We used data from four studies, which, together, provide data for the three wearing locations, i.e., pendant, left-side of the chest, and left lower rib (see Figure 1
), and for various populations and walking conditions. Each of the studies complied with the principles laid down in the Declaration of Helsinki and all of the studies have been approved by the appropriate ethical committees that are related to the institution(s) in which they were performed. All of the participants provided informed consent. In total, 159 volunteers participated in the four studies, which resulted in a dataset with sufficient variation in walking speeds and conditions for all three wearing positions for algorithm performance assessment. Two types of acceleration sensors were used: GENEActiv, referred to here as “GA”, from Activinsights, 43 × 40 × 13 mm, recording three-dimensional (3D) accelerations at sampling frequency of 100 Hz, with +/−8 g range at 3.9 mg resolution, and a pendant device (Philips Research, Eindhoven, The Netherlands, approximate size: 39 × 12 × 63 mm), referred to here as “SMM” (more details and prior use have been described, for example, by Saporito et al. [10
]), with a triaxial accelerometer (Analog Devices ADXL362, range of ±8 G, sampling rate 50 Hz).
The first study, referred to here as “Young”, was carried out at Philips Research, Eindhoven, The Netherlands. Employees (18–65 years) without movement disorders that volunteered walked 100 steps over ground six times; at normal, slow, medium and irregular pace, and as asymmetric conditions walking with a weight in one hand and with an eraser fixed under one shoe. Three-dimensional (3D) accelerations were recorded at pendant (SMM, worn over the clothes), left chest (GA, worn in a belt strapped around the chest), and left lower rib (GA, attached to the skin using adhesive tape) locations. The reference speed was obtained by taking the distance from a laser distance meter at start and end of each condition, and while taking the time from the video annotations.
The second study, referred to here as “Out-Patients”, was carried out at Maxima Medical Center, Veldhoven, The Netherlands. Elderly patients presenting at the Outpatient Department of Internal Medicine were recruited for participation in the study. The inclusion criteria were age above 65 years, patients not using walking aids, not having allergies for leather, and not carrying any pacemaker device. The volunteers were asked to walk at normal pace for approximately one minute, back and forth over a 20 m distance, and finishing at one of the two turning points. 3D accelerations were recorded at pendant (SMM, worn over the clothes) and left chest (GA worn in a belt strapped around the chest) locations. The reference speed was obtained by video annotating time and distance.
The third study, referred to here as “Simulated Hospital”, was carried out at Philips Research, Eindhoven, The Netherlands. Adult (18–65 year) volunteers without movement disorders or allergies or sensitivities to leather, stainless steel, or medical grade adhesives were asked to walk on a treadmill at different speeds for two minutes, to simulate patient walking over ground with a walker, crutches, a rollator, and a pole for 1 min. each, and to perform a 6-min. walk test for maximum distance, referred to here as “Treadmill”, “Walking Aid”, and “6MWT”, respectively. 3D accelerations were recorded at pendant (GA, worn over the clothes), left chest (GA, attached with medical tape to the torso), and left lower rib (GA, attached with medical tape to the torso) locations. The reference speed for walking at the treadmill was taken as the speed that was indicated by the treadmill. The over ground walking activities were carried out indoors on a marked 30 m course and the distance was measured by the researcher at the end of each activity (timed using a stop watch), with video present to check annotations, if needed. More details of this data collection study can be found in the paper of Fridriksdottir and Bonomi [11
The fourth study, referred to here as “Community”, was carried out under the iStoppFalls project [12
]. Older (≥ 65 years), medically stable volunteers living in the community and not suffering from major cognitive impairment or neurogenerative disease were assessed in the laboratory and then walked a distance of 14 m twice at their comfortable normal walking speed, while wearing an SMM around at the pendant location under their clothes. The middle 10 m were timed with a stopwatch. To enable this, there were tape lines on the floor at 0, 2, 12, and 14 m, and recording started when the person made first contact with the 2m line and it was stopped when the person made first contact with 12 m line. Table 1
presents the demographics of the four studies.
2.3. Estimation of Walking Speed
The IP method for speed estimation assumes that, during the single support phase, the body center of mass (CoM) follows a circular trajectory with a radius l
equal to leg length, thereby leading to CoM height changes that are directly related to step lengths s
, where ∆h is the maximum height difference within a step. The average speed estimation is obtained by dividing the sum of step lengths by the sum of step durations, and then multiplying by an empirical factor of 1.25 as
]. The method that we evaluated was similar to the one used in [13
], which estimates the length of each half step as
, where ∆h is the absolute peak-to-peak height change. We now estimated the peak-to-peak height change as the absolute difference between each peak and the average of the two adjacent peaks with an opposite sign; therefore, per step, we estimated two half step lengths, one for a negative and one for a positive peak. The height signal was estimated as the second integral of the vertical acceleration, which was estimated by the acceleration norm. We high pass filtered the signal forward and backward at each process of integration to derive the height from acceleration (i.e., as accelerations, velocities, and heights) with a second order Butterworth filter with a cut-off frequency of 0.5 Hz. The cut-off frequency was increased from 0.1 Hz in the paper from Zijlstra and Hoff [7
] to 0.5 Hz, in order to further limit effects of integration drift that may lead to large errors in height differences. This may be especially relevant when using a pendant, because of short bounces. The cut-off frequency was limited to 0.5 Hz to stay below realistic step frequencies.
We updated the method to account for lateral movements in the step trajectory in order to improve estimates for slow walking speeds. First, step lengths become small in slow walking [14
], which makes the effect of lateral movement on the height changes more prominent. To correct for this, we assumed that the circular trajectory of the CoM during a step consists, horizontally, of an anterior and a lateral component, the Euclidian length of which, or the horizontal step length, determines the height change. Thus, in order to account for the lateral movement, we subtracted an estimate of the distance of lateral movement from the estimated horizontal step length in a quadratic way as
is the anterior (or forward step length) and
is the horizontal step length. The lateral movement
was estimated as 5.4° or 0.094 times the leg length l
]. Figure 2
shows the variables that were used in the IP model and in the updated model, including the addition of lateral movement (Figure 2
b), and Figure 3
shows the signals at the different stages of the algorithm.
Secondly, due to movement variability, additional peaks may disturb the limited height changes in slow walking, leading to more than one positive and one negative height peak appearing per step. The additional peaks, even if they are small, can substantially increase the summed step lengths, due to the non-linear relation between height change and step length. Therefore, we filtered peaks by a minimum prominence. The threshold for the minimum prominence was set to , which is equal to a height change that corresponds to a forward step length , given the subtraction of the estimated lateral movement distance .
The mean speed for each walking activity was estimated and compared to the reference speed. As validation statistics, we used Pearson correlation (R), root mean square error (RMSE), and mean absolute error (MAE) per study and device location combination. For Simulated Hospital, the results for Treadmill, 6MWT, and Walking Aids were separately determined. We also determined the statistics for all data combined, and for all data from speeds <0.5 m/s as well as for all data from speeds ≥0.5 m/s.
For the (absolute/ squared) errors, we determined the p-values to determine whether the results for the updated IP method were statistically significantly different (p < 0.01) from the IP method for the same data. This was done using Wilcoxon signed-rank tests, as the differences were not normally distributed (Shapiro–Wilk test for normality, p < 0.05). To compare the results between wearing positions, we selected the subset of data for which measurements were available for all three sensor locations and determined MAE per wearing position for all of these data combined, for the data from speeds < 0.5 m/s as well as for the data from speeds ≥ 0.5 m/s. For these MAEs, we calculated the p-values using Wilcoxon signed-rank tests for comparisons between the different positions.