to the acceleration and deceleration of the treadmill at
the start and end of each run the middle 90 steps were
taken from each run to provide a total of 1440 steps
for analysis.
Once data collection was complete the signals
were subsequently downsampled in order to simulate
lower sampling rates. Integer downsampling factors
were used so that interpolation was avoided.
Downsampling for a given downsampling factor,
M, proceeded as a two step process. Firstly, to avoid
aliasing affects, the data was low-pass filtered. A 4th
order butterworth filter was used with a cut off fre-
quency of 0.8 f s
t
where f s
t
=
f s
b
M
and f s
t
is the target
sampling rate with f s
b
the base sampling rate used by
the ION sensor platform (always 1kHz). Secondly,
the resulting signal was decimated by retaining every
M
th
sample.
An Extended Kalman Filter (EKF), paired with an
inertial strapdown algorithm, was used to recreate the
trajectory of the foot from the inertial data (Bailey and
Harle, 2014; Foxlin, 2005). The speed of the treadmill
belt was applied as a pseudo measurement during the
mid-stance phase of gait along with a zero-foot height
pseudo measurement.
As an example of the kind of output that this tech-
nique can enable, Figure 2 contains two example steps
from two different people running at the same speed.
Differences in technique can be seen between the two
in these 2D plots. While 3D plots are possible we use
a 2D plot here to make the differences clearer.
This method was applied to each run from each
participant at each downsampling factor. The down-
sampling factors used produced the equivalent of
500Hz, 250Hz, 125Hz, and 62.5Hz in addition to the
1000Hz raw signal.
The technique creates a rich set of data detailing
the velocity, position and angle of the foot at the time
each inertial sample was taken. For trajectory evalua-
tion the position, velocity and attitude error is calcu-
lated for each step. Errors are calculated stepwise as
offsets in position at the start of the step are irrelevant
for an assessment of the step, therefore the ground
truth and inertial solutions are aligned in space before
calculating the following metrics.
Position error was calculated in the following
way:
s
error
(i, k) = ks
inertial
(i, k) −s
vicon
(i, k)k (1)
and velocity error was calculated as:
v
error
(i, k) = kv
inertial
(i, k) −v
vicon
(i, k)k (2)
where i is the step number and k sample number
within step i. Error in attitude was assessed as
θ
err
(i, k) = arccos
A.B
kAkkBk
(3)
Where A and B represent the vector [0, 0, 1]
T
in the
sensor’s frame of reference as measured by the INS
solution and Vicon respectively.
Figure 3 shows how sampling rates affect the
mean error in position, velocity and attitude. The
graphs show that with sampling rates lower than
250Hz the position and velocity error starts to in-
crease rapidly meaning that 1kHz is unnecessary and
in order to reduce sensor requirements a lower sam-
pling rate may be used without a large affect on accu-
racy up to 250Hz. Attitude errors were not as affected
by lower sampling rates staying stable until 125Hz.
Examples of the full 3D trajectory recovered by
the system are shown for two representative steps in
Figure 4 where the lower sampling rate has resulted
in much poorer performance.
4.2 Sensor Requirements
In order to find optimal sensor parameters we con-
ducted an experiment to determine the requirements
for the range of the accelerometer and gyroscope.
This is important to make sure that sensors do not sat-
urate during running as this may impair the accuracy
of the measurement obtained using strapdown tech-
niques.
Parameters that affect these requirements are sam-
pling rate, running speed and the characteristics of the
running surface.
Sampling rates affect sensor requirements due to
the low pass filtering required before the signals en-
ter the ADC. Before sensor signals are quantised, it
is usually necessary to low-pass filter the signal (in
the analogue domain) to a bandwidth of less than half
of the sampling rate (Nyquist rate) to ensure aliasing
artifacts are avoided. This low-pass filtering has the
effect of reducing peak accelerometer and gyroscope
signals. Sensor range requirements are therefore re-
duced as the sampling rate is also reduced. We there-
fore assess peak accelerations for running while using
differing sampling rates.
The accuracy of the algorithms used in (Bailey
and Harle, 2014) to assess running kinematics have,
so far, been assessed using a treadmill. While in use
treadmills may flex visibly as the runner hits the tread-
mill belt. This may reduce the peak accelerations ob-
served at impact. Since the primary use case of such
sensing is in overground running outside, we investi-
gated the effect of a number of outdoor surfaces on
the sensor range requirements as these are likely to be
larger than for a treadmill. For example, impact accel-
erations on tarmac are likely to be distinct from those
of grass or treadmill running.
Accelerometer and gyroscope data were collected
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