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(a)
2
1.5
1
0.5
0
−0.5
−1
172.04
174.04
176.04
Time (s)
(b)
2
1.5
1
0.5
0
−0.5
−1
243.00
245.00
247.00
Time (s)
Fig. 4.8 Example of inertial signals from the accelerometer while performing two activities:
a walking, b walking upstairs
The acceleration signal is further processed as it is interpreted as the combined
effect of the gravitational force and the acceleration due to body motion. Therefore,
assuming that the gravitational component only affects the lowest frequencies, it is
possible to separate the body motion acceleration signal ( a
(
t
)
) through high-pass
filtering a ˄ (
with a cutoff frequency of 0.3 Hz. This threshold was calculated by
varying the cutoff frequency from 0.0 to 1.0Hz in small increments of 1
t
)
40Hz and
estimating the minimum square error of the filtered gravity signal minus the standard
/
gravity constant 9
s 2 using the experimental data. This findings were similar
to those in (Karantonis et al. 2006 ). The segmentation of the body acceleration is
represented with the transfer function H 2 ()
.
81 m
/
) can be
found by using the total acceleration and body acceleration in the following way:
. Finally, the gravity signal ( g (
t
)
g (
t
) =
a
˄ (
t
)
a
(
t
) .
(4.1)
Other works have also separated body acceleration and gravity in a similar way such
as in (Bruno et al. 2012 ).
Moreover, ω ˄ (
is also high-pass filtered in order to remove anyDCbias affecting
the gyroscope as it is one of the possible calibration errors that can be found in these
sensors. After filtering, using the same frequency values as in H 2 ()
t
)
,the ω (
t
)
signal
was obtained.
 
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