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Gait parameter and event estimation using smartphones
Accepted Manuscript Title: Gait parameter and event estimation using smartphones Author: Lucia Pepa Federica Verdini Luca Spalazzi PII: DOI: Reference:
S0966-6362(17)30234-5 http://dx.doi.org/doi:10.1016/j.gaitpost.2017.06.011 GAIPOS 5457
To appear in:
Gait & Posture
Received date: Revised date: Accepted date:
27-9-2016 13-6-2017 15-6-2017
Please cite this article as: Lucia Pepa, Federica Verdini, Luca Spalazzi, Gait parameter and event estimation using smartphones, (2017), http://dx.doi.org/10.1016/j.gaitpost.2017.06.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Research Highligts
HIGHLIGHTS: · Smartphone accuracy in heel strike, step count, step period, step length estimation 䯠
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· Smartphone performance compared against stereophotogrammetry
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· Smartphone alignment mainly influence step count
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· Smartphone lateral placement does not deteriorate the performance 䯠
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Title: Gait parameter and event estimation using smartphones Authors:
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Lucia Pepaa , Federica Verdinia , Luca Spalazzia Affiliation: a
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Department of Information Engineering , Politecnica delle Marche University Ancona, AN, Italy. ([email protected]; [email protected]; [email protected])
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Corresponding author:
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Lucia Pepa Department of Information Engineering , Politecnica delle Marche University Ancona, AN, Italy. E-mail address: [email protected] Acknowledgment
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The authors would like to thank M. G. Ceravolo and M. Capecci (Department of Experimental and Clinical Medicine, Universit`a Politecnica delle Marche) for fruitful discussions about the topics reported in the paper, and W. Zijlstra for his kind help and suggestions.
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Disclosure:
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The authors declare that there is no conflict of interest regarding the publication of this paper.
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Gait parameter and event estimation using smartphones
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Lucia Pepa, Federica Verdini, Luca Spalazzi
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Abstract
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Keywords: heel strike, step count, step length, step period, inverted pendulum model.
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1. Introduction
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Gait monitoring is important for many applications related to health, wellness and sport. For example, it can help for the early diagnosis of neurodegenerative diseases and to manage motor symptoms arising from them [1, 2]. Quantitative and objective assessment of gait derives from gait parameters, among which velocity, step length (SL), and step period (SP) are the most frequently used [3]. Inertial sensors have been widely applied for gait parameters estimation in out-of-laboratory context, given their low cost, miniaturization and wearability. Several works [4, 5, 6, 7] proposed a single sensor on the lower trunk. SL can be derived from the center of mass acceleration measured along the progression direction using double integration [4, 5]. Indirect estimations can be obtained through empirical or model-based approaches. Empirical approaches rely on relations between SL and other parameters like the difference of maximum and minimum vertical acceleration [8], step frequency and acceleration variance [9], and acceleration magnitude [10]. Ho et al. [11] improved Weinberg’s model to enhance pedestrian dead reckoning at various speeds. Among model-based approaches, the inverted pendulum model of human gait introduced by Zijlstra et al. [12] highlights a relationship between vertical change of body center of mass and SL. Gonzalez et al. [6] improved this model by expressing the missing double stance phase as a quantity proportional to foot length. Zijlstra et al. [13] updated their method by introducing an individual correction factor and assessed its reliability. Technology acceptance is an essential requirement in fields like ambient assisted living, pervasive or ubiquitous healthcare. Perceived usefulness and usability are key factors for acceptability [14]. When dealing with health related applications, other crucial aspects are: miniaturization, embeddedness, inconspicuousness, networking, and context sensitivity [15, 16]. Smartphones are believed to fit these requirements and to be a promising tool to handle healthrelated services, joining usability, acceptability, and suitable technical characteristics [17].
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Background and objectives: The use of smartphones can greatly help for gait parameters estimation during daily living, but its accuracy needs a deeper evaluation against a gold standard. The objective of the paper is a step-bystep assessment of smartphone performance in heel strike, step count, step period, and step length estimation. The influence of smartphone placement and orientation on estimation performance is evaluated as well. Methods: This work relies on a smartphone app developed to acquire, process, and store inertial sensor data and rotation matrices about device position. Smartphone alignment was evaluated by expressing the acceleration vector in three reference frames. Two smartphone placements were tested. Three methods for heel strike detection were considered. On the basis of estimated heel strikes, step count is performed, step period is obtained, and the inverted pendulum model is applied for step length estimation. Pearson correlation coefficient, absolute and relative errors, ANOVA, and Bland-Altman limits of agreement were used to compare smartphone estimation with stereophotogrammetry on eleven healthy subjects. Results: High correlations were found between smartphone and stereophotogrammetric measures: up to 0.93 for step count, to 0.99 for heel strike, 0.96 for step period, and 0.92 for step length. Error ranges are comparable to those in the literature. Smartphone placement did not affect the performance. The major influence of acceleration reference frames and heel strike detection method was found in step count. Conclusion: This study provides detailed information about expected accuracy when smartphone is used as a gait monitoring tool. The obtained results encourage real life applications.
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Preprint submitted to Elsevier
June 20, 2017
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2. Materials and methods
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2.1. Smartphone application
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However, before using smartphones as gait analysis tools, a validation against a gold standard is needed. Such validation exists for other parameters, e.g. center of mass displacement [18], but not for SP and SL estimation. This study also evaluates heel strike (HS) detection and step count (SC), since it aims to carry out a step-by-step assessment of smartphone performance. Several methods have been proposed to identify HS from the acceleration of the lumbar region [5, 9]. Some works investigated the detection of gait events also on pathological subjects [19, 20, 21]. Trojaniello et al. [22] compared the performance of five gait events detection methods. None of these works used smartphones. Hence, the objective of this work was the assessment of smartphone accuracy for the step-by-step estimation of HS, SC, SP, and SL and to compare it to stereophotogrammetric measurements. In addition, three different HS detection methods as well as the influence of smartphone placement and orientation were evaluated. In the literature there are some works that use smartphones to estimate gait parameters like SL [11], however they differ from our contribution for the estimated parameters, the estimation model, the validation methods. Further important contributions of this work are the step-by-step assessment of smartphone performance and the investigation of smartphone orientation effects.
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2.2. Instrumentation and data acquisition
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An iPhone 4s (dimension 115.2 × 58.6 × 9.3 mm and weight 140 g) was used in the study. Fig. 1 shows the smartphone placements and its on-board accelerometer reference frame (RF) (blue). Two wearing placements were assessed: lower back (approximately L3-L4), and lateral side of the pelvis. In order to maintain accelerometer axes aligned to antero-posterior (AP), vertical, and medio-lateral (ML) axes of the subject the smartphone was fixed through an elastic belt and an appropriate socket. The executable file of the app is available among supplementary materials. The app acquires data from onboard sensors approximately1 at 100 Hz and stores them. The following data are saved: tri-axial acceleration in the smartphone RF (Fig. 1, blue RF), rotation matrix of smartphone RF with respect to a north RF, rotation matrix of the smartphone RF with respect to a particular RF defined manually, and finally the timestamp of each sample. The north RF is defined in the following way: positive x points towards magnetic north and positive z has the same direction of gravity but with opposite sign. For what concerns manual RF: positive y direction is inside a plane parallel to the floor and points toward the forward walking direction (like x-axis of laboratory RF in fig. 1), positive z is perpendicular to the floor and points upward. After launching, the application asks the user to calibrate the compass through a dedicated user interface. North RF and manual RF were used since the smartphone may introduce inaccuracies in sensor orientation. Once attached to the human body, contact between the wide phone surface and body contours can cause a misalignment between accelerometer axes and the axes of the laboratory RF (the red one in Fig. 1), that identifies the actual AP, ML, and vertical directions. Acceleration vector can be transformed through rotation matrices from the smartphone RF to north and manual RFs whose orientation with respect to laboratory RF is known.
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The reliability of the smartphone was evaluated by comparison with a stereophotogrammetric system (Elite, BTS Bioengineering) composed of six infrared cameras, which acquired the position of reflective markers in a fixed RF at 100 Hz sample frequency. Nine markers were placed on pelvis and feet, and one in the middle of the smartphone screen. The pelvis was identified by three markers: two over the left and right anterior superior iliac spines and the third on the middle point between the posterior superior iliac spines. Each foot was identified by three markers placed on: heel, first and fifth metatarsal head. HS time instants were identified through the inspection of heel markers trajectory. SP was obtained as difference between two consecutive HSs. SL was calculated as the difference between x coordinates of heel markers at HS time instants. 1 The
smartphone sample rate is not constant and accurate as an ”ad-hoc” inertial measurement unit or as sterephotogrammetry.
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2.4. Data processing Raw acceleration data are filtered through a low-pass and high-pass Butterworth filter (4th order, zero lag) with 20 Hz and 0.5 Hz cut off frequency respectively to avoid noise and drift and preserve frequency band significant for gait [7]. Time alignment between smartphone and infrared cameras was reached using the jump and data resampling. Smartphone’s samples timestamp was used to infer the actual sample frequency. A resample of the signal with lowest frequency between smartphone and infrared cameras was made to reach the same length. Then, the sample corresponding to the point of maximum height in the jump was selected as synchronizing time instant (see Fig. 2). HS identification can influence SC, SP and SL estimation, hence three HS detection methods were selected (on the basis of computational complexity and reported accuracy) from the literature and compared: the method of Zijlstra et al. [7] (M1), the one of Gonzalez et al. (M2) [23], and the one of McCamley et al. (M3) [24]. In M1, AP acceleration is low pass filtered at 2 Hz (4th order, zero lag Butterworth filter), then the zero-crossings from positive to negative are identified. Finally the last AP peak before each zero-crossing in the 20 Hz filtered AP acceleration is selected as HS [7]. In M2, AP acceleration is filtered through an 11th order FIR filter with 2 Hz cut off frequency, which introduces a five-sample delay. The area enclosed by each positive segment of the output signal is calculated. If this area is above a threshold (set at 0.025 [23]), the HS search is started, otherwise it is considered a false positive. The HS search occurs in the 20 Hz filtered AP acceleration, inside the same time interval used to calculate the area. In this time interval there may be several local maxima, but the peak that satisfies three heuristic rules [23] is chosen as HS. In M3, McCamley et al. [24] integrate and then differentiate vertical acceleration using a Gaussian continuous wavelet transform and they take the minima of the resulting smoothed signal as HSs. SC analysis can be done by comparing smartphone HSs and stereophotogrammetry HSs. SP is found as the time interval between two consecutive HSs. The inverted pendulum model [12] was selected as SL estimation method since it was considered the best tradeoff between reported accuracy [13, 10] and computational complexity: √ (1) sl = 2 2lh − h2
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2.3. Experimental procedures Before each experimental session, the visual field of cameras was calibrated by defining a measurement volume of about 3 m (length) × 2 m (width) × 2 m (height). The accuracy of the stereophotogrammetric system was evaluated during the calibration procedure and it reached an average error of (1.43 ± 0.77) mm in measuring a fixed markers distance. Eleven healthy subjects (8 males, 3 females), aged between 22 and 30 years, participated in the tests. Each subject performed 12 walking trials, 4 at preferred speed, 4 at higher speed and 4 at lower speed. One trial for speed was executed with the smartphone on the lateral side of the hip. During each trial, subjects had to walk forth and back along a straight platform (about 10 meters) inside the visual field of infrared cameras. Each trial started with the execution of a jump, which was used as synchronizing event. After each experimental session, the angle between magnetic north and walking platform was measured by a digital compass and used to align the north RF with the walking platform.
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where l is the length of subject’s leg, and h the vertical change of body center of mass during step cycle. The value of h can be computed from double trapezoidal integration of vertical acceleration between two consecutive HSs. The hypothesis of zero velocity at HS time instant provides the initial condition for the first definite integral and eliminates drift errors. The value of SL obtained with Eq. 1 underestimates the real SL, hence a multiplicative correction factor K must be applied. The least square method was used to find a subject specific K, and a leave-one-out crossvalidation method was applied to assess its robustness. Furthermore, a universal factor was also tested through a leave-one-out crossvalidation. The following function was minimized with respect to K: min ϕ(K) = min
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K∈[1;2]
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where [1; 2] is the domain of K, n is the number of steps, yi are the SLs measured from stereophotogrammetry, and sli are the SLs computed with the smartphone using a certain HS detection method and RF. The optimal value of K can 4
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vary across RFs and HS detection methods, hence the optimization process was repeated across all the combinations of RF and HS detection method.
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2.5. Statistical analysis
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3. Results
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Sensitivity and specificity allow the evaluation of SC. They were computed as global percentage score considering all the trials together, and single trials scores. Pearson Correlation Coefficient (PCC) and one-way analysis of variance (ANOVA) were used to evaluate correlations and differences between smartphone detected steps and stereophotogrammetry recorded steps. HS, SL, and SP of smartphone correctly detected steps were compared to the corresponding steps of stereophotogrammetric system through PCC, absolute and relative (only for SL and SP) errors, ANOVA, BlandAltman 95% limits of agreement (only for SL and SP) [25]. Lilliefors normality test was applied to error, sensitivity, and specificity populations to verify the correctness of mean and standard deviation as statistical indicators. Performance metrics could be influenced by the following variables: speed, subject, smartphone placement, RF and HS detection method. Hence, they were computed across all possible scenarios generated by the combination of the involved variables. To be clearer and more concise this work only reports statistically significant scenarios. Statistically significant differences in performance metrics across subjects, velocities, smartphone placements, RFs, and HS detection methods were detected through ANOVA. The level of significance of all statistical tests was set to 0.05.
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The conducted tests collected 1298 steps: 974 with smartphone on the lower back, 324 on the hip. Mean and standard deviation values of subjects’ speed were: 1.08 ± 0.09, 1.41 ± 0.12, 2.25 ± 0.21 m/s for low, normal, high velocity. Subject specific correction factors K varied from 1.11 to 1.49 across the subjects (1.26 ± 0.08)2 ; intersubject mean correction factor is 1.25±0.013 . Velocity, subject, and smartphone placement did not have statistically significant influence on any performance metric. Performance differences between north and manual RF were not significant, hence in the following they will be generally referred as ”corrected RFs”. Experimental results are reported in Table 1, which includes four sections related to the considered variables: HS, SC, SP, and SL estimation. The next subsections present the results for each variable.
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Specificity was always 100%, hence it was not reported. Concerning smartphone alignment, a statistically significant difference between smartphone and corrected RFs was found only for M1 and M2. Both PCC and ANOVA p−values reveal that M3 and M1 (with the smartphone RF) provide a better estimation of walked steps (M2 performance was significantly different).
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A statistically significant difference was found between RFs, but the effect of a corrected RF is different across HS detection methods: performance improved for M1 and M2 and worsened for M3. No statistical significance was found between M1 and M2 in HS estimation, whereas it was observed between M3 and M1 or M2.
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No statistically significant differences were found across RFs, while a significant difference was found between M1 and M3. Absolute errors range from −0.002 ± 0.028 s and 0.00 ± 0.066 s; PCCs are above 0.89 and ANOVA p−values above 0.54. The 95% limits of agreement were ±0.127, ±0.113, ±0.074 s for M1, M2, and M3 (Fig. 3a). 2 Detailed 3 Detailed
values obtained from leave-one-out crossvalidation are shown in file ”intrasubj.xlsx” of supplementary materials. K values and SL estimation performance from leave-one-out crossvalidation are shown in file ”intersubj.xlsx” of supplementary
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4. Discussion
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The objective of this work was the assessment of smartphone accuracy in HS, SC, SP, and SL estimation through a step-by-step comparison with stereophotogrammetry. The influence of smartphone placement and orientation on estimation accuracy were analyzed as well. This work compares three different HS detection methods as each method may influence the other estimations. Smartphone errors in HS detection ranged between −0.007 and 0.012 s, which are comparable to previous works in the literature. Mean values for HS detection error ranged from −0.015 to 0.003 s in the work of Zijlstra and Hof [7], from −0.006 to 0.048 s in the work of McCamley et al. [24] and finally a mean error of 0.013 s was reported by Gonzalez et al. [23]. PCC and p−Value high scores suggest that the smartphone can provide a reliable estimate of HS time instant. SC sensitivity was always above 90% for M1 and M3 and above 80% for M2, with a 100% median value. These values are in accordance with the literature [20, 26]. The results about step-by-step SP and SL errors are not easily comparable with previous works, since they generally estimated mean values only. SP mean absolute errors ([−0.002, 0.000] s) and standard deviations ([0.028, 0.066] s) are in accordance with the literature [24], while lower standard deviations are reached by Zijlstra and Hof [7], possibly due to hardware differences. For what concern SL estimation, obtained error ranges (mean errors: [0.48, 1.12] cm, standard deviations: [5.21, 7.81] cm) highlighted that the smartphone does not deteriorate SL estimation accuracy with respect to previous works using dedicated hardware [13, 27, 6], confirming the potential of this device as a gait monitoring tool. Kose et al. [5], who performed a stepby-step evaluation, obtained mean errors of 0.9 ± 1.7 cm for right steps and −0.8 ± 1.6 cm for left steps. Lower errors may be due to the dedicated inertial measurement unit and the different estimation method, which requires the identification of other gait events than HS. Although smartphone placement and orientation could be possible sources of error, statistical analysis revealed that the placement does not affect the estimation accuracy. This is an important finding since the interest of the paper was to assess a technology that could be easily applied in a daily living context, and the sensor placement is a key factor for technology acceptance. Regarding the orientation, the most important influence of smartphone orientation regards SC. The decrease observed in performance metrics for M1 and M2 sensitivity with a corrected RF can be explained by acceleration components used for HS detection: AP for M1 and M2 (M2 uses also the vertical one in some conditions), vertical for M3. The rotation matrices used to obtain the north and manual RF were acquired from the smartphone, which computes them through an internal fusion algorithm4 integrating information of onboard sensors (gyroscope, magnetometer, accelerometer). In accordance with previous works [28, 26], the above finding suggests that smartphone’s internal algorithm that computes the rotation matrices can make mistakes in correcting traversal directions (e.g. due to a transient lost of compass calibration or an electromagnetic interference), while it is more robust for vertical direction. In conclusion, RF correction is suitable when using the vertical component, but not for AP or ML directions. For what concerns the influence of HS detection method, no influence was found in HS detection. Instead, for SC, SP, and SL estimation, statistical analysis indicated M1 and M3 as suitable solutions to maximize sensitivity, while M2 and M3 to reach lower errors in SP and SL estimation. Hence, the best choice might be application related, depending on real-time needs or application objectives. The need for a calibration of the correction factor K can be a possible drawback of this method. For interesting scenarios, like the monitoring of pathological gait [2], the calibration process could be carried out during the standard clinical examinations. Alternatively, the smartphone app could ask periodically the user to walk for a known distance and then use these data to calibrate the correction factor. For what concerns the possibility of using a universal
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3.4. Step length Differences between smartphone and corrected RFs are not significant for SL estimation. For what concerns HS detection method, although PCC values are always above 0.84, a significant difference was found between M1 and M3, and between M2 and M3. ANOVA p−values suggest M2 and M3 (p > 0.05) as better SL estimators than M1 (p < 0.05). Fig. 3b shows SL Bland-Altman plots: 95% limits of agreement are ±15.31, ±13.65, ±10.63 cm for M1, M2, and M3.
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correction factor, our results confirm the findings of [13], that suggested 1.25 as standard value and found lower errors with a custom value.
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References
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The work was motivated by the necessity of an acceptable and usable tool for gait monitoring during daily living. The objective was the assessment of smartphone accuracy for the step-by-step estimation of HS, SC, SP, and SL against stereophotogrammetric measurements. Two important sources of error introduced by the smartphone were studied: smartphone placement and orientation. The obtained results revealed a good accuracy of smartphone estimation, thus justifying the use of the smartphone for gait monitoring. In particular, it was found that smartphone placement does not affect estimation accuracy, while the orientation mainly influences SC. The detailed information about expected accuracy can help choosing the best smartphone configuration (placement, reference frame, HS detection method) on the basis of the specific application scenario (e.g. which gait parameters should be monitored).
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[21] N. Chia Bejarano, E. Ambrosini, A. Pedrocchi, G. Ferrigno, M. Monticone, S. Ferrante, A novel adaptive, real-time algorithm to detect gait events from wearable sensors, Neural Systems and Rehabilitation Engineering, IEEE Transactions on 23 (3) (2015) 413–422. doi:10.1109/TNSRE.2014.2337914. [22] D. Trojaniello, A. Cereatti, U. D. Croce, Accuracy, sensitivity and robustness of five different methods for the estimation of gait temporal parameters using a single inertial sensor mounted on the lower trunk, Gait and Posture 40 (4) (2014) 487 – 492. doi:http://dx.doi.org/10.1016/j.gaitpost.2014.07.007. [23] R. Gonzlez, A. Lpez, J. Rodriguez-Ura, D. lvarez, J. Alvarez, Real-time gait event detection for normal subjects from lower trunk accelerations, Gait and Posture 31 (3) (2010) 322 – 325. doi:http://dx.doi.org/10.1016/j.gaitpost.2009.11.014. [24] J. McCamley, M. Donati, E. Grimpampi, C. Mazza, An enhanced estimate of initial contact and final contact instants of time using lower trunk inertial sensor data, Gait and Posture 36 (2) (2012) 316 – 318. doi:http://dx.doi.org/10.1016/j.gaitpost.2012.02.019. [25] J. M. Bland, D. Altman, Originally published as volume 1, issue 8476 statistical methods for assessing agreement between two methods of clinical measurement, The Lancet 327 (8476) (1986) 307 – 310. doi:http://dx.doi.org/10.1016/S0140-6736(86)90837-8. [26] X. Yang, B. Huang, An accurate step detection algorithm using unconstrained smartphones, in: Control and Decision Conference (CCDC), 2015 27th Chinese, 2015, pp. 5682–5687. doi:10.1109/CCDC.2015.7161816. [27] T. Sayeed, A. Sama, A. Catala, J. Cabestany, Comparison and adaptation of step length and gait speed estimators from single belt worn accelerometer positioned on lateral side of the body, in: Intelligent Signal Processing (WISP), 2013 IEEE 8th International Symposium on, 2013, pp. 14–20. doi:10.1109/WISP.2013.6657475. [28] M. Gietzelt, S. Schnabel, K.-H. Wolf, F. Bsching, B. Song, S. Rust, M. Marschollek, A method to align the coordinate system of accelerometers to the axes of a human body: The depitch algorithm, Computer Methods and Programs in Biomedicine 106 (2) (2012) 97 – 103, design of Environments for Ageing. doi:http://dx.doi.org/10.1016/j.cmpb.2011.10.014.
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Figure 1: Smartphone placements and reference frame of the onboard accelerometer (blue); laboratory reference frame (red).
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Figure 2: Comparison between the marker (blue line) and the smartphone (green line) vertical position during a jump. The smartphone position was obtained from double integration of acceleration signal. Red dots indicate the point of maximum height in the two shapes. (a) Smartphone position in the smartphone reference frame. (b) Smartphone position in the north reference frame.
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Figure 3: (a) Bland-Altman plots for step period. (b) Bland-Altman plots for step length. In both graphs, the red line in the middle indicates the mean error and the other two lines the 95% limits of agreement.
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Table 1: Results about smartphone performance metrics. The table comprises four sections related to investigated variables: HS, SC, SP, and SL estimation. Table sections include nine rows related to the combinations of smartphone RFs and HS detection methods. Columns of each table section are the performance metrics chosen to evaluate the corresponding variable. They are reported as mean ± standard deviation, unless differently specified.
M1
M2
M3
SM NO MA SM NO MA SM NO MA
Step period M1
0.95 0.60 0.68 0.67 0.33 0.46 0.99 0.99 0.99
F(1, 262) = 0.29, p = 0.590 F(1, 262) = 9.96, p = 0.001 F(1, 262) = 8.56, p = 0.003 F(1, 262) = 16.87, p < 0.001 F(1, 262) = 38.72, p < 0.001 F(1, 262) = 35.02, p < 0.001 F(1, 262) = 0.01, p = 0.927 F(1, 262) = 0.01, p = 0.927 F(1, 262) = 0.01, p = 0.927
Error [s]
Error [%]
PCC
0.012 ± 0.056 0.005 ± 0.051 0.005 ± 0.050 0.010 ± 0.048 0.003 ± 0.044 0.005 ± 0.045 −0.003 ± 0.032 −0.007 ± 0.034 −0.007 ± 0.034
− − − − − − − − −
0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
Absolute Error [s]
Relative Error
PCC
ANOVA a
0.00 ± 0.09 0.00 ± 0.09 0.00 ± 0.1 0.00 ± 0.09 0.00 ± 0.08 0.00 ± 0.09 0.01 ± 0.05 0.00 ± 0.06 0.00 ± 0.06
0.90 0.90 0.89 0.91 0.93 0.92 0.97 0.96 0.96
F(1, 2566) = 0.37, p = 0.544 F(1, 2362) = 0.26, p = 0.608 F(1, 2388) = 0.29, p = 0.591 F(1, 2282) < 0.01, p = 0.939 F(1, 2078) = 0.01, p = 0.906 F(1, 2204) = 0.03, p = 0.857 F(1, 2592) < 0.01, p = 0.937 F(1, 2592) < 0.01, p = 0.953 F(1, 2592) < 0.01, p = 0.975
Relative Error
PCC
ANOVA a
0.01 ± 0.1 0.01 ± 0.09 0.01 ± 0.1 0.01 ± 0.09 0.01 ± 0.09 0.01 ± 0.09 0.00 ± 0.07 0.00 ± 0.07 0.00 ± 0.07
0.84 0.85 0.84 0.87 0.87 0.87 0.90 0.92 0.92
F(1, 2566) = 4.17, p = 0.041 F(1, 2362) = 3.70, p = 0.055 F(1, 2388) = 3.37, p = 0.067 F(1, 2282) = 2.40, p = 0.121 F(1, 2078) = 2.92, p = 0.088 F(1, 2204) = 2.25, p = 0.133 F(1, 2592) = 1.20, p = 0.274 F(1, 2592) = 0.89, p = 0.345 F(1, 2592) = 0.88, p = 0.349
0.000 ± 0.064 0.000 ± 0.064 0.000 ± 0.066 −0.001 ± 0.050 −0.001 ± 0.055 −0.001 ± 0.059 −0.003 ± 0.031 −0.002 ± 0.028 −0.002 ± 0.029
M3
Step length
M1
M2
M3
SM NO MA SM NO MA SM NO MA
Absolute [cm]
1.12 ± 7.68 1.07 ± 7.44 1.05 ± 7.81 0.98 ± 6.98 1.13 ± 6.86 0.91 ± 7.12 0.61 ± 5.95 0.49 ± 5.23 0.48 ± 5.21
Error
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SM NO MA SM NO MA SM NO MA
98.61 90.52 91.29 87.75 80.15 81.12 99.77 99.77 99.77
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Heel strike
ANOVA a
ANOVA a
F(1, 3092) = 0.06, p = 0.806 F(1, 2870) = 0.01, p = 0.920 F(1, 2908) = 0.01, p = 0.924 F(1, 2796) = 0.04, p = 0.842 F(1, 2574) < 0.01, p = 0.954 F(1, 2634) = 0.01, p = 0.926 F(1, 3120) < 0.01, p = 0.955 F(1, 3120) = 0.03, p = 0.871 F(1, 3120) = 0.03, p = 0.869
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SM NO MA SM NO MA SM NO MA
Median(25th, 75th) [%]
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Abbreviations: PCC, Pearson correlation coefficient; SM, smartphone RF; NO, north RF; MA, manual RF. Heel strike detection methods: Zijlstra et al. [7] (M1), Gonzalez et al. (M2) [23], McCamley et al. (M3) [24]. a p < 0.05: smartphone and stereophotogrammetric measures do not come from the same distribution.
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Conflict of interest: NONE.
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S0966-6362(17)30234-5 http://dx.doi.org/doi:10.1016/j.gaitpost.2017.06.011 GAIPOS 5457
To appear in:
Gait & Posture
Received date: Revised date: Accepted date:
27-9-2016 13-6-2017 15-6-2017
Please cite this article as: Lucia Pepa, Federica Verdini, Luca Spalazzi, Gait parameter and event estimation using smartphones, (2017), http://dx.doi.org/10.1016/j.gaitpost.2017.06.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Research Highligts
HIGHLIGHTS: · Smartphone accuracy in heel strike, step count, step period, step length estimation 䯠
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· Smartphone performance compared against stereophotogrammetry
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· Smartphone alignment mainly influence step count
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· Smartphone lateral placement does not deteriorate the performance 䯠
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Title: Gait parameter and event estimation using smartphones Authors:
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Lucia Pepaa , Federica Verdinia , Luca Spalazzia Affiliation: a
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Department of Information Engineering , Politecnica delle Marche University Ancona, AN, Italy. ([email protected]; [email protected]; [email protected])
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Corresponding author:
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Lucia Pepa Department of Information Engineering , Politecnica delle Marche University Ancona, AN, Italy. E-mail address: [email protected] Acknowledgment
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The authors would like to thank M. G. Ceravolo and M. Capecci (Department of Experimental and Clinical Medicine, Universit`a Politecnica delle Marche) for fruitful discussions about the topics reported in the paper, and W. Zijlstra for his kind help and suggestions.
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Disclosure:
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The authors declare that there is no conflict of interest regarding the publication of this paper.
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Gait parameter and event estimation using smartphones
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Lucia Pepa, Federica Verdini, Luca Spalazzi
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Abstract
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Keywords: heel strike, step count, step length, step period, inverted pendulum model.
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1. Introduction
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Gait monitoring is important for many applications related to health, wellness and sport. For example, it can help for the early diagnosis of neurodegenerative diseases and to manage motor symptoms arising from them [1, 2]. Quantitative and objective assessment of gait derives from gait parameters, among which velocity, step length (SL), and step period (SP) are the most frequently used [3]. Inertial sensors have been widely applied for gait parameters estimation in out-of-laboratory context, given their low cost, miniaturization and wearability. Several works [4, 5, 6, 7] proposed a single sensor on the lower trunk. SL can be derived from the center of mass acceleration measured along the progression direction using double integration [4, 5]. Indirect estimations can be obtained through empirical or model-based approaches. Empirical approaches rely on relations between SL and other parameters like the difference of maximum and minimum vertical acceleration [8], step frequency and acceleration variance [9], and acceleration magnitude [10]. Ho et al. [11] improved Weinberg’s model to enhance pedestrian dead reckoning at various speeds. Among model-based approaches, the inverted pendulum model of human gait introduced by Zijlstra et al. [12] highlights a relationship between vertical change of body center of mass and SL. Gonzalez et al. [6] improved this model by expressing the missing double stance phase as a quantity proportional to foot length. Zijlstra et al. [13] updated their method by introducing an individual correction factor and assessed its reliability. Technology acceptance is an essential requirement in fields like ambient assisted living, pervasive or ubiquitous healthcare. Perceived usefulness and usability are key factors for acceptability [14]. When dealing with health related applications, other crucial aspects are: miniaturization, embeddedness, inconspicuousness, networking, and context sensitivity [15, 16]. Smartphones are believed to fit these requirements and to be a promising tool to handle healthrelated services, joining usability, acceptability, and suitable technical characteristics [17].
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Background and objectives: The use of smartphones can greatly help for gait parameters estimation during daily living, but its accuracy needs a deeper evaluation against a gold standard. The objective of the paper is a step-bystep assessment of smartphone performance in heel strike, step count, step period, and step length estimation. The influence of smartphone placement and orientation on estimation performance is evaluated as well. Methods: This work relies on a smartphone app developed to acquire, process, and store inertial sensor data and rotation matrices about device position. Smartphone alignment was evaluated by expressing the acceleration vector in three reference frames. Two smartphone placements were tested. Three methods for heel strike detection were considered. On the basis of estimated heel strikes, step count is performed, step period is obtained, and the inverted pendulum model is applied for step length estimation. Pearson correlation coefficient, absolute and relative errors, ANOVA, and Bland-Altman limits of agreement were used to compare smartphone estimation with stereophotogrammetry on eleven healthy subjects. Results: High correlations were found between smartphone and stereophotogrammetric measures: up to 0.93 for step count, to 0.99 for heel strike, 0.96 for step period, and 0.92 for step length. Error ranges are comparable to those in the literature. Smartphone placement did not affect the performance. The major influence of acceleration reference frames and heel strike detection method was found in step count. Conclusion: This study provides detailed information about expected accuracy when smartphone is used as a gait monitoring tool. The obtained results encourage real life applications.
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Preprint submitted to Elsevier
June 20, 2017
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2. Materials and methods
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2.1. Smartphone application
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However, before using smartphones as gait analysis tools, a validation against a gold standard is needed. Such validation exists for other parameters, e.g. center of mass displacement [18], but not for SP and SL estimation. This study also evaluates heel strike (HS) detection and step count (SC), since it aims to carry out a step-by-step assessment of smartphone performance. Several methods have been proposed to identify HS from the acceleration of the lumbar region [5, 9]. Some works investigated the detection of gait events also on pathological subjects [19, 20, 21]. Trojaniello et al. [22] compared the performance of five gait events detection methods. None of these works used smartphones. Hence, the objective of this work was the assessment of smartphone accuracy for the step-by-step estimation of HS, SC, SP, and SL and to compare it to stereophotogrammetric measurements. In addition, three different HS detection methods as well as the influence of smartphone placement and orientation were evaluated. In the literature there are some works that use smartphones to estimate gait parameters like SL [11], however they differ from our contribution for the estimated parameters, the estimation model, the validation methods. Further important contributions of this work are the step-by-step assessment of smartphone performance and the investigation of smartphone orientation effects.
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An iPhone 4s (dimension 115.2 × 58.6 × 9.3 mm and weight 140 g) was used in the study. Fig. 1 shows the smartphone placements and its on-board accelerometer reference frame (RF) (blue). Two wearing placements were assessed: lower back (approximately L3-L4), and lateral side of the pelvis. In order to maintain accelerometer axes aligned to antero-posterior (AP), vertical, and medio-lateral (ML) axes of the subject the smartphone was fixed through an elastic belt and an appropriate socket. The executable file of the app is available among supplementary materials. The app acquires data from onboard sensors approximately1 at 100 Hz and stores them. The following data are saved: tri-axial acceleration in the smartphone RF (Fig. 1, blue RF), rotation matrix of smartphone RF with respect to a north RF, rotation matrix of the smartphone RF with respect to a particular RF defined manually, and finally the timestamp of each sample. The north RF is defined in the following way: positive x points towards magnetic north and positive z has the same direction of gravity but with opposite sign. For what concerns manual RF: positive y direction is inside a plane parallel to the floor and points toward the forward walking direction (like x-axis of laboratory RF in fig. 1), positive z is perpendicular to the floor and points upward. After launching, the application asks the user to calibrate the compass through a dedicated user interface. North RF and manual RF were used since the smartphone may introduce inaccuracies in sensor orientation. Once attached to the human body, contact between the wide phone surface and body contours can cause a misalignment between accelerometer axes and the axes of the laboratory RF (the red one in Fig. 1), that identifies the actual AP, ML, and vertical directions. Acceleration vector can be transformed through rotation matrices from the smartphone RF to north and manual RFs whose orientation with respect to laboratory RF is known.
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The reliability of the smartphone was evaluated by comparison with a stereophotogrammetric system (Elite, BTS Bioengineering) composed of six infrared cameras, which acquired the position of reflective markers in a fixed RF at 100 Hz sample frequency. Nine markers were placed on pelvis and feet, and one in the middle of the smartphone screen. The pelvis was identified by three markers: two over the left and right anterior superior iliac spines and the third on the middle point between the posterior superior iliac spines. Each foot was identified by three markers placed on: heel, first and fifth metatarsal head. HS time instants were identified through the inspection of heel markers trajectory. SP was obtained as difference between two consecutive HSs. SL was calculated as the difference between x coordinates of heel markers at HS time instants. 1 The
smartphone sample rate is not constant and accurate as an ”ad-hoc” inertial measurement unit or as sterephotogrammetry.
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2.4. Data processing Raw acceleration data are filtered through a low-pass and high-pass Butterworth filter (4th order, zero lag) with 20 Hz and 0.5 Hz cut off frequency respectively to avoid noise and drift and preserve frequency band significant for gait [7]. Time alignment between smartphone and infrared cameras was reached using the jump and data resampling. Smartphone’s samples timestamp was used to infer the actual sample frequency. A resample of the signal with lowest frequency between smartphone and infrared cameras was made to reach the same length. Then, the sample corresponding to the point of maximum height in the jump was selected as synchronizing time instant (see Fig. 2). HS identification can influence SC, SP and SL estimation, hence three HS detection methods were selected (on the basis of computational complexity and reported accuracy) from the literature and compared: the method of Zijlstra et al. [7] (M1), the one of Gonzalez et al. (M2) [23], and the one of McCamley et al. (M3) [24]. In M1, AP acceleration is low pass filtered at 2 Hz (4th order, zero lag Butterworth filter), then the zero-crossings from positive to negative are identified. Finally the last AP peak before each zero-crossing in the 20 Hz filtered AP acceleration is selected as HS [7]. In M2, AP acceleration is filtered through an 11th order FIR filter with 2 Hz cut off frequency, which introduces a five-sample delay. The area enclosed by each positive segment of the output signal is calculated. If this area is above a threshold (set at 0.025 [23]), the HS search is started, otherwise it is considered a false positive. The HS search occurs in the 20 Hz filtered AP acceleration, inside the same time interval used to calculate the area. In this time interval there may be several local maxima, but the peak that satisfies three heuristic rules [23] is chosen as HS. In M3, McCamley et al. [24] integrate and then differentiate vertical acceleration using a Gaussian continuous wavelet transform and they take the minima of the resulting smoothed signal as HSs. SC analysis can be done by comparing smartphone HSs and stereophotogrammetry HSs. SP is found as the time interval between two consecutive HSs. The inverted pendulum model [12] was selected as SL estimation method since it was considered the best tradeoff between reported accuracy [13, 10] and computational complexity: √ (1) sl = 2 2lh − h2
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2.3. Experimental procedures Before each experimental session, the visual field of cameras was calibrated by defining a measurement volume of about 3 m (length) × 2 m (width) × 2 m (height). The accuracy of the stereophotogrammetric system was evaluated during the calibration procedure and it reached an average error of (1.43 ± 0.77) mm in measuring a fixed markers distance. Eleven healthy subjects (8 males, 3 females), aged between 22 and 30 years, participated in the tests. Each subject performed 12 walking trials, 4 at preferred speed, 4 at higher speed and 4 at lower speed. One trial for speed was executed with the smartphone on the lateral side of the hip. During each trial, subjects had to walk forth and back along a straight platform (about 10 meters) inside the visual field of infrared cameras. Each trial started with the execution of a jump, which was used as synchronizing event. After each experimental session, the angle between magnetic north and walking platform was measured by a digital compass and used to align the north RF with the walking platform.
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where l is the length of subject’s leg, and h the vertical change of body center of mass during step cycle. The value of h can be computed from double trapezoidal integration of vertical acceleration between two consecutive HSs. The hypothesis of zero velocity at HS time instant provides the initial condition for the first definite integral and eliminates drift errors. The value of SL obtained with Eq. 1 underestimates the real SL, hence a multiplicative correction factor K must be applied. The least square method was used to find a subject specific K, and a leave-one-out crossvalidation method was applied to assess its robustness. Furthermore, a universal factor was also tested through a leave-one-out crossvalidation. The following function was minimized with respect to K: min ϕ(K) = min
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K∈[1;2]
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where [1; 2] is the domain of K, n is the number of steps, yi are the SLs measured from stereophotogrammetry, and sli are the SLs computed with the smartphone using a certain HS detection method and RF. The optimal value of K can 4
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vary across RFs and HS detection methods, hence the optimization process was repeated across all the combinations of RF and HS detection method.
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Sensitivity and specificity allow the evaluation of SC. They were computed as global percentage score considering all the trials together, and single trials scores. Pearson Correlation Coefficient (PCC) and one-way analysis of variance (ANOVA) were used to evaluate correlations and differences between smartphone detected steps and stereophotogrammetry recorded steps. HS, SL, and SP of smartphone correctly detected steps were compared to the corresponding steps of stereophotogrammetric system through PCC, absolute and relative (only for SL and SP) errors, ANOVA, BlandAltman 95% limits of agreement (only for SL and SP) [25]. Lilliefors normality test was applied to error, sensitivity, and specificity populations to verify the correctness of mean and standard deviation as statistical indicators. Performance metrics could be influenced by the following variables: speed, subject, smartphone placement, RF and HS detection method. Hence, they were computed across all possible scenarios generated by the combination of the involved variables. To be clearer and more concise this work only reports statistically significant scenarios. Statistically significant differences in performance metrics across subjects, velocities, smartphone placements, RFs, and HS detection methods were detected through ANOVA. The level of significance of all statistical tests was set to 0.05.
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The conducted tests collected 1298 steps: 974 with smartphone on the lower back, 324 on the hip. Mean and standard deviation values of subjects’ speed were: 1.08 ± 0.09, 1.41 ± 0.12, 2.25 ± 0.21 m/s for low, normal, high velocity. Subject specific correction factors K varied from 1.11 to 1.49 across the subjects (1.26 ± 0.08)2 ; intersubject mean correction factor is 1.25±0.013 . Velocity, subject, and smartphone placement did not have statistically significant influence on any performance metric. Performance differences between north and manual RF were not significant, hence in the following they will be generally referred as ”corrected RFs”. Experimental results are reported in Table 1, which includes four sections related to the considered variables: HS, SC, SP, and SL estimation. The next subsections present the results for each variable.
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Specificity was always 100%, hence it was not reported. Concerning smartphone alignment, a statistically significant difference between smartphone and corrected RFs was found only for M1 and M2. Both PCC and ANOVA p−values reveal that M3 and M1 (with the smartphone RF) provide a better estimation of walked steps (M2 performance was significantly different).
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A statistically significant difference was found between RFs, but the effect of a corrected RF is different across HS detection methods: performance improved for M1 and M2 and worsened for M3. No statistical significance was found between M1 and M2 in HS estimation, whereas it was observed between M3 and M1 or M2.
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No statistically significant differences were found across RFs, while a significant difference was found between M1 and M3. Absolute errors range from −0.002 ± 0.028 s and 0.00 ± 0.066 s; PCCs are above 0.89 and ANOVA p−values above 0.54. The 95% limits of agreement were ±0.127, ±0.113, ±0.074 s for M1, M2, and M3 (Fig. 3a). 2 Detailed 3 Detailed
values obtained from leave-one-out crossvalidation are shown in file ”intrasubj.xlsx” of supplementary materials. K values and SL estimation performance from leave-one-out crossvalidation are shown in file ”intersubj.xlsx” of supplementary
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4. Discussion
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The objective of this work was the assessment of smartphone accuracy in HS, SC, SP, and SL estimation through a step-by-step comparison with stereophotogrammetry. The influence of smartphone placement and orientation on estimation accuracy were analyzed as well. This work compares three different HS detection methods as each method may influence the other estimations. Smartphone errors in HS detection ranged between −0.007 and 0.012 s, which are comparable to previous works in the literature. Mean values for HS detection error ranged from −0.015 to 0.003 s in the work of Zijlstra and Hof [7], from −0.006 to 0.048 s in the work of McCamley et al. [24] and finally a mean error of 0.013 s was reported by Gonzalez et al. [23]. PCC and p−Value high scores suggest that the smartphone can provide a reliable estimate of HS time instant. SC sensitivity was always above 90% for M1 and M3 and above 80% for M2, with a 100% median value. These values are in accordance with the literature [20, 26]. The results about step-by-step SP and SL errors are not easily comparable with previous works, since they generally estimated mean values only. SP mean absolute errors ([−0.002, 0.000] s) and standard deviations ([0.028, 0.066] s) are in accordance with the literature [24], while lower standard deviations are reached by Zijlstra and Hof [7], possibly due to hardware differences. For what concern SL estimation, obtained error ranges (mean errors: [0.48, 1.12] cm, standard deviations: [5.21, 7.81] cm) highlighted that the smartphone does not deteriorate SL estimation accuracy with respect to previous works using dedicated hardware [13, 27, 6], confirming the potential of this device as a gait monitoring tool. Kose et al. [5], who performed a stepby-step evaluation, obtained mean errors of 0.9 ± 1.7 cm for right steps and −0.8 ± 1.6 cm for left steps. Lower errors may be due to the dedicated inertial measurement unit and the different estimation method, which requires the identification of other gait events than HS. Although smartphone placement and orientation could be possible sources of error, statistical analysis revealed that the placement does not affect the estimation accuracy. This is an important finding since the interest of the paper was to assess a technology that could be easily applied in a daily living context, and the sensor placement is a key factor for technology acceptance. Regarding the orientation, the most important influence of smartphone orientation regards SC. The decrease observed in performance metrics for M1 and M2 sensitivity with a corrected RF can be explained by acceleration components used for HS detection: AP for M1 and M2 (M2 uses also the vertical one in some conditions), vertical for M3. The rotation matrices used to obtain the north and manual RF were acquired from the smartphone, which computes them through an internal fusion algorithm4 integrating information of onboard sensors (gyroscope, magnetometer, accelerometer). In accordance with previous works [28, 26], the above finding suggests that smartphone’s internal algorithm that computes the rotation matrices can make mistakes in correcting traversal directions (e.g. due to a transient lost of compass calibration or an electromagnetic interference), while it is more robust for vertical direction. In conclusion, RF correction is suitable when using the vertical component, but not for AP or ML directions. For what concerns the influence of HS detection method, no influence was found in HS detection. Instead, for SC, SP, and SL estimation, statistical analysis indicated M1 and M3 as suitable solutions to maximize sensitivity, while M2 and M3 to reach lower errors in SP and SL estimation. Hence, the best choice might be application related, depending on real-time needs or application objectives. The need for a calibration of the correction factor K can be a possible drawback of this method. For interesting scenarios, like the monitoring of pathological gait [2], the calibration process could be carried out during the standard clinical examinations. Alternatively, the smartphone app could ask periodically the user to walk for a known distance and then use these data to calibrate the correction factor. For what concerns the possibility of using a universal
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3.4. Step length Differences between smartphone and corrected RFs are not significant for SL estimation. For what concerns HS detection method, although PCC values are always above 0.84, a significant difference was found between M1 and M3, and between M2 and M3. ANOVA p−values suggest M2 and M3 (p > 0.05) as better SL estimators than M1 (p < 0.05). Fig. 3b shows SL Bland-Altman plots: 95% limits of agreement are ±15.31, ±13.65, ±10.63 cm for M1, M2, and M3.
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algorithm is unknown because it is covered by trade secret.
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correction factor, our results confirm the findings of [13], that suggested 1.25 as standard value and found lower errors with a custom value.
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References
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The work was motivated by the necessity of an acceptable and usable tool for gait monitoring during daily living. The objective was the assessment of smartphone accuracy for the step-by-step estimation of HS, SC, SP, and SL against stereophotogrammetric measurements. Two important sources of error introduced by the smartphone were studied: smartphone placement and orientation. The obtained results revealed a good accuracy of smartphone estimation, thus justifying the use of the smartphone for gait monitoring. In particular, it was found that smartphone placement does not affect estimation accuracy, while the orientation mainly influences SC. The detailed information about expected accuracy can help choosing the best smartphone configuration (placement, reference frame, HS detection method) on the basis of the specific application scenario (e.g. which gait parameters should be monitored).
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[21] N. Chia Bejarano, E. Ambrosini, A. Pedrocchi, G. Ferrigno, M. Monticone, S. Ferrante, A novel adaptive, real-time algorithm to detect gait events from wearable sensors, Neural Systems and Rehabilitation Engineering, IEEE Transactions on 23 (3) (2015) 413–422. doi:10.1109/TNSRE.2014.2337914. [22] D. Trojaniello, A. Cereatti, U. D. Croce, Accuracy, sensitivity and robustness of five different methods for the estimation of gait temporal parameters using a single inertial sensor mounted on the lower trunk, Gait and Posture 40 (4) (2014) 487 – 492. doi:http://dx.doi.org/10.1016/j.gaitpost.2014.07.007. [23] R. Gonzlez, A. Lpez, J. Rodriguez-Ura, D. lvarez, J. Alvarez, Real-time gait event detection for normal subjects from lower trunk accelerations, Gait and Posture 31 (3) (2010) 322 – 325. doi:http://dx.doi.org/10.1016/j.gaitpost.2009.11.014. [24] J. McCamley, M. Donati, E. Grimpampi, C. Mazza, An enhanced estimate of initial contact and final contact instants of time using lower trunk inertial sensor data, Gait and Posture 36 (2) (2012) 316 – 318. doi:http://dx.doi.org/10.1016/j.gaitpost.2012.02.019. [25] J. M. Bland, D. Altman, Originally published as volume 1, issue 8476 statistical methods for assessing agreement between two methods of clinical measurement, The Lancet 327 (8476) (1986) 307 – 310. doi:http://dx.doi.org/10.1016/S0140-6736(86)90837-8. [26] X. Yang, B. Huang, An accurate step detection algorithm using unconstrained smartphones, in: Control and Decision Conference (CCDC), 2015 27th Chinese, 2015, pp. 5682–5687. doi:10.1109/CCDC.2015.7161816. [27] T. Sayeed, A. Sama, A. Catala, J. Cabestany, Comparison and adaptation of step length and gait speed estimators from single belt worn accelerometer positioned on lateral side of the body, in: Intelligent Signal Processing (WISP), 2013 IEEE 8th International Symposium on, 2013, pp. 14–20. doi:10.1109/WISP.2013.6657475. [28] M. Gietzelt, S. Schnabel, K.-H. Wolf, F. Bsching, B. Song, S. Rust, M. Marschollek, A method to align the coordinate system of accelerometers to the axes of a human body: The depitch algorithm, Computer Methods and Programs in Biomedicine 106 (2) (2012) 97 – 103, design of Environments for Ageing. doi:http://dx.doi.org/10.1016/j.cmpb.2011.10.014.
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Figure 1: Smartphone placements and reference frame of the onboard accelerometer (blue); laboratory reference frame (red).
(a)
(b)
Figure 2: Comparison between the marker (blue line) and the smartphone (green line) vertical position during a jump. The smartphone position was obtained from double integration of acceleration signal. Red dots indicate the point of maximum height in the two shapes. (a) Smartphone position in the smartphone reference frame. (b) Smartphone position in the north reference frame.
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Figure 3: (a) Bland-Altman plots for step period. (b) Bland-Altman plots for step length. In both graphs, the red line in the middle indicates the mean error and the other two lines the 95% limits of agreement.
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Table 1: Results about smartphone performance metrics. The table comprises four sections related to investigated variables: HS, SC, SP, and SL estimation. Table sections include nine rows related to the combinations of smartphone RFs and HS detection methods. Columns of each table section are the performance metrics chosen to evaluate the corresponding variable. They are reported as mean ± standard deviation, unless differently specified.
M1
M2
M3
SM NO MA SM NO MA SM NO MA
Step period M1
0.95 0.60 0.68 0.67 0.33 0.46 0.99 0.99 0.99
F(1, 262) = 0.29, p = 0.590 F(1, 262) = 9.96, p = 0.001 F(1, 262) = 8.56, p = 0.003 F(1, 262) = 16.87, p < 0.001 F(1, 262) = 38.72, p < 0.001 F(1, 262) = 35.02, p < 0.001 F(1, 262) = 0.01, p = 0.927 F(1, 262) = 0.01, p = 0.927 F(1, 262) = 0.01, p = 0.927
Error [s]
Error [%]
PCC
0.012 ± 0.056 0.005 ± 0.051 0.005 ± 0.050 0.010 ± 0.048 0.003 ± 0.044 0.005 ± 0.045 −0.003 ± 0.032 −0.007 ± 0.034 −0.007 ± 0.034
− − − − − − − − −
0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
Absolute Error [s]
Relative Error
PCC
ANOVA a
0.00 ± 0.09 0.00 ± 0.09 0.00 ± 0.1 0.00 ± 0.09 0.00 ± 0.08 0.00 ± 0.09 0.01 ± 0.05 0.00 ± 0.06 0.00 ± 0.06
0.90 0.90 0.89 0.91 0.93 0.92 0.97 0.96 0.96
F(1, 2566) = 0.37, p = 0.544 F(1, 2362) = 0.26, p = 0.608 F(1, 2388) = 0.29, p = 0.591 F(1, 2282) < 0.01, p = 0.939 F(1, 2078) = 0.01, p = 0.906 F(1, 2204) = 0.03, p = 0.857 F(1, 2592) < 0.01, p = 0.937 F(1, 2592) < 0.01, p = 0.953 F(1, 2592) < 0.01, p = 0.975
Relative Error
PCC
ANOVA a
0.01 ± 0.1 0.01 ± 0.09 0.01 ± 0.1 0.01 ± 0.09 0.01 ± 0.09 0.01 ± 0.09 0.00 ± 0.07 0.00 ± 0.07 0.00 ± 0.07
0.84 0.85 0.84 0.87 0.87 0.87 0.90 0.92 0.92
F(1, 2566) = 4.17, p = 0.041 F(1, 2362) = 3.70, p = 0.055 F(1, 2388) = 3.37, p = 0.067 F(1, 2282) = 2.40, p = 0.121 F(1, 2078) = 2.92, p = 0.088 F(1, 2204) = 2.25, p = 0.133 F(1, 2592) = 1.20, p = 0.274 F(1, 2592) = 0.89, p = 0.345 F(1, 2592) = 0.88, p = 0.349
0.000 ± 0.064 0.000 ± 0.064 0.000 ± 0.066 −0.001 ± 0.050 −0.001 ± 0.055 −0.001 ± 0.059 −0.003 ± 0.031 −0.002 ± 0.028 −0.002 ± 0.029
M3
Step length
M1
M2
M3
SM NO MA SM NO MA SM NO MA
Absolute [cm]
1.12 ± 7.68 1.07 ± 7.44 1.05 ± 7.81 0.98 ± 6.98 1.13 ± 6.86 0.91 ± 7.12 0.61 ± 5.95 0.49 ± 5.23 0.48 ± 5.21
Error
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100(100, 100) 100(100, 100) 100(100, 100) 100(80.91, 100) 100(63.64, 100) 100(65.48, 100) 100(100, 100) 100(100, 100) 100(100, 100)
Ac ce
M2
SM NO MA SM NO MA SM NO MA
98.61 90.52 91.29 87.75 80.15 81.12 99.77 99.77 99.77
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Heel strike
ANOVA a
ANOVA a
F(1, 3092) = 0.06, p = 0.806 F(1, 2870) = 0.01, p = 0.920 F(1, 2908) = 0.01, p = 0.924 F(1, 2796) = 0.04, p = 0.842 F(1, 2574) < 0.01, p = 0.954 F(1, 2634) = 0.01, p = 0.926 F(1, 3120) < 0.01, p = 0.955 F(1, 3120) = 0.03, p = 0.871 F(1, 3120) = 0.03, p = 0.869
an
M3
PCC
M
M2
SM NO MA SM NO MA SM NO MA
Median(25th, 75th) [%]
ed
M1
Sensitivity [%]
pt
Step count
Abbreviations: PCC, Pearson correlation coefficient; SM, smartphone RF; NO, north RF; MA, manual RF. Heel strike detection methods: Zijlstra et al. [7] (M1), Gonzalez et al. (M2) [23], McCamley et al. (M3) [24]. a p < 0.05: smartphone and stereophotogrammetric measures do not come from the same distribution.
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Conflict of interest: NONE.
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