Information Technology Reference
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Table 4.3
Main signal
processing operations applied
to the smartphone sensors
inertial signals
Name
Symbol
Formulation
Total acceleration
a
˄
(
t
)
H
1
(
a
r
(
t
))
Body acceleration
a
(
t
)
H
2
(
a
˄
(
t
))
Gravity
g
(
t
)
a
˄
(
t
)
−
a
(
t
)
a
(
Body jerk
t
)
d
(
a
(
t
))/
dt
Body acc magnitude
a
mag
(
t
)
a
(
t
)
Angular speed
ω
(
t
)
H
2
(
H
1
(
ω
r
(
t
)))
ω
(
Angular acceleration
t
)
d
(
ω
(
t
))/
dt
Angular speed magnitude
ˉ
mag
(
t
)
ω
(
t
)
The outcome after noise filtering and signal segmentation consists of three signals:
a
. They are informative about the user's body motion, the person's
orientation (e.g. helpful for the distinction of lying-down and standing states), and
motion patterns people have for performing some activities (e.g. for recognizing AAs
and PTs). An additional transformation is performed to (
a
(
t
)
,
g
(
t
)
and
ω
(
t
)
(
t
)
and
ω
(
t
)
). This is the
derivative with respect to time (
a
(
and
ω
(
) which has shown to be informative in
order to extract relevant activity-related features and it has already been successfully
used in some applications such as in the detection of ON/OFF states on PD patients
(Samà et al.
2011
). Lastly, the magnitude (Euclidean norm) is also applied to the
triaxial inertial signals in order to obtain
a
mag
(
t
)
t
)
t
)
and
ˉ
mag
(
t
)
. A compilation of the
signal transformations is presented in Table
4.3
.
Following these steps, the signals are segmented into window samples which
are the activity unit of this work. In this manner, every window unequivocally has
an associated activity. Window sampling is done in a fixed-width sliding windows
fashion. We use a 50% overlap between windows as it has shown to be suitable for
various recognition applications (Bao and Intille
2004
; Van Laerhoven and Cakmakci
2000
) in order to avoid missing events and activity truncation. Moreover, we chose
an activity window length of 2.56 s guided by the following reasons:
•
The cadence of an average person walking is within [90
,
130] steps/min
(Abdelkader et al.
2002
), i.e. a minimum of 1.5 steps/s;
•
At least a full walking cycle is preferred on each window sample, this corresponds
to a minimum of two steps;
•
People with slower cadence such as elderly and disabled people withmotor impair-
ments should also benefit from this method. We supposed a minimum speed equal
to 50% of average human cadence;
•
Signals are also mapped in the frequency domain through the Fast Fourier
Transform (FFT), which is optimized for vectors with power of two length:
N
=
(
2
.
56 s
×
50 Hz
=
128 cycles
)
.
•
Longer windows sizes were not preferred as they would increase the latency times
in the prediction of activities when used online.
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