose is explained in the following subsections, and the presentation is structured as follows. Separately for each foot, we use the recorded sensor data to separate phases in which the foot is in full contact with the ground from phases in which the foot moves, i.e., we detect when strides take place (section 3.3). For each detected stride, we then detect toe-off (section 3.5) and initial contact (section 3.6). The gait events from the ipsilateral and contralateral foot are combined to define gait phases. We calculate the relative duration of each gait phase and the cadence (section 3.7). We then estimate the sensor orientation by sensor fusion of the gyroscope and accelerometer readings (section 3.8) and double-integrate the acceleration to obtain a position trajectory (section 3.9). From this position trajectory, we obtain the stride length and the walking speed (section 3.10). Figure 2 provides an overview of the proposed set of methods.

In the remainder of this section, we define parameters used by the method. For an overview of those parameters and proposed values, please refer to Table 2 in section 4. Our aim is to define the parameters in a way that they are not sensitive to different gait styles or velocities. In section 4, we demonstrate that this approach works by only employing one common set of parameters for validation on a very broad data set with healthy and non-healthy subjects walking at different speeds.

In this section, we aim to show that the less restrictive IMU-based setup combined with the methods proposed in section 3 is able to determine the same parameters as stationary systems that are used in clinical practice while providing similar accuracy. To this end, with a large data set consisting of three different subject groups, we compare the parameters calculated by the proposed methods with values reported by instrumented treadmills.

In the present contribution, we have proposed a set of methods for spatiotemporal gait analysis based on two inertial sensors attached to the feet. Our methods allow for the calculation of the main spatiotemporal gait parameters that are also reported by stationary laboratory systems: gait phase durations, stride length, walking speed, and cadence. Using a large data set consisting of healthy subjects walking at three different speeds, subjects with orthopedic diseases, and subjects with neurological diseases, we have validated the calculation of those parameters, using a Zebris Rehawalk instrumented treadmill as reference. All parameters show a very strong correlation (Pearson's r between 0.83 and 0.99, p < 0.01) (51). Figures 10–12 display consistent results over this large and diverse group of subjects. Averaged over all trials, the MAD with respect to the reference system is 1.4 % for the gait phase durations, 1.7 cm for the stride length, 0.04 km/h for the walking speed, and 0.7 steps/min for the cadence.

In clinical practice and research, the presented parameters are used to quantify gait abnormalities and to document changes in the walking behavior of patients. Associations between spatiotemporal gait parameters and functional capacity, or increased mortality, have been demonstrated (52–54). A positive correlation with cardiovascular-related mortality was found for cadence (55). A reduction in walking speed has been shown to correlate with fall risk, frequency of hospitalization, and mortality (56–58). Stride length describes a strong correlation with walking speed according to the research of (59). Slower walking speed, altered gait phase duration, and increased variability of walking increase the risk of falls (60). Furthermore, it was found that psychological modalities, such as fear of falling, can also influence stride length and gait phase duration (61). The minimal clinically important difference (MCID) can be used to determine how precisely these changes must be detected in order to make a statement about their relevance. Despite thorough research, specific values for the MCID could only be found for the walking speed, ranging from 0.36 to 0.72 km/h (62–64). For IMU-based measurement with the proposed methods, the smallest detectable change (SDC) for walking speed is 0.21 km/h and clearly within the MCID for all examined groups. For the other parameters, no reported MCID values could be found, which is consistent with the statement of (29).

The SDC for the cadence is 2.01 steps/min across all studied groups of subjects. This allows for much more accurate changes to be detected than those described as relevant in the literature [e.g., reduction in cadence of 10 steps per minute increases mortality by 4 % (65)]. The achieved SDC for stride length of 5.3 cm in the patients with neurological diseases seems to be sufficiently accurate to capture the differences occurring, for example, in Parkinson's disease (66). The stance and swing phase durations show an SDC of 6.5 % across all trials.

Unlike many existing contributions, we showed that the proposed methods reliably work on patients in addition to healthy subjects and still produce accurate results. This is noteworthy since it has been shown that pathological walking deteriorates the accuracy of many gait analysis methods (45) and specifically the neurologically induced gait abnormalities are challenging for IMU-based gait analysis (29).

A fundamental challenge of IMU-based gait event detection is that IMUs do not directly measure the gait parameters of interest. For toe-off detection, the time instant of load relief cannot directly be measured, and instead, the inversion of the direction of rotation is used. Similarly, initial contact is not detected based on the onset of load but based on the change of acceleration. It is therefore important to properly validate the IMU-based methods by comparing the estimated gait parameters to a reliable ground truth.

As reference system, treadmills instrumented with Zebris pressure measurement platforms were used, which are frequently employed for gait analysis in clinical practice as well as scientific data collection (12). This system shows good reliability (67), but no studies could be found in which the validity of the gait parameters was investigated. It should be noted that due to the length of the pressure sensors (FDM-THM-M-3i: 0.85 cm; FDM-THM-M-2i: 1.27 cm) there may be inaccuracies in the recording of spatial parameters, which may have an effect on the results of the comparative measurements. Moreover, calibration and proper thresholding pose challenges in gait event detection based on pressure measurements (12).

For the neurological patients, the reported duration of stance is, on average, 2 % longer than the reference duration. While this is still a small deviation, it is worth noting because this bias suggests a pattern that is common to this subject group. One likely explanation is that toe-off is being detected later than with the Zebris system. This might be due to a comparatively long phase of load relief that causes the pressure to fall below the threshold too early. Furthermore, the reversal of rotation direction might happen later than for healthy subjects or orthopedic patients. Still, even though both systems measure inherently different phenomena, the observation deviation is only 2 %.

As a replacement for traditional stationary gait analysis systems, which are commonly used in clinical practice, IMU-based gait analysis offers several advantages. Measurement is possible both on treadmills and overground and not restricted to a dedicated laboratory. The small and lightweight IMUs do not restrict the movement of the subject and can be used in conjunction with walking aids such as wheeled walkers. Furthermore, only a very short setup time is required before starting the actual measurement.

Unlike most existing methods (cf. section 2), the proposed method makes gait analysis easier and faster by not requiring any specific sensor attachment, which we demonstrated by simulating a different random sensor-to-foot orientation in each trial. It does not make use of magnetometers and can therefore be used in both indoor and outdoor environments.

While evaluation was limited to the gait phases reported by the reference system, our proposed set of methods further allows for the calculation of many gait phases (Figure 4), i.e., swing and stance for each foot, four unilateral gait phases for each foot, five bilateral gait phases following standard literature (44) for each foot, and finally the distinction between double and single support. To the best of our knowledge, no existing work on IMU-based gait analysis describes the calculation of this set of gait phases.

Besides the more fine-grained gait phases, there are many more parameters that can be extracted, e.g., from the velocity and position trajectories, such as the maximum velocity during swing, foot clearance, and symmetry parameters. While it is not surprising that the prevalence of pressure-based systems has led researchers to focus on features based on ground contact, it is to be expected that the focus of clinical gait analysis will be directed toward other parameters as IMU-based systems become more popular.

Furthermore, miniaturized lightweight sensors with a long battery life open up possibilities for objective gait analysis outside of clinical laboratories. Daily-life gait assessment over the course of multiple days can bring insights that are not possible with short sessions in a laboratory. If patients place the sensors on or in the shoes themselves in an unsupervised telemedicine setting, not requiring the sensor to be oriented in a special way becomes even more important.

Technological advancement also facilitates real-time biofeedback applications. While there are methods for real-time applications that require event detection during a step (41), e.g., to trigger FES, the proposed set of methods is real-time capable in the sense that during walking, sections of data containing a small number of strides can be processed and used to provide feedback to the subject.

The presented work exhibits a few remaining limitations. In the statistical analysis, the gait parameters were averaged over the duration of the trial before comparison with the reference. While it allows for single-stride errors to cancel out, this methodology corresponds well with the use case of clinical gait analysis, in which a subject is asked to walk for several steps, and averaged parameters are then used to assess the gait. An additional stride-by-stride comparison was not performed because the employed reference system can only export averaged gait parameters. In addition, it should be noted that all recordings were made on treadmills and not while walking overground, which has an influence on the movement pattern of gait (68, 69). Despite the known differences between treadmill walking and overground walking, treadmill gait analysis is considered a standard method in clinical practice (70, 71), especially when weight support and handrails are required for safety reasons.

In the present contribution, we have proposed a set of methods for IMU-based gait analysis. Based on gyroscope and accelerometer measurements from two inertial sensors on the feet, we estimate durations of five gait phases, stride length, walking speed, and cadence. Using a Zebris Rehawalk instrumented treadmill as reference, we validated the proposed methods based on a large data set consisting of healthy subjects (n = 39) walking at three different speeds, subjects with orthopedic diseases (n = 62), and subjects with neurological diseases (n = 36). Averaged over all trials, the MAD with respect to the reference system are 1.4 % for the gait phase durations, 1.7 cm for the stride length, 0.04 km/h for the walking speed, and 0.7 steps/min for the cadence. We also demonstrated that the proposed methods work reliably not only in healthy subjects but also in patients and still provide accurate results under different pathological gait patterns.

This shows that the proposed setup in combination with the proposed methods can accurately calculate relevant gait parameters from the inertial sensor data and thus has the potential to replace traditional stationary gait analysis systems.

Furthermore, we validated that the proposed methods work well regardless of the orientation in which the sensor is attached to the foot, and dedicated calibration movements and magnetometer measurements are completely avoided. The combination of these advantages facilitates long-term ambulatory gait analysis in day-to-day situations without the need for supervision by health professionals.

Future research will focus on the estimation of additional gait parameters, on the validation on stairs and slopes, and the validation against marker-based optical motion capture systems.

The datasets presented in this article are not readily available because sharing of the data is not covered by the ethical approval. Requests to access the datasets should be directed to Andreas J. Jocham, andreas.jocham@fh-joanneum.at.

The studies involving human participants were reviewed and approved by the Ethics Committee of the University of Graz (GZ. 39/55/63 ex 2017/18, 28 May 2018). The patients/participants provided their written informed consent to participate in this study.

DL and TS devised and developed the mathematical method. DL implemented the method, performed the data analysis, and drafted the manuscript. AJ, BG, KA, and MF planned and organized the data collection. AJ, BG, and KA conducted the data collection and post-processed the data. DL, AJ, BG, KA, MF, and TS revised the manuscript. All authors approved the submitted version.

We acknowledge support by the German Research Foundation and the Open Access Publication Fund of TU Berlin.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.