Unsupervised nonparametric method for gait ... - Semantic Scholar

Applied Soft Computing 14 (2014) 72–80

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

Unsupervised nonparametric method for gait analysis using a waist-worn inertial sensor Mitchell Yuwono a,∗ , Steven W. Su a , Ying Guo b , Bruce D. Moulton a , Hung T. Nguyen a a b

Faculty of Engineering and Information Technology, University of Technology, Sydney, 15 Broadway, Ultimo 2007, NSW, Australia CSIRO ICT Centre, Marsfield, NSW 2122, Australia

a r t i c l e

i n f o

Article history: Received 31 March 2013 Received in revised form 22 July 2013 Accepted 22 July 2013 Available online 5 September 2013 Keywords: Wearable sensors Activity of daily living (ADL) technologies Gait analysis Heel-strike segmentation Hidden Markov Model Feature extraction Discrete wavelet transforms Principal component analysis Unsupervised learning Data clustering Bayesian methods

a b s t r a c t This paper describes a nonparametric approach for analyzing gait and identifying bilateral heel-strike events in data from an inertial measurement unit worn on the waist. The approach automatically adapts to variations in gait of the subjects by including a classifier that continuously evolves as it “learns” aspects of each individual’s gait profile. The novel data-driven approach is shown to be capable of adapting to different gait profiles without any need for supervision. The approach has several stages. First, cadence episode is detected using Hidden Markov Model. Second, discrete wavelet transforms are applied to extract peak features from accelerometers and gyroscopes. Third, the feature dimensionality is reduced using principal component analysis. Fourth, Rapid Centroid Estimation (RCE) is used to cluster the peaks into 3 classes: (a) left heel-strike, (b) right heel-strike, and (c) artifacts that belongs to neither (a) nor (b). Finally, a Bayes filter is used, which takes into account prior detections, model predictions, and step timings at time segments of interest. Experimental results involving 15 participants suggest that the system is capable of detecting bilateral heel-strikes with greater than 97% accuracy. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Gait analysis is beneficial for assessing treatment effectiveness, quality of mobility and general health [1,2]. Information about gait parameters can provide important diagnostic information relevant to balance, functional ability and risk of falls [1]. The current methods for assessing gait parameters are mostly laboratory-based. They are expensive and not practical for application in daily life [3]. Force platforms, as the gold standard, can be used to precisely record the ground reaction forces exerted by the feet during the gait cycle [4]. Other popular methods use lowerlimb sensors [5], pressure insoles [6], or stereo-photogrammetric cameras [7]. An Inertial Measurement Unit (IMU) consists of accelerometers and gyroscopes to provide measurements of velocity, orientation and accelerations. IMUs are relatively low-cost devices, and can be used to generate data from which gait parameters can be extracted [1,3,8,2,9]. For example, waist-worn triaxial accelerometers were

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (M. Yuwono). 1568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2013.07.027

used by Moe-Nilssen and Tura to estimate gait regularity using an autocorrelation function (ACF) of the mediolateral (ML) and anteroposterior (AP) accelerations [1,3]. Similarly, Bugane´ extracted gait parameters by identifying heel-strike (HS) and toe-off (TO) events by performing peak detection and thresholding of AP and ML accelerations [8]. In addition, Köse used stationary wavelet transform and peak thresholding for detecting HS & TO events from data generated by waist-worn triaxial accelerometers attached to the right side of the ML axis [2]. The above methods tend to perform poorly in real-world situations where the data is noisy, where gait patterns vary in real-time, and where there is a degree of drift in the placement of the sen´ method, for example, requires the subject to stand sors. Bugane’s still for a few seconds before starting and after stopping in order to ensure adequate “initialization” [8]. Köse’s HS detection method uses a stationary wavelet transform with fixed thresholds that are finely tuned for each level of decomposition [2]. One of the limitations of the above methods is that artifacts that happen to have similar time-frequencies to those of gait events can be misclassified. Another limitation is that the methods are typically unable to detect lower magnitude HS and TO signals. A recent paper by Aung [9] proposed a method for extracting unilateral gait events using accelerometric features. The

M. Yuwono et al. / Applied Soft Computing 14 (2014) 72–80

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Fig. 1. Algorithm flow diagram.

generalization approach used continuous wavelet transform, manifold embedding, and Bayesian inference. In contrast to [9], our approach seeks personalization rather than generalization. In addition, we also consider the contributions of gyroscopic sensors, movement artifacts, and variations in gait. We summarize the main contributions of this paper to three main points as follows: 1 A non-parametric approach for analyzing gait and identifying bilateral heel-strike events in data from an inertial measurement unit worn on the waist based on unsupervised learning approach is proposed. This proposed approach allows the device to evolve to be subject-specific as it learns the gait pattern of the wearer. To our understanding, this novel approach has not yet been proposed in the literatures. 2 An effective feature extraction and high precision detection method based on the Markovian characteristics of the gait cycle have been designed. The proposed method exploits the features that best characterize bilateral HS events in both the accelerometric and gyroscopic signals. 3 A comparative study is done using various features. Based on this study we see that the gyroscopic features are important measures for characterizing bilateral HS. The project was conducted in compliance with the Helsinki Declaration, and in accordance with the University of Technology Sydney (UTS) research guidelines and clearance granted by the UTS Human Research Ethics Committee. A long-term goal of the research is to develop improved gait-cycle-analysis techniques for our ambulatory monitoring systems [10–12]. This current paper reports our attempt in designing a minimally obtrusive gait analysis system using an inertial measurement unit (IMU). This paper is organized as follows. Section 2 explains the proposed method. Section 3 presents the experimental settings, results and analysis. Section 4 concludes and suggests directions for future research. 2. Method This paper describes a new nonparametric adaptive method for the identification of bilateral HS events based on data clustering, discrete wavelet transform (DWT), principal component analysis (PCA), and Bayesian filtering. A flow diagram of the approach is presented in Fig. 1. The HS classifier continuously evolves as it learns each wearer’s gait profile. We use DWT to extract the peak features, and PCA for dimensionality reduction. The HS features are clustered into 3 classes (left HS (LHS), right HS (RHS), and artifacts) using a Rapid Centroid Estimation (RCE) algorithm which we have described and benchmark tested in a previous article [13]. Bayes filtering is used for recovering missing detections and

correcting out-of-phase detections. The identification of both LHS and RHS allows the identification of stride-related and bilateral TO events, which are used to estimate gait phase. Experimental results from 15 participants shows accurate identification of LHS and RHS. In addition, it is found that gyroscopic information is more valuable than accelerometric information for HS identification. For this study, we used a Shimmer Wireless Microelectromechanical systems (MEMS) kinematic sensor module with a 9DoF Kinematic daughterboard. The Shimmer base package contains an MSP430 16-bit microcontroller operating at 8 MHz clock, a Freescale MMA7361 tri-axial accelerometer, and a TI CC2420 Roving Networks RN-42 Class 2 Bluetooth module. A daughterboard provides a Honeywell HMC5843 magnetometer and an InvenSense500 gyroscope [14]. For this study we used the gyroscope, but not the magnetometer. The sensor is attached to a belt and positioned on the right side of the ML axis in a position that is similar to the position used by Köse [2]. The device is aligned such that the positive x axis points downwards towards the gravity vector, positive y axis points forward towards AP vector, and positive z axis points sideways towards ML vector. The IMU is sampled at 51.2 Hz. We have developed an Android application to interface with the Shimmer sensor. The application utilizes the Shimmer Instrument Driver [15] under Android 4.0.4 [16]. Prototyping is done using Matlab. 2.1. Cadence and stride-rate estimation using Hidden Markov Model (HMM) Cadence and stride-rate can be estimated by calculating the ACF of aAP and aML signals [1]. Our method first attempts to extract these parameters from the fundamental frequencies f0 of a fast Fourier transform (FFT) of the aV , aAP and aML signals at each specified time segment t. Cadence frequencies typically range from 0.6 to 2.5 steps per seconds (i.e. 36–150 steps per minute) [17]. Moving average filters are applied to the raw signals to reject local sampling noises. Fundamental frequencies f0 V , f0 AP and f0 ML are found from the peak values of the resulting power spectra of each signal at the specified time segment P(f, t), P(f, t) = |FFT (x(t))|,

(1)

f0 (t) = arg maxP(f, t),

(2)

f

where x(t) represents a signal at a time segment of interest. f0 V and f0 AP time-frequency continuity represent cadence, while f0 ML time-frequency continuity represents stride-rate [1,17]. An “episode” of cadence is characterized by the condition |f0 V − f0 AP | ≈ 0 and consistency of f0 AP /f0 ML . Hidden Markov Model (HMM) is a statistical model in which the system being modeled is assumed to be a Markov process with

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Fig. 2. HMM cadence detector design.

unknown parameters. A Markov process is a mathematical model for the random evolution of a memoryless system. That is, the likelihood of a given future state at any given moment depends only on its present state and not on any past states. HMM is especially useful for modeling systems that exhibits Markovian process such as described in [18]. The proposed method uses HMM to model the characteristics of a continuous human gait based on the time-frequency continuity of waist-worn accelerometer signals. Fig. 2 shows the HMM design used in this proposed

application. Two hidden units and one mixture is used for the HMM parameters. The training process is performed using the recursive Baum–Welch algorithm, as described in [19,18]. The training data is accumulated from 30 s gait segments from all subjects. A cadence detection episode using signals from subject 8 is presented in Fig. 3. The raw accelerometric signals in Fig. 3 shows that a continuous gait episode is initiated at t = 110 s and finished at t = 620 s. The dominant frequency plot in Fig. 3 shows the consistency of f0 AP /f0 ML and |f0 V − f0 AP | ≈ 0 during gait. Fig. 3 shows the HMM output. Fig. 3 shows that a continuous gait is detected when the log-likelihood ≥0. 2.2. HS feature extraction DWT provides information on frequency localizations at specific instants in a signal. A large value at a given time-frequency localization indicates high similarity between the mother wavelet and the signal itself at that specified instant. Given that this is the case, DWT is useful for extracting instantaneous pattern and frequency changes such as those that occur at HS and TO events [4].

Fig. 3. A cadence detection episode using signals from subject 8.


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Fig. 4. The LHS and RHS pattern of subject 7 averaged over 273 RHS and 276 LHS events.

HS events produce signals that are morphologically similar to the Debauchies 4-tap wavelet (db4). This can be seen by observing the peaks and valleys in the sensory signals around HS events. HS frequencies are localized at around 6–8 Hz. For fs = 51.2 Hz, DWT at the 2nd level of decomposition effectively focuses on frequency localization around 6.4–12.8 Hz. Hence we use 2nd level DWT for detecting HS events. The wavelet features that we use are: the 2nd level detail coefficients (d2) of aAP , aML , aV , sagittal angular velocity ωS , and transverse angular velocity ωT , and the 2nd level approximation coefficients (a2) of coronal angular velocity ωC . Each coefficient has a dimensionality of 11; the total dimensionality is 66. Examples of typical raw signals for one subject’s LHS and RHS patterns together with the corresponding wavelet features are presented in Fig. 4. We sought to increase classification performance and decrease the computational complexity of the clustering process by applying principal component analysis (PCA) transformations on the wavelet features to reduce dimensionality. The reduced-dimensionality features, up to the 6th principal component, are shown in Fig. 5. Looking at the degree of cluster separation, it appears that the first six principal components are sufficiently separable to be used as features for the classifier. 2.3. Gait event clustering and identification Identification of gait phase requires the identification of HS and TO events. General templates for HS signals are described in prior works [2,8]. However, the HS patterns of individuals change over

time, and are also affected by clothes, footwear, walking surface, cadence, and emotional condition [20]. Thus to implement a system that is adaptable to changes in HS patterns, we developed a datadriven approach that makes use of data clustering. 2.3.1. Gait event clustering Recent studies in University of Technology Sydney (UTS) have demonstrated the potential of particle swarm algorithms for solving pattern recognition and signal modeling problems in biomedical signal processing including power wheelchair control [21], hypoglycemia detection [22–24], fall detection [10], gait analysis [17], and feature extraction from Hartman–Shack images [25,26]. One of the major researches includes a recently proposed lightweight clustering algorithm inspired by swarm-intelligence that we term RCE [13]. The RCE algorithm has previously been applied to benchmark datasets from UC Irvine machine learning repository [13], spectrogram data of cadence episodes [17], and Hartman–Shack images [26]. Interested readers are encouraged to refer to [13] for technical details regarding RCE. Feature distributions visualized using the first and second principal components for accelerometric and gyroscopic features are shown in Fig. 6a and b respectively. The accelerometric and gyroscopic feature distributions are shown individually. The LHS and RHS principal components look Gaussian in both distributions. However, compared to the distribution of accelerometric features, the distribution of gyroscopic features appears to show more-distinct intra-cluster and extra-cluster correlations.

Fig. 5. Subject 7’s RHS and LHS PCA features up to the 6th principal components.

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Fig. 6. Principal components distribution for subject 7, clustered using RCE+. It can be seen that, compared to the distribution of accelerometric features (a), the distribution of gyroscopic features (b) appears to show more-distinct cluster correlations.

2.3.2. Correcting HS detection using Bayesian filtering Sequential Bayesian filtering can be useful for analyzing Markovian processes by way of recursive predictions and state observations [27]. Recurring HS events can be modeled as a simple three-state Markov process, as shown in Fig. 7. For our purposes here, states Q = { q1 , q2 , q3 } correspond to: q1 = LHS; q2 = RHS; and q3 = Idle. A transition matrix M that corresponds to our proposed Markov model for recurring HS events can be defined as:

q1 M = q2 q3

q1 q2 ⎛ ⎜⎜⎜ 0 0.9 ⎜⎜⎜ 0 ⎜⎜ 0.9 ⎝ 0.333 0.333

q3 ⎞ 0.1 ⎟⎟⎟ ⎟ 0.1 ⎟⎟⎟⎟. 0.333 ⎠

The probability of state observation Z given the estimated state q can be defined as:

z1 p(Z|Q)= z2 z3

q2 q3 q1 ⎞ ⎛ ⎜⎜⎜ 0.8 0.2 0.0 ⎟⎟⎟ ⎟ ⎜⎜⎜ ⎜⎜ 0.2 0.8 0.0 ⎟⎟⎟⎟. ⎝ 0.45 0.45 0.1 ⎠

(4)

The belief p( Q ) is updated at tk interval using recursive Bayesian update as shown in Eq. (5). k

(3)

In the case of HS estimation, a state change occurs at a transition time t. tk is the time taken at the kth step (tstepk ), which fluctuates depending on the changes in user’s cadence. tstepk = 1/f0 is calculated using the method described in Section 2.1. The observations Z = { z 1 , z 2 , z 3 } are the states observed by the HS detector which correspond to: z 1 = LHS; z 2 = RHS; and z 3 = no detection. As a starting point, we assume that the HS detector has an 80% probability of giving state detections that agree with the Markov state estimate (e.g. p( z 1 | q1 ) = p( z 2 | q2 ) = 0.8) and a 20% probability of mis-detecting a contralateral HS (e.g. p( z 2 | q1 ) = p( z 1 | q2 ) = 0.2). When there is no detection ( z 3 ), we assume that the observation corresponds to 45% probability of an undetected HS (e.g. p( z 3 | q1 ) = p( z 3 | q2 ) = 0.45), and 10% probability of an idle condition (e.g. p( z 3 | q3 ) = 0.1). We assume p( z 3 | q3 ) = 0.1 because the state would probably not change much due to the fact that t = tstep is indefinite when a person is not walking.

p(Q (0) , . . ., Q (k) , Z (0) , . . ., Z (k) ) = p(Q (0) )

p(Z (i) |Q (i) )p(Q (i) |Z (i−1) ).

i=1

(5)

The Bayes filter is used to recover missing detections and remove detections that are out of phase. Detections that are out of phase often occur due to noises from unrelated movement artifacts. An example is given in Fig. 8. 2.3.3. Gait phase and stride profile identification Once LHS and RHS are properly identified, LTO and RTO events can be recognized by simply getting the subsequent aAP peak after the occurrence of a contralateral HS event (e.g. a RHS followed by a LTO; or a LHS followed by a RTO). A particular TO detection result is shown in Fig. 9a. The corresponding gait phase identification is shown in Fig. 9b. The stride profile is arrived at by calculating the average and standard deviation of the stride signals based on the gait phase of each limb. 3. Experimental results and discussion

Fig. 7. Recurring HS described as a Markov process.

The data was collected from 15 healthy subjects (9 male, 6 female) aged from 22 to 67 years old. A Shimmer 9DoF IMU was attached to each subject’s waist at the right side of the ML axis. Each subject was asked to walk for five minutes at a personally selected pace. The number of steps was counted. The experimental data collection was done in a public area at the University of Technology Sydney (UTS) known as the Atrium. The Atrium is a square with sides of approximately 20 m. Each subject walked in a circuit along the sides of the Atrium.


Fig. 8. The recovery of a previously “missing” HS using a Bayes filter. The corresponding aAP signal is depicted. × denotes HS detections without a Bayes filter; detections with a Bayes filter.

The HS and stride profiles of each subject are presented in Table 1. It can be observed from both tables that both HS and stride signals constitute a consistent general pattern over all subjects. However, when considering the signal details and artifacts, each subject’s signal pattern is unique with respect to each other. The temporal gait parameters, including cadence and step symmetry, are calculated from the identified stride profile (Section 2.3.3) using Moe-Nilssen’s method [1]. Accuracy is calculated by dividing the number of HS positive detections by the total number of steps counted during the experiment. The HS profile for each subject is obtained by averaging the correct detections. The general HS profile for all subjects is obtained by averaging the HS data of all of the subjects. Table 2 shows the results relating to HS detection. The resulting LHS and RHS detection accuracies of using only accelerometric features were 76.8% ± 14.9% and 86.3% ± 15.0% respectively. Detection accuracies using accelerometric features

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denotes HS

had the lowest means and largest standard deviations. For example, subject 6 detection accuracy only reached up to 40.3% and 38.8%. Another observed case was unbalanced accuracies presented in a number of subjects, where the RHS detector achieved greater accuracy than the LHS detector. A severe example can be observed in subject 3 where the LHS accuracy reached only 50.8% compared to 84.5% on the RHS. This phenomenon was mainly due to the unbalanced installation of the sensor – on the right side of the waist – which amplified signals on the right limb and attenuated the left. Higher accuracies (86.1% ± 9.9% and 93.4% ± 2.4%) were achieved using the gyroscopic features. Gyroscopic features seemed to improve the detection stability of the acceleration features. On subject 6, for example, LHS and RHS detection accuracies increased from 40.3% and 38.8% to 64.6% and 87.6%, respectively. When both accelerometric and gyroscopic features

Fig. 9. TO, gait phase, and stride profile identification.

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Table 1 Subject-specific profiles.

were used, the LHS accuracy level increased up to 88.4%. However, adding accelerometric features to the feature vector appeared to have minimal effect to the overall increase of detection accuracy. Using gyroscopic together with accelerometric information increased the accuracies of LHS to 87.8% ± 8.2% but decreased RHS

to 92.6% ± 4.5%. This experiment showed that gyroscopic features appeared to be sufficient for determining bilateral HS. A major increase in accuracy could be seen when Bayes filter was used together with acceleration and gyroscopic features. Overall, LHS and RHS detection accuracies of 97.5% ± 1.5% and 97.9% ± 1.3%


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Table 2 The performance of the HS detector. No.

Age (gender)

Cadence (steps/min)

1

45 (M)

110.0 ± 11

2

27 (F)

130.9 ± 4

3

34 (M)

141.5 ± 10

4

67 (M)

114.0 ± 13

5

35 (M)

97.6 ± 3

6

36 (M)

108.8 ± 8

7

62 (F)

111.9 ± 7

8

44 (M)

89.4 ± 2

9

24 (F)

101.1 ± 3

10

33 (M)

100.4 ± 2

11

36 (M)

91.8 ± 5

12

44 (M)

105.0 ± 4

13

22 (F)

104.7 ± 4

14

25 (F)

108.7 ± 4

15

23 (F)

114.5 ± 7

Summary

37.13 ± 13.5: M = 41.6 ± 10.6; F = 30.5 ± 15.5

108.55 ± 14

Symmetry, L/R 50.3% 49.8% 50.1% 50.0% 49.9% 49.7% 51.1% 49.2% 50.0% 50.9% 50.2% 51.0% 51.4% 52.4% 49.8% 50.1% 50.0% 48.5% 50.3% 49.9% 50.1% 49.0% 49.3% 49.5% 48.2% 52.1% 49.7% 49.9% 50.0% 50.6%

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

7% 3% 2% 1% 5% 3% 5% 8% 2% 2% 4% 3% 3% 4% 1% 1% 2% 2% 1% 1% 3% 4% 6% 2% 2% 2% 2% 2% 2% 4%

49.96% ± 0.8% 50.17% ± 1.1%

Accuracies using various featuresa , b (a) 72.4%/90.5% (b) 83.5%/93.0% (a) 84.0%/94.5% (b) 83.5%/95.0% (a) 50.8%/84.5% (b) 94.1%/95.2% (a) 85.1%/67.4% (b) 89.7%/92.3% (a) 93.8%/91.7% (b) 95.0%/95.2% (a) 40.3%/38.8% (b) 64.6%/87.6% (a) 81.1%/84.5% (b) 94.5%/93.9% (a) 93.3%/93.9% (b) 95.0%/95.0% (a) 77.7%/95.0% (b) 94.2%/95.2% (a) 82.2%/90.3% (b) 82.2%/91.9% (a) 70.9%/85.5% (b) 82.1%/89.1% (a) 77.0%/94.1% (b) 77.7%/95.2% (a) 75.2%/95.2% (b) 95.0%/94.1% (a) 94.0%/94.5% (b) 95.0%/95.0% (a) 74.6%/93.4% (b) 76.2%/93.4%

(c) 84.2%/92.7% (d) 96.1%/97.4% (c) 84.2%/95.0% (d) 99.2%/99.2% (c) 94.8%/95.2% (d) 97.8%/97.8% (c) 90.3%/79.3% (d) 94.3%/98.0% (c) 95.0%/95.2% (d) 95.1%/98.2% (c) 88.4%/87.6% (d) 97.1%/93.6% (c) 94.5%/94.6% (d) 98.0%/98.2% (c) 95.0%/95.0% (d) 98.6%/98.6% (c) 94.2%/95.2% (d) 98.7%/97.1% (c) 82.2%/89.5% (d) 98.3%/98.5% (c) 81.0%/89.1% (d) 96.4%/98.1% (c) 77.7%/95.2% (d) 95.2%/98.9% (c) 95.2%/95.2% (d) 98.7%/98.7% (c) 95.0%/95.2% (d) 98.7%/98.7% (c) 75.5%/94.1% (d) 98.5%/98.3%

(a) 76.8% ± 14.9%/86.3% ± 15.0% (b) 86.1% ± 9.9%/93.4% ± 2.4%

(c) 87.8% ± 8.2%/92.6% ± 4.5% (d) 97.5% ± 1.5%/97.9% ± 1.3%

a Feature: (a) aV , aAP , and aML features; (b) ωT , ωC , and ωS features; (c) both (a) and (b) features; (d) both (a) and (b) features + Bayes filter. PCA reduces dimensions of features (a)–(d) to 6 principal components. b Shaded cells indicates best classifier performance.

were observed. The Bayes filter exploits the Markovian characteristics of the human gait: the causal recursivity of consecutive contra-lateral HS events. For example, a positive LHS detection would most likely follow a positive RHS detection or vice versa given that the user is still walking. This benefit was apparent in all subjects, including in subject 6 where the data were noisy.

4. Conclusions and future directions The ability to accurately identify heel-strike (HS) events is usually of critical importance when analyzing human gait. This study shows that when using a waist-worn Inertial Measurement Unit (IMU) on the mediolateral (ML) axis, HS events can be identified with greater than 97% accuracy. The HS detection algorithm makes use of Hidden Markov Model (HMM) for cadence estimation, discrete wavelet transform (DWT) for feature extraction, principal component analysis (PCA) for feature reduction, Rapid Centroid Estimation (RCE) for unsupervised data segmentation, and a Bayes filter for phase corrections and detection recoveries. It is found that gyroscopic information is more useful than accelerometric information for accurately identifying bilateral HS events, and that using both together further improves accuracy. It is also found that using a Bayes filter provides additional accuracy. The current method is limited to measuring the temporal gait parameters. In order to continually improve this method, further works are required. In the near future, methods for extracting spatial gait parameters using IMU are to be studied. Furthermore, an experiment involving greater number of participants is required. Finally, a comparative study using precision sensors such as camera, force plates, or pressure insoles is also needed.

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