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Online Decoding of Hidden Markov Models for Gait Event Detection Using Foot-Mounted Gyroscopes Andrea Mannini, Vincenzo Genovese, and Angelo Maria Sabatini, Senior Member, IEEE

Abstract—In this paper, we present an approach to the online implementation of a gait event detector based on machine learning algorithms. Gait events were detected using a uniaxial gyro that measured the foot instep angular velocity in the sagittal plane to feed a four-state left–right hidden Markov model (HMM). The short-time Viterbi algorithm was used to overcome the limitation of the standard Viterbi algorithm, which does not allow the online decoding of hidden state sequences. Supervised learning of the HMM structure and validation with the leave-one-subject-out validation method were performed using treadmill gait reference data from an optical motion capture system. The four gait events were foot strike, flat foot (FF), heel off (HO), and toe off. The accuracy ranged, on average, from 45 ms (early detection, FF) to 35 ms (late detection, HO); the latency of detection was less than 100 ms for all gait events but the HO, where the probability that it was greater than 100 ms was 25%. Overground walking tests of the HMM-based gait event detector were also successfully performed. Index Terms—Gait event detection, gyroscope, hidden Markov model (HMM), human movement analysis, short-time Viterbi (STV).

I. INTRODUCTION INIATURE solid-state inertial sensors (accelerometers and gyros) are steadily gaining interest because of their low cost, limited power consumption, and the good user compliance when they are embedded in wearable sensor systems [1]. Hence, the application niches of these sensors extend well beyond the traditional fields of, e.g., automotive industry and factory automation, to include consumer and medical electronics [2]. Currently, several human-centric applications of miniature solid-state inertial sensors are investigated, including ambulatory human movement analysis [3], [4], activity monitoring and classification [5], [6], assessment of neurological and movement disorders [7], [8], and mixed and augmented reality [9], [10].

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Manuscript received January 3, 2013; revised September 30, 2013; accepted November 30, 2013. Date of publication December 5, 2013; date of current version June 30, 2014. This work was supported in part by the Italian Ministry of Education and Research through the relevant interest national project (PRIN) “A quantitative and multi-factorial approach for estimating and preventing the risk of falls in the elderly people,” and by the EC funded project I-DONTFALL “Integrated prevention and Detection sOlutioNs Tailored to the population and Risk Factors associated with FALLs” (CIP-ICT-PSP-2011–5–297225). The views expressed in this paper are not necessarily those of the I-DONT-FALL consortium. The authors are with the BioRobotics Institute, Scuola Superiore Sant’Anna, Pisa 56127, Italy (e-mail: [email protected]; vincenzo.genovese@sssup. it; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2013.2293887

Using inertial sensors (either accelerometer or gyros) mounted on different parts of the lower limbs (waist, thigh, shank, and foot) is widespread in systems for ambulatory human movement analysis and, of interest in this paper, for gait events and phases detection. Henceforth, with the term gait event detection, we denote the detection of a sequence of events that can be used to specify the transition from one gait phase to another during each gait cycle. The detection of gait events and phases is of great importance in nearly all aspects of gait analysis and restoration. Gait parameters estimated from detecting gait events and phases can be associated with specific functional impairments and are widely used to quantify improvements occurring after therapeutic and rehabilitative treatment [11]–[14]. Gait event detectors that address the online detection of the phases of gait are essential components of controllers for functional electrical stimulation (FES) gait [15]. Either simple stance/swing detectors or more complex detectors that added further states for FES control through the detection of multiple gait phases (e.g., loading response, midstance, terminal stance, preswing, and swing) have been considered [16], [17]. Moreover, even pedestrian navigation systems that estimate the location of a walking person using on-foot inertial measurement units (IMUs)—a.k.a, on-foot PNS—may benefit from the capability of accurately detecting gait phases online, in particular midstance and preswing. This is because, in order to decrease navigation errors, angular rates and linear accelerations are integrated in the time interval from the heel-off event to the successive heel off (HO) of the same foot [18] from initial conditions that are specified when the foot is steady during midstance [19]. In this paper, we disclose the method of online gait event and phase detection we intend to exploit in an ongoing project concerning the development of an on-foot IMU-based PNS. The gait events we are interested in detecting are heel strike (HS), flat foot (FF), HO, and toe off (TO); HS and TO detection allows us to estimate temporal parameters of gait, such as stride time, cadence, and normalized stance; FF and HO detection will be used to estimate parameters of gait, such as stride length and walking speed, using strap-down navigation techniques. The inertial sensor-based approach to gait event detection presents many advantages over using, e.g., optical motion capture systems and shoe-mounted force sensors: compared to optical motion capture systems, the inertial sensor-based approach allows measurements to be made in unrestrained conditions; compared to insole force sensors, the durability of inertial sensors is higher and factors, such as load changes and weight shifting, have no influence on the measurements [20]. Although accelerometers are the most popular choice among practitioners [21], [22], gyros are also very attractive, because they are

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MANNINI et al.: ONLINE DECODING OF HIDDEN MARKOV MODELS FOR GAIT EVENT DETECTION USING FOOT-MOUNTED GYROSCOPES

not influenced by gravity, and shock and vibrations affect their output less than accelerometers [18]. As for the gait detection methods, functional data analysis (FDA) and, to a more limited extent, machine learning (ML) methods have been considered [15]. Usually, FDA methods employ techniques of curve tracing to search for features occurring in sensor signals (e.g., by detection of local extrema or threshold crossings), while ML methods learn to recognize stable patterns that may recur in the signals from a sensor (or combination of sensors) due to the cyclical nature of gait. Simple threshold rules were applied to the angular velocity from a foot-mounted gyro in [18]; a biaxial accelerometer was then used for estimating the spatial parameters of gait via strapdown integration. Wavelet transformation and peak detection algorithms were applied to the angular velocity from pairs of gyros affixed to the thigh and the shank in [23]; the estimation of gait spatial parameters was then performed using simple biomechanical models of the lower limb. Common to the approaches described in [18] and [23] is that careful hand-crafted thresholds were needed to overcome variations across different subjects and walking conditions: in other words, these are approaches that may suffer from limited generalization capabilities. In this regard, ML methods, such as adaptive logic networks and fuzzy logic, were shown to outperform FDA methods for their capability of accommodating the relatively large stride-to-stride variability observed especially in pathologic gait [16], [17]. Recently, a four-state left–right hidden Markov model (HMM) was developed in [24] and [25], where a sensor unit composed of a foot-mounted uniaxial gyro was used for detecting HS, FF, HO, and TO gait events, with good results during treadmill walking of healthy subjects; the HMM-based method outperformed the threshold-based method described in [18]. Mannini and Sabatini [24], [25] took inspiration from [26], where HMMs were applied to identify and segment into strides, data from a trunk-mounted IMU in galloping horses. Another approach with some resemblance to [24] and [25] was presented in [27], where a body area network composed of eight sensor nodes, each with one triaxial accelerometer and one biaxial gyro, was employed to estimate temporal parameters of gait using HMM. However, the problem of online decoding the HMM hidden states, which is a prerequisite for online operation of a HMM-based gait event detector, has never been considered in biomechanics research [24]–[27]. In the attempt to fill the gap, we propose a solution to this problem starting from the same sensor unit and HMM structure as in our previous work on gait events and phases detection. To this aim, we adopted the short-time Viterbi (STV) algorithm [28] to this particular problem. STV is a variant of the Viterbi algorithm, namely the standard method used to estimate the sequence of hidden states in HMMs [29], which cannot indeed operate in online conditions [30]. The tradeoff between accuracy and latency of detection by the STV algorithm was analyzed offline; the performance of the method was compared with that of the Viterbi algorithm using data that were logged to the memory of the ARM-based controller of the sensor unit during treadmill walking trials (HMM learning and validation). The decoder running the validated STV algorithm was ported to the ARM-based

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Fig. 1. (a) Screenshot of the GUI on the smartphone. (b) GPS-assisted geolocalization on an outdoor athletic track.

controller; overground walking trials were then performed for testing, during which sensor data and the estimated gait events were transmitted to a smartphone running Android as operating system (OS) for graphical rendering and user feedback. II. MATERIALS AND METHODS A. System Architecture and Experimental Procedure A wireless IMU developed in our laboratory was used for carrying out the experiments described in this paper. The sensor unit is endowed with a 32-bit ARM Cortex processor (NXP Semiconductors LPC1768). Data logging to ARM memory was allowed with sampling rates up to 500 Hz for the IMU sensors: a digital triaxial gyro (InvenSense ITG-3200), with measurement range ±2000◦ /s, and 16-bit analog-to-digital conversion, a digital triaxial accelerometer (Bosch BMA180), and a digital triaxial magnetic sensor (Honeywell HMC5843). The IMU board was equipped with a Bluetooth transceiver for data communication with a host computer; the host computer was an Android-based smartphone (Samsung Galaxy SII, GT-I9100), to which IMU sensor data were delivered at a maximum rate of 100 Hz. Data visualization on the smartphone was possible through a graphical user interface (GUI) written in Java using the Eclipse integrated development environment; the GUI also allowed to set parameters such as sensor measurement range, filter type, and bandwidth (e.g., second-order Butterworth filter; cut-off frequency 25 Hz), sampling rate, recording time (see Fig. 1); moreover, data from inertial sensors embedded in the smartphone and the built-in GPS receiver could be polled and timestamped for joint analyses with data from the external sensors. The integrity of the wireless communication link was successfully checked by comparing the frequency at which samples were received with the nominal sampling frequency. A first dataset for algorithm validation was acquired focusing on treadmill walking whereas a second dataset concerned overground walking tests on a straight corridor.

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Fig. 2. Subject performs his walking trial on the treadmill machine, while the STV decoder running in the ARM-based controller of the sensor unit estimates gait phases and events. Measured angular velocity data and estimated gait events are transmitted to the smartphone using a Bluetooth connection. The angular velocity is plotted on the smartphone with different colors that are based on which gait phase is detected by the STV decoder.

Nine young healthy subjects were recruited to perform treadmill walking after providing informed consent. The IMU was placed on the instep of the (left) foot and attached to the shoe with a Velcro strap; no particular care was taken to align the IMU with respect to the anatomical planes of the body. Subjects were asked to perform walking trials at five speeds (from 4 to 8 km/h, at 1 km/h steps). Each walking trial lasted 2 min (see Fig. 2). Only the output from the gyro whose sensitivity axis was approximately oriented in the mediolateral direction was collected in the experiments of this paper. Data from the second minute were retained for HMM training and validation. A six-camera optical motion capture system (Vicon-460, Vicon, Oxford, U.K.) was used to collect data at 100 Hz from two reflective markers (diameter: 14 mm) that were placed in correspondence of the heel and the second metatarsal head of the instrumented foot. The IMU and Vicon data streams were electronically time synchronized. A stride was defined as the period from the beginning of the stance phase at FS to the beginning of the next stance phase of the same leg. The temporal parameters of gait were the stride time, namely the time between two consecutive strikes of the instrumented foot, and the relative stance, namely the time between FS and TO of the instrumented foot, normalized to the stride time of the same gait cycle. The kinematic data from the optical motion capture system were used to create the reference data needed to learn and validate the HMM: FS, FF, and HO were estimated using the method described in [20]; TO was estimated using the method described in [31]. As for the overground walking trials, recruited subjects were asked to walk along a 45-m long corridor two times at their freely selected walking speed. They wore the IMU in the same configuration as described previously. Data from nine subjects were considered; only two of these subjects were also involved in the treadmill walking trials. Reference points (waypoints) at relative distances of 5 m were marked along the corridor. One researcher annotated the time instants when subjects crossed each waypoint using a computercontrolled stopwatch. Gyro data corresponding to the time inter-

val from the 5-m waypoint to the 40-m waypoint were retained for further processing (steady-state walking conditions). Average walking speed for each 5-m segment of the traveled path was then computed. The STV algorithm running on the ARM-based controller of the sensing units employed the HMM learnt using all treadmill walking data. The HMM-based gait event detector delivered the estimated stride time and relative stance of each detected stride. In Figs. 3 and 4, two flowcharts are reported to illustrate the various steps of the proposed method. In Fig. 3, the model validation using treadmill walking data is described while the flowchart of Fig. 4 indicates how overground walking data were processed. Detailed information concerning validation and test activities will be reported in following sections. B. HMM-Based Method for Gait Event Detection The observation that, during normal walking, the angular velocity of the foot in the medial lateral direction repeats itself indefinitely, with a sequence of humps and plateaus [24], [25], is central to the use of HMMs for gait event detection (see Fig. 5). Inter/intrasubject variability and walking conditions (e.g., speed and grade) do not influence the angular velocity patterns too much, unless the foot contact with the ground occurs at the toe rather than at the heel. In Fig. 5(a), the angular velocity was sketched in a plot where the abscissa was normalized to the stride time—0% corresponded to FS (HS). Since four gait phases were extracted from the reference data, one state was associated with each of these phases using a Q-state left–right model (Q = 4) [see Fig. 5(b)]. Hence, the state S1 was paired to the gait phase delimited by the FS and FF events; further pairings were S2 : FF–HO; S3 : HO–TO; and S4 : TO–FS of the next stride. The emissions from each state were feature vectors that included, at any sampling time, the measured angular velocity and the angular acceleration, computed by first-order finitedifference approximation; the statistical properties of emissions were modeled using a bivariate Gaussian mixture of three components for each state. The availability of reference data allowed us to perform HMM supervised training. The HMM parameters were trained using a leave-one-subject-out validation approach: the HMM training was performed using data from all subjects but one, the HMM testing was then applied using data from the remaining subject. This procedure was repeated for all subjects in turn. The performance metrics, see next, were then averaged and presented. As compared with other validation methods, e.g., the popular N fold cross validation, the leave-one-subject-out cross validation allowed to stress the inter-subject generalization capabilities of the HMM-based gait event detector [25]. C. Online Decoding of HMM Hidden States The HMM structure establishes a connection between states of the model and gait phases; gait phase detection is achieved by estimating the most likely sequence of hidden states given an observed sequence of feature vectors, henceforth referred

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Fig. 3. Flowchart that illustrates how treadmill walking data were used to validate the methodology. Treadmill data were split between a training set and a test set, using data from one subject as the test set. A model was then trained after applying the preprocessing steps (feature extraction) and tested using the feature vectors available from the test set. Model performance assessment was based on the availability of reference data from the optoelectronic movement analysis system. The procedure was repeated so as each subject had the chance to become a tester; hence, a number of models equal to the number of subjects were trained.

Fig. 4. Flowchart that illustrates how overground test data were processed. A model was trained using treadmill walking data from all subjects. It was then applied to the overground walking dataset. Temporal gait parameters were evaluated by the HMM-based gait event detector and experimenter annotations were used for performance assessment.

to as the optimal path, using the Viterbi algorithm (maximum a posteriori criterion). The Viterbi algorithm is a dynamic programming technique to find the optimal path by tracing back through an array of back-pointers, starting from the end of the observed sequence of feature vectors. Two main steps are involved in the Viterbi algorithm [29]. First, a forward pass is performed to compute δ(t, i) which is the score of the best path ending in state Si at time t, namely the value of the partial likelihood for each hidden state i (i = 1, . . . , Q), given observed feature vectors up to the time t (t = 1, . . . , T ). A back-pointer ψ(t, i) is computed to indicate the best state predecessor, namely the most probable predecessor of the state Si at time t. Second, a backtracking search on ψ(t, i) starts from the state with the highest score at the final time T to find the optimal path. In spite of the fact

that the Viterbi algorithm is very efficient computationally, its standard implementation is not suitable for online decoding of hidden states, since the backtracking search must start from the end of the observed sequence of feature vectors. Different approaches have been proposed to deal with this problem. A simple windowing approach consists of processing windows containing a finite set of observed feature vectors; before moving the window ahead in time, just the first decoded states are accepted. The delay of the decoding process is dependent on the window length: any attempt to decrease the delay is thus at the expense of the decoding accuracy. Another approach consists of comparing different partial path hypotheses, which are constructed by incorporating new feature vectors in a variable-length window, until the different hypotheses converge to a unique solution [28], [30].

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Fig. 5. (a) Stride-normalized plot of the angular velocity measured from the foot-mounted gyro. (b) HMM is a left–right model with four states, each of one associated with a gait phase (see text).

In the STV algorithm when a feature vector is available at time t, it is entered in a data buffer whose length (BL) is variable and the computation of the best score proceeds as in the standard Viterbi algorithm [29]. It is the backtracking search to mark the difference between the two algorithms. Rather than restricting the search from the state with the highest score at time t as in the standard Viterbi algorithm, all states are considered in turn as the starting point for the backtracking search in the statetime lattice. The local paths for each starting point are then backtracked. Suppose that a fusion point (FP) is reached at the τ th sample of the buffer [an FP is where the local paths from all states at time t converge; see Fig. 6(a)]: the decoded sequence of states from the previous FP up to the current FP is retained as the optimal subpath delivered by the STV algorithm. Then, the feature vectors that lead up to the FP are eliminated from the buffer and the prior probabilities are set to one for the state occupied at the FP and zero elsewhere [see Fig. 6(b)]. This is done, differently to [28], so as to preserve the left–right structure of the model chosen for analyzing gait in this paper. The STV decoder is forced indeed to start from the state at the FP, jumping to the next state allowed by the HMM structure. Otherwise, the chance would exist to resume the path from any state. In [28], the transition probabilities were not allowed to be zero to retain the chance to reach all states from the FP on. Iteratively, the feature vectors at each sampling time are appended to the data buffer, whose BL is due then to increase [see Fig. 6(c)]; when a new FP is found, the buffer content is updated as described previously, in preparation for the next iteration [see Fig. 6(d)]. A maximum BLM AX is specified for bounding the delay of detection [28]: when the data buffer is full, the (suboptimal) path with the highest score is accepted, and the whole procedure starts anew from the last feature vector. The HMM-based gait event detector including the standard Viterbi was implemented in MATLAB using the HMM toolbox [32]. The STV algorithm and the scripts used to train and cross validate the HMM structure were also written in MATLAB.

Fig. 6. State-time lattice of the STV algorithm. The dot size of each lattice point is proportional to the partial likelihood value. (a) Back-tracking search and FP detection; (b) path saving and buffer update, upon FP detection; (c) back-tracking search and FP detection; and (d) path saving and buffer update, upon FP detection.

Finally, the STV algorithm learned using all treadmill data was ported to the ARM-based controller of the sensor unit using a dynamic link library written in ANSI-C, for further testing of the method. D. Performance Assessment The STV algorithm was validated using two performance metrics: 1) the timing error e(i, k) incurred in estimating when the ith gait phase transition took place in the kth gait stride, namely the difference between estimated and reference gait events tSTV (i, k) and tREF (i, k); 2) the latency l(i, k) namely the difference between when tSTV (i, k) was actually delivered by the STV algorithm and tREF (i, k). The two performance metrics were assessed for different values of the maximum data buffer length. Furthermore, the STV algorithm was tested against the standard Viterbi algorithm for any difference in the optimal paths, which was quantified by counting how many times the two methods were in disagreement divided by the observed data sequence length. The Viterbi decoding in this scenario is known to be affected by erroneous events that consist of missed and additionally detected gait strides (deletions and insertions, respectively) [24], [25]. Deletions and insertions were quantified by the number of occurrences of each of them, and then normalized

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watch read-outs and the fractional number of strides counted in each 5-m segment of the walked path. In presenting the data of Table II, cadence and stride time were defined using all four detected gait events as stride markers (previously, only the FS gait event was considered for this purpose). This generalization was helpful to assess the good behavior of the HMM-based method. It is worth noting that during the overground walking trials no insertions were introduced by the HMM-based gait event detector. In Table III, the gait temporal parameters are reported for the two subjects that were involved in both the treadmill and the overground walking trials (the FS was used as the stride marker). The experimental data distributions of the gait temporal parameters estimated in the two walking conditions (treadmill and overground) were tested for normality using normal q − q plots, as shown in Fig. 9. IV. DISCUSSION

Fig. 7. Stride-normalized whisker plots for (a) reference gait events and (b) gait events estimated by the STV algorithm (BL M A X = 100 ms). (c) Stride-normalized plot reporting the median value of the BL, in samples.

to the number of correctly detected gait strides. The timing error statistics were computed after outlying values of estimated gait events had been excluded. III. RESULTS The whisker plots reported in Fig. 7(a) and (b) help showing how the estimated gait events were scattered along the stride-normalized time axis relative to the beginning of each detected stride [0% and 100% were marked by the reference FS in Fig. 7(a) and by the FS estimated by the STV algorithm in Fig. 7(b)]. Fig. 7(c) shows the stride-normalized BL, which indicates how many feature vectors were needed by the STV algorithm, on average, to estimate the gait phase at each point along the gait cycle when BLM AX = ∞. Table I reports the results of the leave-one-subject-out validation study, for different values of BLM AX . The timing error provides an assessment of the accuracy of the HMM-based gait event detector in capturing the reference gait events when the STV algorithm was used for decoding the sequence of hidden states; the latency yields the information needed to grasp the feasibility of an online implementation of the STV algorithm. Finally, the empirical distribution of the values of the latency for the various gait events was investigated from data across subjects and walking speeds [see Fig. 8]. The values of the cadence, stride time, and relative stance estimated for the overground walking trials are reported in Table II, together with the corresponding values estimated during the treadmill walking trials at the walking speeds closest to the freely selected walking speed (4.8 ± 0.5 km/h). The values of the cadence and stride time were also estimated using the stop-

The stride-normalized whisker plots of Fig. 7(a) and (b) indicate the extent to which the HMM-based gait event detector performs in detecting gait events as compared to the reference detector. The two methods performed similarly, although the stride-normalized plot may be somewhat misleading since the FS event is frozen at 0% on the abscissa axis. An interesting point of discussion comes from analyzing the plot of Fig. 7(c): the length of the data buffer used by the STV algorithm is an indicator of how much information was needed before the uncertainty was reduced to a point where a decision could be made. In our left–right model, the transition probabilities from one state to the next were typically low [25]. For example, given a stride lasting about 1 s and a sampling rate of 100 Hz, only four state transitions were expected over the span of about 100 feature vectors. Hence, the HMM training gave rise to transition probability matrices that are almost diagonal. This implies that the model uncertainty was substantial at the time when a gait phase transition actually occurred; in fact, several feature vectors from the new gait phase had to be acquired before the a posteriori probabilities were modified to the extent needed for a reliable FP detection. In Fig. 7(c), three peaks are present. The first two peaks are related to the FS and FF estimation processes, while the third peak merges the HO and TO estimation processes. Remarkably, the path estimated by the STV algorithm was the same as the standard Viterbi algorithm for BLM AX greater than 200 ms (20 feature vectors at 100 Hz), which means that their timing error statistics were identical. The path difference between the STV and the standard Viterbi algorithms was very small when BLM AX was greater than 100 ms, and generally small down to BLM AX = 60 ms. Moreover, the timing errors incurred by the STV algorithm did not significantly depend on BLM AX . This was especially true for the FF, HO, and TO gait events; in particular, the HO gait event was the one whose estimate was affected by the higher variability (about 60 ms), with a late detection of 35 ms, on average; the best case occurred for the TO gait event, where the variability was about 12 ms (early detection of about 8 ms, on average).

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TABLE I PERFORMANCE METRICS OF THE HMM-BASED GAIT EVENT DETECTOR FOR TREADMILL DATA

Fig. 8. Empirical distributions of the latency in determining the gait events FS, FF, HO, and TO. Left column: BL M A X = ∞; right column: BL M A X = 100 ms. The estimated probability, expressed in percent, that the latency in estimating the gait event exceeds 100 ms is reported close to the vertical line. TABLE II STATISTICS OF THE GAIT TEMPORAL PARAMETERS, EXPRESSED AS MEAN VALUE ± SD

TABLE III STATISTICS OF THE GAIT TEMPORAL PARAMETERS FOR SUBJECTS WHO PERFORMED BOTH TREADMILL AND OVERGROUND WALKING TRIALS

The systematic error incurred by the STV algorithm in determining the time instant of foot contact at the beginning of the stance phase corresponded to an early detection going from

about 16 ms (BLM AX = ∞) to 26 ms (BLM AX = 100 ms), with standard deviations of 15 and 69 ms, respectively. In [25], the HMM-based gait event detector in its offline version outperformed a reference threshold-based method, i.e., [18], showing higher generalization capabilities against intra- and intersubject

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Fig. 9. q − q plots of temporal parameters of gait: stride time on the left column and relative stance on the right column. Parameters are estimated during overground and treadmill walking trials performed in almost identical conditions of speed/cadence (Subject #2, 110 bpm). (a) Quantiles of the overground data are represented compared with quantiles of the treadmill walking data. (b) Experimental quantiles against the theoretical quantiles from a normal distribution.

variability. Results in this paper show that the STV performs similarly to the standard Viterbi: since the procedures of algorithmic validation in this paper are the same used in [25], where the HMM-based method was shown to outperform the reference threshold-based method described in [18], we conclude that the STV as well would perform better than this reference threshold-based method, although we have not implemented it in this paper. A comparison of the HMM-based method for gait event detection with other ML methods is beyond the scope of this paper; it should also be observed that the ML methods that are already available in the literature are based on sensor configurations different from ours, e.g., [16], [17]. It comes as no surprise that the latency did depend on BLM AX , as shown in Table I. Higher latencies affected the determination of FS, HO, and TO gait events, which was also confirmed by looking at Fig. 7(c). In particular, the uncertainty affecting the detection of the HO gait event was reflected in both the high variability of gyro signals observed in Fig. 5(b), and in the difficulties encountered by the same reference method [see Fig. 7(a)]. Interestingly, the empirical distributions of Fig. 8 tended to be less skewed when BLM AX = 100 ms, as compared with the case when the BL constraint was inactive. Moreover, the probability that the latency values were less than 100 ms increased with lower values of BLM AX . This probability was

about 0.75 for the HO event and 1 for the remaining gait events, in a situation where the penalty in terms of detection accuracy was minimal as compared with BLM AX = ∞. To put the matter in another perspective, a latency in determining the HO event of about 100 ms was suggested in [33] as acceptable in prostheses that attempt to provide foot drop correction via FES. This is not to say that the proposed method can be used for drop foot stimulators as it is: different patterns of angular velocity are expected in pathologic gait compared with the patterns analyzed in this paper; hence statistical models adapted to pathologic gait are likely to be developed [34]. Moreover, it is reasonable to assume that the STV algorithm performance may be improved, namely with smaller latency, when more complex sensor configurations, feature vectors, and emission models are considered in the HMM development. These issues are the focus of our current research. The behavior of the HMM-based gait event detector was also tested in overground walking conditions. It is still debated whether the limb kinematics is modified, and to which extent, in overground walking compared to treadmill walking. However, we were not able to generate the reference overground walking data needed for training and validating the HMM-based gait event detector and our aim was simply to check any change in the way the proposed method worked, e.g., whether the

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experimental distribution of temporal parameters of gait (stride time and relative stance) changed and to which extent. As shown in Tables II and III, the statistics of stride time and relative stance did not differ much in both walking conditions, the walking speed being almost the same. Moreover, the estimated parameters turned out to be marginally normally distributed, and the q − q plots of Fig. 9 did not highlight any difference between their experimental distributions in both walking conditions. V. CONCLUSION The development of a HMM-based method for online detection of gait events and phases has been described. The method revolves around a STV algorithm for online decoding of the sequence of hidden states using a uniaxial gyro that measured the foot instep angular velocity in the sagittal plane. The HMM was trained with treadmill walking data and validated using the leave-one-subject-out validation method to stress its generalization capabilities across different users. The HMM-based gait event detector was also shown accurate and fast during overground walking trials. The STV decoder was ported to the ARM-based controller of the sensor unit, and a smartphone running an Android OS was used for data collection and visualization. The online version of the HMM gait event detector performed similarly to the offline version, in terms of estimation accuracy. The latencies introduced by the online implementation were small and are deemed acceptable, especially in the perspective of developing an on-foot IMU-based PNS for telehealth applications. REFERENCES [1] G. F. Welch and E. Foxlin, “Motion tracking: No silver bullet, but a respectable arsenal,” IEEE Comput. Graph. Appl., vol. 22, no. 6, pp. 24–38, Nov./Dec. 2002. [2] N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sens. J., vol. 1, no. 4, pp. 332–339, Dec. 2001. [3] R. Zhu and Z. Zhou, “A real-time articulated human motion tracking using tri-axis inertial/magnetic sensors package,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 12, no. 2, pp. 295–302, Jun. 2004. [4] S. J. M. Bamberg, A. Y. Benbasat, D. M. Scarborough, D. E. Krebs, and J. A. Paradiso, “Gait analysis using a shoe-integrated wireless sensor system,” IEEE Trans. Inf. Technol. Biomed., vol. 12, no. 4, pp. 413–423, Jul. 2008. [5] D. N. Karantonis, M. R. Narayanan, M. Mathie, N. H. Lovell, and B. G. Celler, “Implementation of a real-time human movement classifier using a triaxial accelerometer for ambulatory monitoring,” IEEE Trans. Inf. Technol. Biomed., vol. 10, no. 1, pp. 156–167, Jan. 2006. [6] S. J. Preece, J. Y. Goulermas, L. P. J. Kenney, and D. Howard, “A comparison of feature extraction methods for the classification of dynamic activities from accelerometer data,” IEEE Trans. Biomed. Eng., vol. 56, no. 3, pp. 871–879, Mar. 2009. [7] A. Salarian, H. Russmann, F. J. G. 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 Trans. Biomed. Eng., vol. 51, no. 8, pp. 1434–1443, Aug. 2004. [8] S. Patel, K. Lorincz, R. Hughes, N. Huggins, J. Growdon, D. Standaert, M. Akay, J. Dy, M. Welsh, and P. Bonato, “Monitoring motion fluctuations in patients with Parkinson’s disease using wearable sensors,” IEEE Trans. Inf. Technol. Biomed., vol. 13, no. 6, pp. 864–873, Nov. 2009. [9] E. Foxlin, “Pedestrian tracking with shoe-mounted inertial sensors,” IEEE Comput. Graph. Appl., vol. 25, no. 6, pp. 38–46, Nov./Dec. 2005. [10] X. Yun and E. R. Bachmann, “Design, implementation, and experimental results of a quaternion-based Kalman filter for human body motion tracking,” IEEE Trans. Robot., vol. 22, no. 6, pp. 1216–1227, Dec. 2006. [11] H. P. von Schroeder, R. D. Coutts, P. D. Lyden, E. Billings, Jr., and V. L. Nickel, “Gait parameters following stroke : A practical assessment,” J. Rehabil. Res. Dev., vol. 32, no. 1, pp. 25–31, 1995.

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