Estimation of Vertical Walking Ground Reaction Force in 1 Real-life Environments using Single IMU Sensor 2

32 Monitoring natural human gait in real-life environments is essential in many 33 applications, including quantification of disease progression, monitoring the effects of 34 treatment, and monitoring alteration of performance biomarkers in professional sports. 35 Walking ground reaction forces are among the key parameters necessary for gait 36 analysis. However, these parameters are commonly measured using force plates or 37 instrumented treadmills which are expensive and bulky and can only be used in a 38 controlled laboratory environment. Despite the importance of real-life gait 39 measurement, developing reliable and practical techniques and technologies necessary 40 for continuous real-life monitoring of gait is still an open challenge, mainly due to the 41 lack of a practical and cost-effective wearable technology for ground reaction force 42 measurement. This paper presents a methodology to estimate the total walking ground 43 reaction force 𝐺𝑅𝐹 𝑣 (𝑡) in the vertical direction using data from a single inertial 44 measurement unit. Correlation analysis of the vertical acceleration of different body 45 segments with 𝐺𝑅𝐹 𝑣 (𝑡) indicated that the 7 th cervical vertebrae is one of the best 46 locations for the sensor. The proposed method improves the accuracy of the state-of- 47 the-art 𝐺𝑅𝐹 𝑣 (𝑡) estimation by 25%, by utilising the time-varying ratio of the vertical 48 acceleration of the human body centre of mass and measured C7 vertical acceleration. 49 Results of this study showed that the proposed method estimated consistently the 50 𝐺𝑅𝐹 𝑣 (𝑡) in both indoor and urban outdoor environment, with a 4-8% peak-to-peak 51 normalised root mean square error. 52

This study shows that this assumption might be simplistic and aims to advance the 70 state-of-the-art in estimation of ( ) from measured body acceleration by 71 proposing an alternative methodology, termed 'Scaled Acceleration' (SA) method, to 72 estimate ( ) with higher accuracy and versatility. This research is an initial step 73 towards developing a practical wearable sensory system to measure full body 3D 74 kinematics and tri-axial walking ground reactions. Such system is envisaged to 75 ultimately enable full gait analysis (including inverse dynamics) in real-life 76 systems at the beginning of each test. The raw kinematic data (tri-axial displacements) 125 were filtered using a low pass zero lag fourth-order Butterworth digital filter with a 126 cut-off frequency of 12 Hz to remove noise while preserving the frequency contents 127 related to the first four harmonics of ( ). The displacement signals from the 128 motion capture system were then differentiated twice to find the corresponding 129 acceleration signals (Zijlstra, 2004). The motion capture data were used in Section 2.2, 130 and only the IMU-measured accelerations were used in the rest of the study for model 131 development and validation. 132 From the six test participants (25 tests), 20 randomly selected tests pertinent to the 133 subjects S1-S4 were chosen for developing the methodology, and the remaining five 134 test data, including S5 and S6 tests, were used for validation. 135 For the purpose of the analysis presented in this study, the data pertinent to each 136 complete gait cycle were extracted from the measured time histories and saved as 137 separate data blocks. In total, 2,134 complete gait cycles were extracted from 25 tests. 138 As the proposed SA method (Section 2.3.2) relies on identification of each gait cycle 139 from measured ̈, 7 ( ) signal to estimate ( ), a complete gait cycle was 140 assumed to start and finish at the ̈, 7 ( ) single-stance local minima for a specific leg 141 ( Figure 2). This assumption was made based on our observation that the single-stance 142 local minimum point could be identified robustly and with high accuracy from 143 measured ̈, 7 ( ) data for different walking regimes. 144

Relation between
( ) and body kinematics 145 Based on the second Newton law and assuming that the human body is comprised of n 146 solid segments, walking ( ) can be estimated using: 147 where, is the segment 'i' mass and ̈, ( ) is its CoM vertical acceleration. For each 149 segment 'i', ̈, ( ) is calculated using motion capture data and the relative location of 150 markers on the segment with respect to the location of it's CoM. 151 The ( ) signal estimated using measured ̈, ( ) of all 13 segments (n=13) in 152 Equation 2 is termed 'reference estimated GRF' ( , ( )) in this paper. 153 These errors are mostly associated with assuming solid body segments, frictionless pin 161 joints, anthropometric measurements, and skin artefacts (Winter, 1991). 162 For long-term continuous measurement, however, it is not practical to measure ̈, ( ) 163 of all 13 segments and the number of sensors has to be minimised. To find the best 164 location(s) on the body for IMU sensor(s), the Pearson linear correlation of the 165 measured ̈, ( ) and corresponding ( ) signals were analysed for all tests, and 166 their average values are compared in Figure 3a. The cross-correlation coefficients 167 were calculated for each test using Equations 4 and 5 (Fisher, 1958;Kendall, 1979) as CCM generally tends to overestimate ( ) peak-to-peak values (IEEE, 2003). 210 Figure 4b shows the optimal coefficient corresponding to the subjects S1-S4 tests. 211 For each test, is found so that it minimises the NRMSE error between the estimated 212 and measured ( ) signals. As can be seen in Figure 4b, the optimal coefficient 213 varies between 0.78-0.96, with no obvious dependence on the walking speed. It was 214 further found that, similar to the walking speed, γ shows no significant correlation during a gait cycle (Figure 4c This is based on the observation that ( ) signals pertinent to different gait cycles 223 exhibit similar patterns, as is shown in Figure 5 for tests pertinent to subjects S1-S4. 224 This means a 'template' ( ) signal can be found for a gait cycle and used to 225 estimate ( ) from measured ̈, 7 ( ) in Equation 7. The overarching idea is to 226 find a template ( ) signal for a specific cohort of people and type of activity, and 227 then use that template ( ) to estimate ( ) from measured ̈, 7 ( ) in Equation 228 7. The procedure to find ( ), as explained below, requires the direct measurement of 229 ( ). However, once the ( ) signal is calculated, the SA method can estimate 230 ( ) (for that cohort/activity/gait pathology) only using the measured ̈, 7 ( ). 231 The following process was carried on tests pertinent to subjects S1-S4 to calculate 232 To increase the accuracy of the estimated ( ), it is desirable to be able to adjust 281 both the timing and amplitude of the ( ) for each gait cycle. The timing of the ( ) 282 cycle, so that the resulted gait-specific ( ) yield the best prediction of ( ). 286 To adjust the ( ) amplitude, for each gait cycle, a scaling coefficient β was found 287 with trial and error, where β× ( ) best matches (minimum NRMSE) the 288 corresponding ( ). Then, the correlation of β and max (̈, 7 ( ))/max (̈, 7 ( )) 289 ( Figure 7a) and min (̈, 7 ( ))/min (̈, 7 ( )) ( Figure 7b) were analysed. It was found 290 that β and = min (̈, 7 ( ))/min (̈, 7 ( )) have the higher correlation (Figure 7). 291 Therefore, Equation 9, which describes their linear relationships, was incorporated 292 into the SA method to adjust the amplitude of the ( ) for each gait cycle: 293 = 0.62 + 0.63 (Eq. 9) 294

( ) ESTIMATION PROCEDURE 295
The SA method proposed in this study estimates ( ) using the ̈, 7 ( ) measured 296 using a single IMU at C7 and the weight of the subject. The SA method involves the 297 following steps: 298 I.
The tri-axial acceleration signals measured by the IMU at C7 in its local 299 coordinate system are re-oriented to the global/earth coordinate system using 300 the orientation of the sensor measured by the IMU (quaternions) in the global 301 coordinate system. 302

II.
The measured ̈, 7 ( ) signal is filtered using a low pass zero lag fourth-order 303 Butterworth digital filter with a cut off frequency of 12Hz, and the 304 gravitational constant is removed. 305 III.
The start and end point of gait cycles are identified by finding single-stance 306 local minima for a specific leg, i.e. every other single-stance local minima in 307 the measured ̈, 7 ( ) signal (Figure 8a). 308

IV.
For each gait cycle q with a period of (0 ≤ ≤ ): 309 a. The template ̈, 7 ( ) and ( ) signals that were calculated earlier, 310 are resampled to match the length of the measured ̈, 7 ( ) signal. 311 b. The resampled ̈, 7 ( ) signal is warped to the measured ̈, 7 ( ) 312 using the modified DTW method (Figure 8b). 313 c. The same warping adjustments are applied to the ( ) signal to 314 adjust its timing to the gait cycle q (Figure 8c).  method, for a randomly selected measured ( ) signal from the tests dataset. As 346 can be seen in Figure 10a, the accuracy and fidelity of the ( ) estimated by the 347 SA method is considerably better than the corresponding synthetic ( ). 348

349
To analyse the performance of the SA method in real-life environment, a set of tests 350 were carried out where 10 subjects (5 males, 5 females, age: 21 ± 4 years, weight: 73 351 ± 17 kg and height: 1.70 ± 0.18 m) were asked to walk normally in an urban 352 environment around the University of Sheffield campus on pedestrian footpaths, while 353 wearing a pair of Tekscan F-Scan in-shoe pressure insoles (Tekscan, 2016) and an 354 Opal IMU at C7. The walking pathway was characterised with flat parts as well as 355 mild up-hills and down-hills. The IMU's tri-axial acceleration signals were reoriented 356 from the sensor's local coordinate system to the laboratory fixed coordinate system 357 using the orientation (quaternions) measured by the sensor. All the measured data 358 were re-sampled at 100Hz and synced in MATLAB software (Mathworks, 2016) 359 using a trigger sync signal recorded on Opal and Tekscan systems at the beginning of 360 each test. 361 The pressures measured under both feet were used to calculate ( ). The pressure 362 data were calibrated using the instrumented treadmill GRFs before and after each trial 363 to minimise the time-varying calibration errors. The calibration analysis showed that, 364 even with calibration both at the beginning and end of each test, an NRMSE of 2-5% 365 is inevitable in the measured ( ) signals using pressure sensors data. 366 Figure 10b shows a typical performance of the SA method in estimating ( ) in an 367 outdoor environment. The NRMSEs of the estimated ( ) in these outdoor tests 368 were found to be between 7-11%. Considering the NRMSE of 2-5% due to pressure 369 insoles data (compared with the instrumented treadmill data), it was concluded that the 370 performance of the SA method in the outdoor and laboratory environment was similar. information is otherwise absent, and currently impossible to predict using synthetic 379 walking force models. Further research is needed to improve the accuracy, versatility 380 and robustness of these data-driven models. 381 The key limitations of this study are: