This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
1
A Novel Approach for Toe Off Estimation during Locomotion and Transitions on Ramps and Level Ground Deepak Joshi, Bryson H. Nakamura, and Michael E. Hahn* Abstract— Identification of the toe off event is critical in many gait applications. Accelerometer threshold based algorithms lack adaptability and have not been tested for transitions between locomotion states. We describe a new approach for toe off identification using one accelerometer in over ground and ramp walking, including transitions. The method uses invariant foot acceleration features in the segment of gait where toe off is probable. Wavelet analysis of foot acceleration is used to derive a unique feature in a particular frequency band, yielding estimated toe off occurrence. We tested the new method for five conditions: over ground walking (W), ramp ascending (RA), ramp descending (RD); transitions between states (W-RA, WRD). Mean absolute estimation error was 17.4 ± 12.5, 13.8 ± 8.5 and 22.0 ± 16.4 ms for steady states W, RA and RD, 20.1 ± 15.5 and 17.1 ± 13.7 ms for transitions W-RA and W-RD, respectively. Algorithm performance was equivalent across all pairs of transition and locomotion state except between RA and RD (p = 0.03), demonstrating adaptability. The db1 wavelet outperformed db2 across states and transitions (p < 0.01). The presented algorithm is a simple, robust approach for toe off detection. Index Terms— Toe off, ramp, over ground, wavelet decomposition, foot acceleration
I. INTRODUCTION Identification of gait events (i.e. initial contact (IC) and toe off (TO)) is integral to calculation of spatialtemporal gait parameters used to analyze normal and pathological gait [1-5]. Toe off is the primary event which marks the transition between stance and swing Manuscript received August 12, 2014, revised October 16, 2014. This work was supported by the Department of Defense under Grant W81XWH-09-2-0144. D. Joshi, B. H. Nakamura, and M. E. Hahn* are with the Human Physiology Department, University of Oregon, Eugene, OR 97403 USA (e-mail: [email protected], [email protected], [email protected]; phone: 541-346-3554; fax: 541-346-2841). Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to [email protected].
phase. For comparison between various gait cycles phase wise normalization is needed, which requires toe off estimation. Ground reaction force (GRF) data [6] and kinematic data using motion capture have been the popular choices for detection of IC and TO during over ground [7] and treadmill gait [8]. Such measurements are expensive, have limited capture volume, and require specific expertise. Further, they are restricted to laboratory settings. There are numerous applications like functional electrical stimulation (FES) and monitoring of activity of daily living (ADL) where ambulatory monitoring systems are required. The restrictions of GRF and kinematic data using motion capture in ambulatory monitoring led us to search for an alternate method of toe off detection. Inertial sensors have been used with some success towards producing a robust gait event detection approach. Many algorithms have been published for accurate identification of toe off in normal gait [5, 914]; specifically over ground walking [7, 15] over ground running [16, 17], treadmill walking [18] and treadmill running [19]. These algorithms are based on basic thresholds of the source signal, leading to multiple thresholds, peak detection, acceleration, deceleration, and hence are sensitive to walking speed. However a recently published technique which accounts for speed has produced improved accuracy [2]. With recent advancements in computational methodology, fuzzy logic [20], multi-objective optimization techniques using genetic algorithms [21], cross correlation [22] and machine learning [23] have also been explored. Compared to studies of over ground and treadmill walking and running, there is relatively little reported about toe off detection in ramp locomotion [24, 25]. Furthermore, no method has been reported for detection of toe off during the transition from over ground to ramp locomotion. As toe off marks the transition from stance to swing phase, we can expect a discontinuity at this transition in
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
2
the vertical component of acceleration which should be easily detected by wavelet decomposition. We explored the orthogonality of acceleration data to derive features for toe off detection. In this paper, we propose a method that uses invariant signal features from foot acceleration to focus on the particular segment of a gait cycle where toe off is likely to occur. We then perform wavelet analysis of foot within this data segment to determine a unique feature in a particular frequency band, yielding an estimate of toe off occurrence. We assessed estimation accuracy for over ground and ramp surface locomotion. We further assessed the adaptability of the detection algorithm for the gait cycle corresponding to transition from over ground to ramp locomotion.
(Noraxon, Scottsdale, AZ) placed slightly medial to the collection site, to the portable data collection unit. Footswitch and accelerometer data were sampled at a frequency of 1500 Hz from the data collection unit.
(a)
(b)
(c)
(d)
II. METHODS A. Instrumentation and Data Collection This study was approved by the university’s Institutional Review Board. All subjects provided written informed consent prior to involvement in the study. Data were collected from six subjects (5 male and 1 female; 25.7 ± 5.0 years, 173.0 ± 10.5 cm, 73.6 ± 12.2 kg) while walking over ground (W), ascending ramp (RA), descending ramp (RD) and the transition between locomotion states (W-RA and W-RD). The ramp was measured as 24 feet long with inclination of 5 degrees. Foot switches were placed below the foot to provide a repeatable reference of toe off (Figure 1(a)) as the experiments were conducted in the field, outside of the laboratory setting. A tri-axial accelerometer (5.7grams, ±6g output range, ±0.67 V/g sensitivity, 5Hz – 1.8kHz bandwidth) was placed on the dorsum of the foot as shown in the figure 1(c). With respect to a global coordinate reference of anterior-posterior (X) and vertical direction (Z), placement of the accelerometer on the foot led to primary measurement directions as Ax and Az (Figure 1(d)), with Ay representing the mediallateral direction, orthogonal to Ax and Az. As noted in Figure 1(d), Az and Ax were not purely aligned with the global vertical and Z, being dependent upon the orientation of the dorsum of the foot. The transitions W-RA and W-RD were defined as the gait cycle when two heel strikes for over ground and ramp occurred consecutively (see Figure 1(b). Data were wirelessly transmitted, using local transmitters
Fig 1. Sensor placement and data collection overview: a) Foot switch placement b) Locomotion mode and the transition cycle c) Accelerometer placement d) Global coordinate reference and local acceleration components; Az and Ax are measured acceleration with respect to shown global anterior posterior (AP) and vertical direction. Ay (not shown) is orthogonal to Ax and Az. Arrow shows positive direction with respect to local coordinate system and g is the acceleration due to gravity.
Subjects practiced on the pathway before data were collected to ensure that they were able to consistently walk at a self-selected speed while making the transitions between locomotion modes. Data were then collected while each subject performed three trials walking from over ground to each ramp surface. B. Data Processing Foot movement during walking is generally in a low frequency range. To reduce data redundancy, we downsampled the original data by a factor of 5, resulting in an effective sampling frequency of 300Hz. The data were further filtered with a low pass second order Butterworth filter with 10Hz cut off frequency. This cutoff frequency, compared to other options like 20 and 40 Hz, avoided the local minima and maxima in the acceleration data while maintaining meaningful information of source signal to develop the algorithm. To remove the gravity component, the residual acceleration value in all directions during a period of quiet stance, was removed from the filtered data.
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
3
C. Data Segment Identification For a complete trial, the gait cycles were extracted using foot switch data. The gait cycles were labelled as W, RA, RD, W-RA and W-RD based on event markers placed in the data set. For every gait cycle the true toe off event was marked using the foot switch data. From repeated observations, the toe off event was found to be always between two distinct points of the Ax acceleration data, across the locomotion (W, RA and RD) and the transition (W-RA and W-RD) states, shown as A and point B in Figure 2. 5 4 3
2
volt
1 0
-1 -2
Fig. 2. The Ax and Ay with foot switch data during ramp walking (ascending, RA). Three separate cycles are shown from one example subject; representing those with minimum, maximum and median stride duration. The Y-axis unit for acceleration and foot switch are ±g and Volt, respectively and are shown with respect to timenormalized gait cycle. The marker C corresponds to the region of Toe-off for all the three stride cycles showing that it lies between point A and B exclusively. A similar pattern was observed in W, RD, W-RA and W-RD (data not shown). Note: Acceleration in Ay direction is shown with an offset of +2g for visualization purposes.
Point A and B were identified utilizing mutual information in the Ax and Ay acceleration data. Specifically, point M is the maximum Ay acceleration peak in a gait cycle, and is the closest unique point in proximity to point A, which is the peak Ax acceleration. Further, point C is the maximum negative Ax peak prior to point A. We segmented Az acceleration of a gait cycle between point A and point B to locally search for the toe off. The algorithm for determining the segment between point A and B for Az acceleration (as just described), is presented as a flowchart in Figure 3.
Fig. 3. A flowchart to illustrate the complete algorithm. The acceleration in each direction is calibrated by removing the residual gravity component during a static standing position. Signals are filtered at 10 Hz (low pass, 2nd order Butterworth) before applying this algorithm.
feature towards toe off detection at the decomposed level. Increasing the decomposition level decreases the time resolution; however it increases the frequency resolution. In this particular case, as we need to estimate toe off as accurately as possible in time, we limited the decomposition level. We utilized low vanishing moment family members, db1 and db2 of Daubechies wavelet family, as the accelerometer data may be visualized as having limited oscillatory behavior (Figure 4). Over repeated observations, we could consistently estimate the toe off corresponding to minimum approximation coefficient at decomposition level 2, which corresponds to frequency band of 0 - 2.5 Hz (Figure 4). E. Estimation Error Estimation error was first defined as the time difference between the toe off detection by foot switch and toe off detection by the proposed algorithm. We took the absolute value of this error value and averaged across the subjects to report mean absolute estimation error. Note: As the effective sampling frequency was 300 Hz, the error of a single sample of time corresponds to 3.3 ms.
D. Wavelet Decomposition The segmental Az acceleration was decomposed using Daubechies wavelet family. We sought an invariant
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
4
db1 and db2 wavelet performance across locomotion modes and transitions.
Fig. 4. Wavelet decomposition (at level 2) for segmented Az signal with respective frequency bands. The location of toe off was estimated as the minimum value of approximation coefficient at decomposition level 2 (shown with blue dot).
III. RESULTS The average stride durations for steady state locomotion were 1.08 ± 0.078, 1.07 ± 0.10 and 1.06 ± 0.067 seconds for W, RA and RD, respectively and 1.07 ± 0.081 and 1.06 ± 0.076 seconds for the transition WRA and W-RD respectively. No significant differences were found between any possible pairs of within or between transition and steady state locomotion (paired ttest, α = 0.05). Point A, B, C and M were detected with 100 percent accuracy utilizing the Ax and Ay acceleration data; no trial was missed in examining toe off due to misidentification of any instance of point A, B or C. Hence, the Az acceleration was segmented correctly in all the trials across all subjects. Though every event was detected with Az, there were measurable differences between the timing of those events, as assessed by foot switch data and the proposed detection algorithm. The mean absolute estimation error using db1 was 17.4 ± 12.5 ms, 13.8 ± 8.5 ms and 22.0 ± 16.4 ms for steady states W, RA and RD, respectively and 20.1 ± 15.5 ms and 17.1 ± 13.7 ms for the transitions W-RA and W-RD, respectively. A matched paired t-test showed no significant difference of algorithm performance across any possible pair of within and between transition and steady state locomotion except between RA and RD (p = 0.03), shown in figure 5. For W-RA and RA the estimated toe off was always delayed compared with the true toe off detection. The mean absolute estimation error using db2 was 25.6 ± 18.3, 32.5 ± 15.3, 33.2 ± 21.7, 32.5 ± 19.5 and 26.8 ± 16.2ms compared to 17.4 ± 12.5, 13.8 ± 8.5, 22.0 ± 16.4, 20.1 ± 15.5 and 17.1 ± 13.7ms using db1 wavelet, for W, RA, RD, W-RA, and W-RD, respectively. The db1 wavelet performed significantly better than db2 in identifying toe off with high accuracy (p < 0.01). Figure 5 shows the summary comparison of
Fig. 5. Estimation error compared between db1 and db2 wavelet decomposition. Error values were significantly higher in RD compared to RA (p = 0.03). ** indicates significant difference between decomposition levels (p < 0.01).
IV. DISCUSSION The purpose of this paper was to develop and test a novel method of toe off detection, using accelerometry and wavelet decomposition, in two different locomotion modes and transitions between modes. Using a single 3axis accelerometer resulted in accuracy levels superior to those previously reported in the literature [12, 25]. For example, Jasiewicz et al. [12] utilized a heuristic approach with foot acceleration data as input, reporting an error of 19 ± 34 ms in over ground walking using healthy subjects. This is higher than our estimation error of 17.4 ± 12.5 ms, with higher variation across the subjects. However their study involved twenty six subjects (5-79 years) and the larger variation in estimation may be accounted for in the large range of ages within their sample. Sabatani et al. [25] reported an average systematic error of 35 ms, averaged across ramp and over ground walking, which is nearly two to three times as large as our estimation errors of 17.4 ms and 13.8 ms for over ground and ramp walking, respectively. In more recent work, Aung et al. [24] utilized a wavelet approach and machine learning for automated detection of instantaneous gait events, reporting an estimation error of 18.3 ± 27.0 ms, from eight healthy subjects. Their source of data for toe off detection was from simulated accelerometer data derived from the positions of marker clusters attached to the foot while walking in a motion analysis laboratory. However, they reported an outstanding reduction in estimation error to 5.1 ± 12.2 ms for ramp walking when true accelerometer data were used. Our proposed approach provides equivalent
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
5
TABLE I
COMPARISON OF ESTIMATION ERROR (MEAN ± STD, MS) USING THE CURRENT ALGORITHM AND OTHER REPORTED APPROACHES Author Jasiewicz et al (2006) Aung et al (2013) Aung et al (2013) Sabatini et al (2005) Current Method
Data Foot accelerometer Foot acceleration (simulated + measured) Ankle accelerometer
Over ground 19 ± 34 18.3 ± 27.0
Foot gyroscope Foot accelerometer
35 17.4 ± 12.5
19.5 ± 27.1
estimation error with less variation across six subjects, in addition to estimating the transitions between locomotion modes. A summary comparison of our approach to the closest respective literature in terms of sensor type and placement is presented in Table 1. Removal of the gravity component was done by removing the residual acceleration, during standing, from the acceleration signal. This works fairly well for walking assuming the foot does not rotate by a large magnitude. However, utilizing a more thorough method for removing the gravity component, using goniometer to measure foot rotation or employing other computational methods like those suggested by van Hees [26], might further enhance the estimation accuracy of this algorithm. The ’gold standard’ for toe off detection in this study relied on foot switch data, which itself has some inherent error, due to variations in the size and shape of subjects’ feet. This can lead to large variation in estimation error across subjects. It may be necessary to determine any biasing or offset between the estimations derived from foot switch and GRF plates. This offset could be further added or subtracted from the estimation of the proposed algorithm to test it against the GRF true estimation. In future work, it would be good to test this algorithm in pathological, prosthesis and treadmill gait conditions, which would help to determine modifications to make the algorithm more robust in varied applications. Further, the algorithm could be extended to heel strike detection for complete detection of spatio-temporal gait parameters. The non-significant difference between mean absolute estimate errors across all locomotion types and transitions shows that the new approach is robust and adaptable for different terrains and transitions. The better performance of db1 over db2 wavelet decomposition is likely due to less oscillatory behavior during the data segment where toe off occurs. In some of the trials the algorithm resulted in perfectly accurate toe off estimation (estimation error = 0).
V. CONCLUSIONS In conclusion, the findings of this study lead us to observe that the combination of signal processing and a
Ramp N/A 5.1 ± 12.1 (smooth) 15.2 ± 41.7 (tactile) 32.5 ± 63.0 (smooth) 21.1 ± 53.1 (tactile) 35 13.8 ± 8.5
Transition N/A N/A N/A N/A 20.1 ± 15.5
Algorithm type Heuristic Heuristic + Wavelet + Machine learning Heuristic + Wavelet + Machine learning Heuristic Heuristic + Wavelet
heuristic approach is better than a heuristic approach alone at identifying toe off using accelerometry data. This may be due to the fact that heuristic approaches are generally subjective, while signal processing approaches are data driven and hence more adaptive to signal source. A fusion of approaches can capture the advantages of both, leading to high accuracy as well as reduction in computation time. This may be effective in real time applications where toe off has to be anticipated prior to actual toe off with high accuracy, such as the case of critical damping of powered prostheses which must be controlled for swing phase. ACKNOWLEDGMENT We gratefully acknowledge the assistance of Daniel Jones and Eileen Deming during data collection and processing. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
A. Bregou Bourgeois, B. Mariani, K. Aminian, P. Y. Zambelli, and C. J. Newman, "Spatio-temporal gait analysis in children with cerebral palsy using, foot-worn inertial sensors," Gait Posture, vol. 39, pp. 436-42, 2014. D. A. Bruening and S. T. Ridge, "Automated event detection algorithms in pathological gait," Gait Posture, vol. 39, pp. 472-7, 2014. E. Desailly, Y. Daniel, P. Sardain, and P. Lacouture, "Foot contact event detection using kinematic data in cerebral palsy children and normal adults gait," Gait Posture, vol. 29, pp. 76-80, Jan 2009. B. Mariani, M. C. Jimenez, F. J. Vingerhoets, and K. Aminian, "On-shoe wearable sensors for gait and turning assessment of patients with Parkinson's disease," IEEE Trans Biomed Eng, vol. 60, pp. 155-8, Jan 2013. R. W. Selles, M. A. Formanoy, J. B. Bussmann, P. J. Janssens, and H. J. Stam, "Automated estimation of initial and terminal contact timing using accelerometers; development and validation in transtibial amputees and controls," IEEE Trans Neural Syst Rehabil Eng, vol. 13, pp. 81-8, Mar 2005. Y. H. Chang, H. W. Huang, C. M. Hamerski, and R. Kram, "The independent effects of gravity and inertia on running mechanics," J Exp Biol, vol. 203, pp. 229-38, Jan 2000. A. Hreljac and R. N. Marshall, "Algorithms to determine event timing during normal walking using kinematic data," J Biomech, vol. 33, pp. 783-6, Jun 2000.
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
J. K. De Witt, "Determination of toe-off event time during treadmill locomotion using kinematic data," J Biomech, vol. 43, pp. 3067-9, Nov 16 2010. A. R. De Asha, M. A. Robinson, and G. J. Barton, "A marker based kinematic method of identifying initial contact during gait suitable for use in real-time visual feedback applications," Gait Posture, vol. 36, pp. 650-2, Jul 2012. S. Ghoussayni, C. Stevens, S. Durham, and D. Ewins, "Assessment and validation of a simple automated method for the detection of gait events and intervals," Gait Posture, vol. 20, pp. 266-72, Dec 2004. B.-J. Hsue, F. Miller, F.-C. Su, J. Henley, and C. Church, "Gait timing event determination using kinematic data for the toe walking children with cerebral palsy," Journal of Biomechanics, vol. 40, p. S529, 2007. J. M. Jasiewicz, J. H. Allum, J. W. Middleton, A. Barriskill, P. Condie, B. Purcell, et al., "Gait event detection using linear accelerometers or angular velocity transducers in able-bodied and spinal-cord injured individuals," Gait Posture, vol. 24, pp. 502-9, Dec 2006. J.-d.-J. Salazar-Torres, "Validity of an automated gait event detection algorithm in children with cerebral palsy and non-impaired children.," Gait & Posture, vol. 24, pp. 130-131, 2006. W. Zijlstra and A. L. Hof, "Assessment of spatio-temporal gait parameters from trunk accelerations during human walking," Gait Posture, vol. 18, pp. 1-10, Oct 2003. C. M. O'Connor, S. K. Thorpe, M. J. O'Malley, and C. L. Vaughan, "Automatic detection of gait events using kinematic data," Gait Posture, vol. 25, pp. 469-74, Mar 2007. A. Hreljac and N. Stergiou, "Phase determination during normal running using kinematic data," Med Biol Eng Comput, vol. 38, pp. 503-6, Sep 2000. A. Maiwald, T. Sterzing, T. A. Mayer, and T. L. Milani, "Detecting gait events in running from kinematic data," in International Society of Biomechanics, Cape Town, South Africa, 2009. J. A. Zeni, Jr., J. G. Richards, and J. S. Higginson, "Two simple methods for determining gait events during treadmill and overground walking using kinematic data," Gait Posture, vol. 27, pp. 710-4, May 2008. J. Leitch, J. Stebbins, G. Paolini, and A. B. Zavatsky, "Identifying gait events without a force plate during running: a comparison of methods," Gait Posture, vol. 33, pp. 130-2, Jan 2011. C. M. Senanayake and S. M. Senanayake, "Computational intelligent gait-phase detection system to identify pathological gait," IEEE Trans Inf Technol Biomed, vol. 14, pp. 1173-9, Sep 2010. E. Guenterberg, A. Y. Yang, H. Ghasemzadeh, R. Jafari, R. Bajcsy, and S. S. Sastry, "A method for extracting temporal parameters based on hidden Markov models in body sensor networks with inertial sensors," IEEE Trans Inf Technol Biomed, vol. 13, pp. 1019-30, Nov 2009. C. C. Yang, Y. L. Hsu, K. S. Shih, and J. M. Lu, "Realtime gait cycle parameter recognition using a wearable accelerometry system," Sensors (Basel), vol. 11, pp. 731426, 2011.
6
[23]
[24]
[25]
[26]
R. Williamson and B. J. Andrews, "Gait event detection for FES using accelerometers and supervised machine learning," IEEE Trans Rehabil Eng, vol. 8, pp. 312-9, Sep 2000. M. S. Aung, S. B. Thies, L. P. Kenney, D. Howard, R. W. Selles, A. H. Findlow, et al., "Automated detection of instantaneous gait events using time frequency analysis and manifold embedding," IEEE Trans Neural Syst Rehabil Eng, vol. 21, pp. 908-16, Nov 2013. A. M. Sabatini, C. Martelloni, S. Scapellato, and F. Cavallo, "Assessment of walking features from foot inertial sensing," IEEE Trans Biomed Eng, vol. 52, pp. 486-94, Mar 2005. V. T. van Hees, L. Gorzelniak, E. C. Dean Leon, M. Eder, M. Pias, S. Taherian, et al., "Separating movement and gravity components in an acceleration signal and implications for the assessment of human daily physical activity," PLoS One, vol. 8, p. e61691, 2013.
Deepak Joshi received the B.S. degree from Garhwal University, the M.S. degree from the Sant Longowal Institute of Engineering and Technology, and the Ph.D. from the Indian Institute of Technology Delhi. He is currently a post-doctoral fellow in the Department of Human Physiology at the University of Oregon, Eugene, OR.
Bryson H. Nakamura received the B.S. degree in Exercise Science from the University of Puget Sound, the M.S. degree in Human Physiology from the University of Oregon, and is currently a Ph.D. student in the Department of Human Physiology at the University of Oregon, Eugene, OR.
Michael E. Hahn received the B.S. degree from Colorado Mesa University, the M.S. degree from Iowa State University, and the Ph.D. from the University of Oregon. He is currently an Assistant Professor in the Department of Human Physiology at the University of Oregon, Eugene, OR.
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
JBHI-00482-2014
1
A Novel Approach for Toe Off Estimation during Locomotion and Transitions on Ramps and Level Ground Deepak Joshi, Bryson H. Nakamura, and Michael E. Hahn* Abstract— Identification of the toe off event is critical in many gait applications. Accelerometer threshold based algorithms lack adaptability and have not been tested for transitions between locomotion states. We describe a new approach for toe off identification using one accelerometer in over ground and ramp walking, including transitions. The method uses invariant foot acceleration features in the segment of gait where toe off is probable. Wavelet analysis of foot acceleration is used to derive a unique feature in a particular frequency band, yielding estimated toe off occurrence. We tested the new method for five conditions: over ground walking (W), ramp ascending (RA), ramp descending (RD); transitions between states (W-RA, WRD). Mean absolute estimation error was 17.4 ± 12.5, 13.8 ± 8.5 and 22.0 ± 16.4 ms for steady states W, RA and RD, 20.1 ± 15.5 and 17.1 ± 13.7 ms for transitions W-RA and W-RD, respectively. Algorithm performance was equivalent across all pairs of transition and locomotion state except between RA and RD (p = 0.03), demonstrating adaptability. The db1 wavelet outperformed db2 across states and transitions (p < 0.01). The presented algorithm is a simple, robust approach for toe off detection. Index Terms— Toe off, ramp, over ground, wavelet decomposition, foot acceleration
I. INTRODUCTION Identification of gait events (i.e. initial contact (IC) and toe off (TO)) is integral to calculation of spatialtemporal gait parameters used to analyze normal and pathological gait [1-5]. Toe off is the primary event which marks the transition between stance and swing Manuscript received August 12, 2014, revised October 16, 2014. This work was supported by the Department of Defense under Grant W81XWH-09-2-0144. D. Joshi, B. H. Nakamura, and M. E. Hahn* are with the Human Physiology Department, University of Oregon, Eugene, OR 97403 USA (e-mail: [email protected], [email protected], [email protected]; phone: 541-346-3554; fax: 541-346-2841). Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to [email protected].
phase. For comparison between various gait cycles phase wise normalization is needed, which requires toe off estimation. Ground reaction force (GRF) data [6] and kinematic data using motion capture have been the popular choices for detection of IC and TO during over ground [7] and treadmill gait [8]. Such measurements are expensive, have limited capture volume, and require specific expertise. Further, they are restricted to laboratory settings. There are numerous applications like functional electrical stimulation (FES) and monitoring of activity of daily living (ADL) where ambulatory monitoring systems are required. The restrictions of GRF and kinematic data using motion capture in ambulatory monitoring led us to search for an alternate method of toe off detection. Inertial sensors have been used with some success towards producing a robust gait event detection approach. Many algorithms have been published for accurate identification of toe off in normal gait [5, 914]; specifically over ground walking [7, 15] over ground running [16, 17], treadmill walking [18] and treadmill running [19]. These algorithms are based on basic thresholds of the source signal, leading to multiple thresholds, peak detection, acceleration, deceleration, and hence are sensitive to walking speed. However a recently published technique which accounts for speed has produced improved accuracy [2]. With recent advancements in computational methodology, fuzzy logic [20], multi-objective optimization techniques using genetic algorithms [21], cross correlation [22] and machine learning [23] have also been explored. Compared to studies of over ground and treadmill walking and running, there is relatively little reported about toe off detection in ramp locomotion [24, 25]. Furthermore, no method has been reported for detection of toe off during the transition from over ground to ramp locomotion. As toe off marks the transition from stance to swing phase, we can expect a discontinuity at this transition in
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
2
the vertical component of acceleration which should be easily detected by wavelet decomposition. We explored the orthogonality of acceleration data to derive features for toe off detection. In this paper, we propose a method that uses invariant signal features from foot acceleration to focus on the particular segment of a gait cycle where toe off is likely to occur. We then perform wavelet analysis of foot within this data segment to determine a unique feature in a particular frequency band, yielding an estimate of toe off occurrence. We assessed estimation accuracy for over ground and ramp surface locomotion. We further assessed the adaptability of the detection algorithm for the gait cycle corresponding to transition from over ground to ramp locomotion.
(Noraxon, Scottsdale, AZ) placed slightly medial to the collection site, to the portable data collection unit. Footswitch and accelerometer data were sampled at a frequency of 1500 Hz from the data collection unit.
(a)
(b)
(c)
(d)
II. METHODS A. Instrumentation and Data Collection This study was approved by the university’s Institutional Review Board. All subjects provided written informed consent prior to involvement in the study. Data were collected from six subjects (5 male and 1 female; 25.7 ± 5.0 years, 173.0 ± 10.5 cm, 73.6 ± 12.2 kg) while walking over ground (W), ascending ramp (RA), descending ramp (RD) and the transition between locomotion states (W-RA and W-RD). The ramp was measured as 24 feet long with inclination of 5 degrees. Foot switches were placed below the foot to provide a repeatable reference of toe off (Figure 1(a)) as the experiments were conducted in the field, outside of the laboratory setting. A tri-axial accelerometer (5.7grams, ±6g output range, ±0.67 V/g sensitivity, 5Hz – 1.8kHz bandwidth) was placed on the dorsum of the foot as shown in the figure 1(c). With respect to a global coordinate reference of anterior-posterior (X) and vertical direction (Z), placement of the accelerometer on the foot led to primary measurement directions as Ax and Az (Figure 1(d)), with Ay representing the mediallateral direction, orthogonal to Ax and Az. As noted in Figure 1(d), Az and Ax were not purely aligned with the global vertical and Z, being dependent upon the orientation of the dorsum of the foot. The transitions W-RA and W-RD were defined as the gait cycle when two heel strikes for over ground and ramp occurred consecutively (see Figure 1(b). Data were wirelessly transmitted, using local transmitters
Fig 1. Sensor placement and data collection overview: a) Foot switch placement b) Locomotion mode and the transition cycle c) Accelerometer placement d) Global coordinate reference and local acceleration components; Az and Ax are measured acceleration with respect to shown global anterior posterior (AP) and vertical direction. Ay (not shown) is orthogonal to Ax and Az. Arrow shows positive direction with respect to local coordinate system and g is the acceleration due to gravity.
Subjects practiced on the pathway before data were collected to ensure that they were able to consistently walk at a self-selected speed while making the transitions between locomotion modes. Data were then collected while each subject performed three trials walking from over ground to each ramp surface. B. Data Processing Foot movement during walking is generally in a low frequency range. To reduce data redundancy, we downsampled the original data by a factor of 5, resulting in an effective sampling frequency of 300Hz. The data were further filtered with a low pass second order Butterworth filter with 10Hz cut off frequency. This cutoff frequency, compared to other options like 20 and 40 Hz, avoided the local minima and maxima in the acceleration data while maintaining meaningful information of source signal to develop the algorithm. To remove the gravity component, the residual acceleration value in all directions during a period of quiet stance, was removed from the filtered data.
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
3
C. Data Segment Identification For a complete trial, the gait cycles were extracted using foot switch data. The gait cycles were labelled as W, RA, RD, W-RA and W-RD based on event markers placed in the data set. For every gait cycle the true toe off event was marked using the foot switch data. From repeated observations, the toe off event was found to be always between two distinct points of the Ax acceleration data, across the locomotion (W, RA and RD) and the transition (W-RA and W-RD) states, shown as A and point B in Figure 2. 5 4 3
2
volt
1 0
-1 -2
Fig. 2. The Ax and Ay with foot switch data during ramp walking (ascending, RA). Three separate cycles are shown from one example subject; representing those with minimum, maximum and median stride duration. The Y-axis unit for acceleration and foot switch are ±g and Volt, respectively and are shown with respect to timenormalized gait cycle. The marker C corresponds to the region of Toe-off for all the three stride cycles showing that it lies between point A and B exclusively. A similar pattern was observed in W, RD, W-RA and W-RD (data not shown). Note: Acceleration in Ay direction is shown with an offset of +2g for visualization purposes.
Point A and B were identified utilizing mutual information in the Ax and Ay acceleration data. Specifically, point M is the maximum Ay acceleration peak in a gait cycle, and is the closest unique point in proximity to point A, which is the peak Ax acceleration. Further, point C is the maximum negative Ax peak prior to point A. We segmented Az acceleration of a gait cycle between point A and point B to locally search for the toe off. The algorithm for determining the segment between point A and B for Az acceleration (as just described), is presented as a flowchart in Figure 3.
Fig. 3. A flowchart to illustrate the complete algorithm. The acceleration in each direction is calibrated by removing the residual gravity component during a static standing position. Signals are filtered at 10 Hz (low pass, 2nd order Butterworth) before applying this algorithm.
feature towards toe off detection at the decomposed level. Increasing the decomposition level decreases the time resolution; however it increases the frequency resolution. In this particular case, as we need to estimate toe off as accurately as possible in time, we limited the decomposition level. We utilized low vanishing moment family members, db1 and db2 of Daubechies wavelet family, as the accelerometer data may be visualized as having limited oscillatory behavior (Figure 4). Over repeated observations, we could consistently estimate the toe off corresponding to minimum approximation coefficient at decomposition level 2, which corresponds to frequency band of 0 - 2.5 Hz (Figure 4). E. Estimation Error Estimation error was first defined as the time difference between the toe off detection by foot switch and toe off detection by the proposed algorithm. We took the absolute value of this error value and averaged across the subjects to report mean absolute estimation error. Note: As the effective sampling frequency was 300 Hz, the error of a single sample of time corresponds to 3.3 ms.
D. Wavelet Decomposition The segmental Az acceleration was decomposed using Daubechies wavelet family. We sought an invariant
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
4
db1 and db2 wavelet performance across locomotion modes and transitions.
Fig. 4. Wavelet decomposition (at level 2) for segmented Az signal with respective frequency bands. The location of toe off was estimated as the minimum value of approximation coefficient at decomposition level 2 (shown with blue dot).
III. RESULTS The average stride durations for steady state locomotion were 1.08 ± 0.078, 1.07 ± 0.10 and 1.06 ± 0.067 seconds for W, RA and RD, respectively and 1.07 ± 0.081 and 1.06 ± 0.076 seconds for the transition WRA and W-RD respectively. No significant differences were found between any possible pairs of within or between transition and steady state locomotion (paired ttest, α = 0.05). Point A, B, C and M were detected with 100 percent accuracy utilizing the Ax and Ay acceleration data; no trial was missed in examining toe off due to misidentification of any instance of point A, B or C. Hence, the Az acceleration was segmented correctly in all the trials across all subjects. Though every event was detected with Az, there were measurable differences between the timing of those events, as assessed by foot switch data and the proposed detection algorithm. The mean absolute estimation error using db1 was 17.4 ± 12.5 ms, 13.8 ± 8.5 ms and 22.0 ± 16.4 ms for steady states W, RA and RD, respectively and 20.1 ± 15.5 ms and 17.1 ± 13.7 ms for the transitions W-RA and W-RD, respectively. A matched paired t-test showed no significant difference of algorithm performance across any possible pair of within and between transition and steady state locomotion except between RA and RD (p = 0.03), shown in figure 5. For W-RA and RA the estimated toe off was always delayed compared with the true toe off detection. The mean absolute estimation error using db2 was 25.6 ± 18.3, 32.5 ± 15.3, 33.2 ± 21.7, 32.5 ± 19.5 and 26.8 ± 16.2ms compared to 17.4 ± 12.5, 13.8 ± 8.5, 22.0 ± 16.4, 20.1 ± 15.5 and 17.1 ± 13.7ms using db1 wavelet, for W, RA, RD, W-RA, and W-RD, respectively. The db1 wavelet performed significantly better than db2 in identifying toe off with high accuracy (p < 0.01). Figure 5 shows the summary comparison of
Fig. 5. Estimation error compared between db1 and db2 wavelet decomposition. Error values were significantly higher in RD compared to RA (p = 0.03). ** indicates significant difference between decomposition levels (p < 0.01).
IV. DISCUSSION The purpose of this paper was to develop and test a novel method of toe off detection, using accelerometry and wavelet decomposition, in two different locomotion modes and transitions between modes. Using a single 3axis accelerometer resulted in accuracy levels superior to those previously reported in the literature [12, 25]. For example, Jasiewicz et al. [12] utilized a heuristic approach with foot acceleration data as input, reporting an error of 19 ± 34 ms in over ground walking using healthy subjects. This is higher than our estimation error of 17.4 ± 12.5 ms, with higher variation across the subjects. However their study involved twenty six subjects (5-79 years) and the larger variation in estimation may be accounted for in the large range of ages within their sample. Sabatani et al. [25] reported an average systematic error of 35 ms, averaged across ramp and over ground walking, which is nearly two to three times as large as our estimation errors of 17.4 ms and 13.8 ms for over ground and ramp walking, respectively. In more recent work, Aung et al. [24] utilized a wavelet approach and machine learning for automated detection of instantaneous gait events, reporting an estimation error of 18.3 ± 27.0 ms, from eight healthy subjects. Their source of data for toe off detection was from simulated accelerometer data derived from the positions of marker clusters attached to the foot while walking in a motion analysis laboratory. However, they reported an outstanding reduction in estimation error to 5.1 ± 12.2 ms for ramp walking when true accelerometer data were used. Our proposed approach provides equivalent
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
5
TABLE I
COMPARISON OF ESTIMATION ERROR (MEAN ± STD, MS) USING THE CURRENT ALGORITHM AND OTHER REPORTED APPROACHES Author Jasiewicz et al (2006) Aung et al (2013) Aung et al (2013) Sabatini et al (2005) Current Method
Data Foot accelerometer Foot acceleration (simulated + measured) Ankle accelerometer
Over ground 19 ± 34 18.3 ± 27.0
Foot gyroscope Foot accelerometer
35 17.4 ± 12.5
19.5 ± 27.1
estimation error with less variation across six subjects, in addition to estimating the transitions between locomotion modes. A summary comparison of our approach to the closest respective literature in terms of sensor type and placement is presented in Table 1. Removal of the gravity component was done by removing the residual acceleration, during standing, from the acceleration signal. This works fairly well for walking assuming the foot does not rotate by a large magnitude. However, utilizing a more thorough method for removing the gravity component, using goniometer to measure foot rotation or employing other computational methods like those suggested by van Hees [26], might further enhance the estimation accuracy of this algorithm. The ’gold standard’ for toe off detection in this study relied on foot switch data, which itself has some inherent error, due to variations in the size and shape of subjects’ feet. This can lead to large variation in estimation error across subjects. It may be necessary to determine any biasing or offset between the estimations derived from foot switch and GRF plates. This offset could be further added or subtracted from the estimation of the proposed algorithm to test it against the GRF true estimation. In future work, it would be good to test this algorithm in pathological, prosthesis and treadmill gait conditions, which would help to determine modifications to make the algorithm more robust in varied applications. Further, the algorithm could be extended to heel strike detection for complete detection of spatio-temporal gait parameters. The non-significant difference between mean absolute estimate errors across all locomotion types and transitions shows that the new approach is robust and adaptable for different terrains and transitions. The better performance of db1 over db2 wavelet decomposition is likely due to less oscillatory behavior during the data segment where toe off occurs. In some of the trials the algorithm resulted in perfectly accurate toe off estimation (estimation error = 0).
V. CONCLUSIONS In conclusion, the findings of this study lead us to observe that the combination of signal processing and a
Ramp N/A 5.1 ± 12.1 (smooth) 15.2 ± 41.7 (tactile) 32.5 ± 63.0 (smooth) 21.1 ± 53.1 (tactile) 35 13.8 ± 8.5
Transition N/A N/A N/A N/A 20.1 ± 15.5
Algorithm type Heuristic Heuristic + Wavelet + Machine learning Heuristic + Wavelet + Machine learning Heuristic Heuristic + Wavelet
heuristic approach is better than a heuristic approach alone at identifying toe off using accelerometry data. This may be due to the fact that heuristic approaches are generally subjective, while signal processing approaches are data driven and hence more adaptive to signal source. A fusion of approaches can capture the advantages of both, leading to high accuracy as well as reduction in computation time. This may be effective in real time applications where toe off has to be anticipated prior to actual toe off with high accuracy, such as the case of critical damping of powered prostheses which must be controlled for swing phase. ACKNOWLEDGMENT We gratefully acknowledge the assistance of Daniel Jones and Eileen Deming during data collection and processing. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
A. Bregou Bourgeois, B. Mariani, K. Aminian, P. Y. Zambelli, and C. J. Newman, "Spatio-temporal gait analysis in children with cerebral palsy using, foot-worn inertial sensors," Gait Posture, vol. 39, pp. 436-42, 2014. D. A. Bruening and S. T. Ridge, "Automated event detection algorithms in pathological gait," Gait Posture, vol. 39, pp. 472-7, 2014. E. Desailly, Y. Daniel, P. Sardain, and P. Lacouture, "Foot contact event detection using kinematic data in cerebral palsy children and normal adults gait," Gait Posture, vol. 29, pp. 76-80, Jan 2009. B. Mariani, M. C. Jimenez, F. J. Vingerhoets, and K. Aminian, "On-shoe wearable sensors for gait and turning assessment of patients with Parkinson's disease," IEEE Trans Biomed Eng, vol. 60, pp. 155-8, Jan 2013. R. W. Selles, M. A. Formanoy, J. B. Bussmann, P. J. Janssens, and H. J. Stam, "Automated estimation of initial and terminal contact timing using accelerometers; development and validation in transtibial amputees and controls," IEEE Trans Neural Syst Rehabil Eng, vol. 13, pp. 81-8, Mar 2005. Y. H. Chang, H. W. Huang, C. M. Hamerski, and R. Kram, "The independent effects of gravity and inertia on running mechanics," J Exp Biol, vol. 203, pp. 229-38, Jan 2000. A. Hreljac and R. N. Marshall, "Algorithms to determine event timing during normal walking using kinematic data," J Biomech, vol. 33, pp. 783-6, Jun 2000.
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2377749, IEEE Journal of Biomedical and Health Informatics
JBHI-00482-2014
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
J. K. De Witt, "Determination of toe-off event time during treadmill locomotion using kinematic data," J Biomech, vol. 43, pp. 3067-9, Nov 16 2010. A. R. De Asha, M. A. Robinson, and G. J. Barton, "A marker based kinematic method of identifying initial contact during gait suitable for use in real-time visual feedback applications," Gait Posture, vol. 36, pp. 650-2, Jul 2012. S. Ghoussayni, C. Stevens, S. Durham, and D. Ewins, "Assessment and validation of a simple automated method for the detection of gait events and intervals," Gait Posture, vol. 20, pp. 266-72, Dec 2004. B.-J. Hsue, F. Miller, F.-C. Su, J. Henley, and C. Church, "Gait timing event determination using kinematic data for the toe walking children with cerebral palsy," Journal of Biomechanics, vol. 40, p. S529, 2007. J. M. Jasiewicz, J. H. Allum, J. W. Middleton, A. Barriskill, P. Condie, B. Purcell, et al., "Gait event detection using linear accelerometers or angular velocity transducers in able-bodied and spinal-cord injured individuals," Gait Posture, vol. 24, pp. 502-9, Dec 2006. J.-d.-J. Salazar-Torres, "Validity of an automated gait event detection algorithm in children with cerebral palsy and non-impaired children.," Gait & Posture, vol. 24, pp. 130-131, 2006. W. Zijlstra and A. L. Hof, "Assessment of spatio-temporal gait parameters from trunk accelerations during human walking," Gait Posture, vol. 18, pp. 1-10, Oct 2003. C. M. O'Connor, S. K. Thorpe, M. J. O'Malley, and C. L. Vaughan, "Automatic detection of gait events using kinematic data," Gait Posture, vol. 25, pp. 469-74, Mar 2007. A. Hreljac and N. Stergiou, "Phase determination during normal running using kinematic data," Med Biol Eng Comput, vol. 38, pp. 503-6, Sep 2000. A. Maiwald, T. Sterzing, T. A. Mayer, and T. L. Milani, "Detecting gait events in running from kinematic data," in International Society of Biomechanics, Cape Town, South Africa, 2009. J. A. Zeni, Jr., J. G. Richards, and J. S. Higginson, "Two simple methods for determining gait events during treadmill and overground walking using kinematic data," Gait Posture, vol. 27, pp. 710-4, May 2008. J. Leitch, J. Stebbins, G. Paolini, and A. B. Zavatsky, "Identifying gait events without a force plate during running: a comparison of methods," Gait Posture, vol. 33, pp. 130-2, Jan 2011. C. M. Senanayake and S. M. Senanayake, "Computational intelligent gait-phase detection system to identify pathological gait," IEEE Trans Inf Technol Biomed, vol. 14, pp. 1173-9, Sep 2010. E. Guenterberg, A. Y. Yang, H. Ghasemzadeh, R. Jafari, R. Bajcsy, and S. S. Sastry, "A method for extracting temporal parameters based on hidden Markov models in body sensor networks with inertial sensors," IEEE Trans Inf Technol Biomed, vol. 13, pp. 1019-30, Nov 2009. C. C. Yang, Y. L. Hsu, K. S. Shih, and J. M. Lu, "Realtime gait cycle parameter recognition using a wearable accelerometry system," Sensors (Basel), vol. 11, pp. 731426, 2011.
6
[23]
[24]
[25]
[26]
R. Williamson and B. J. Andrews, "Gait event detection for FES using accelerometers and supervised machine learning," IEEE Trans Rehabil Eng, vol. 8, pp. 312-9, Sep 2000. M. S. Aung, S. B. Thies, L. P. Kenney, D. Howard, R. W. Selles, A. H. Findlow, et al., "Automated detection of instantaneous gait events using time frequency analysis and manifold embedding," IEEE Trans Neural Syst Rehabil Eng, vol. 21, pp. 908-16, Nov 2013. A. M. Sabatini, C. Martelloni, S. Scapellato, and F. Cavallo, "Assessment of walking features from foot inertial sensing," IEEE Trans Biomed Eng, vol. 52, pp. 486-94, Mar 2005. V. T. van Hees, L. Gorzelniak, E. C. Dean Leon, M. Eder, M. Pias, S. Taherian, et al., "Separating movement and gravity components in an acceleration signal and implications for the assessment of human daily physical activity," PLoS One, vol. 8, p. e61691, 2013.
Deepak Joshi received the B.S. degree from Garhwal University, the M.S. degree from the Sant Longowal Institute of Engineering and Technology, and the Ph.D. from the Indian Institute of Technology Delhi. He is currently a post-doctoral fellow in the Department of Human Physiology at the University of Oregon, Eugene, OR.
Bryson H. Nakamura received the B.S. degree in Exercise Science from the University of Puget Sound, the M.S. degree in Human Physiology from the University of Oregon, and is currently a Ph.D. student in the Department of Human Physiology at the University of Oregon, Eugene, OR.
Michael E. Hahn received the B.S. degree from Colorado Mesa University, the M.S. degree from Iowa State University, and the Ph.D. from the University of Oregon. He is currently an Assistant Professor in the Department of Human Physiology at the University of Oregon, Eugene, OR.
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
