gyro ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
g 2
x þ g 2
y
q
ð2Þ
(3) During the process of collecting data, we found that in some cases, the occurrence
of acceleration peaks has a certain degree delay compared to the angular velocity
peaks. The result of the analysis is the same: When the human body falls, the
upper body is first dumped. In this process, the angular velocity reaches a peak at
a certain moment; when the human body touches the ground, the acceleration
reaches a peak. In addition, the acceleration can also reach an acceleration close to
the fall when running and jumping; thus, we consider the importance of angular
velocity > the importance of acceleration.
(4) According to the data analysis (Table 1), in order to distinguish the acceleration
and angular velocity between falling and daily activities, the angle is introduced to
judge the falling. Due to the “90° Euler angle limitation” and the complicated
triangulation in real time, we choose to use the quaternion method to calculate the
angle. Quaternion: An object can reach any attitude by rotating around an axis to a
certain angle. In the process of calculating the angle, the “full-field positioning”
algorithm is used combined with the real-time acceleration correction on angular
velocity: According to the previous gravity unit vector and the gravity unit vector
obtained by this measurement, the cross-product of two is obtained for correcting
angular velocity. Then, quaternion (q 0 , q 1 , q 2 , q 3 ) is updated according to
“Runge–Kutta of the first order,” so that the triaxial rotation angles “t x ”, “t y ”, and
“t z ” relative to the heaven and earth coordinate system are [9, 10]:
t x ¼ a sin À2 Ã q 1 Ã q 3 þ 2 Ã q 0 Ã q 2
ð
Þ Ã 57:3
ð3Þ
t y ¼ a tan 2 2 Ã q 2 Ã q 3 þ 2 Ã q 0 Ã q 1 ; À2 Ã q 1 Ã q 1 À 2 Ã q 2 Ã q 2 þ 1
ð
Þ Ã 57:3
ð4Þ
tz ¼ a tan 2 2 Ã q 1 q 2 þ 2 Ã q 0 q 3 ; À2 Ã q 2 q 2 À 2 Ã q 3 q 3 þ 1
ð
Þ Ã 57:3
ð5Þ
Table 1. Three-dimensional data in different scenes
Design of Elderly Fall Detection Based on XGBoost
49
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
g 2
x þ g 2
y
q
ð2Þ
(3) During the process of collecting data, we found that in some cases, the occurrence
of acceleration peaks has a certain degree delay compared to the angular velocity
peaks. The result of the analysis is the same: When the human body falls, the
upper body is first dumped. In this process, the angular velocity reaches a peak at
a certain moment; when the human body touches the ground, the acceleration
reaches a peak. In addition, the acceleration can also reach an acceleration close to
the fall when running and jumping; thus, we consider the importance of angular
velocity > the importance of acceleration.
(4) According to the data analysis (Table 1), in order to distinguish the acceleration
and angular velocity between falling and daily activities, the angle is introduced to
judge the falling. Due to the “90° Euler angle limitation” and the complicated
triangulation in real time, we choose to use the quaternion method to calculate the
angle. Quaternion: An object can reach any attitude by rotating around an axis to a
certain angle. In the process of calculating the angle, the “full-field positioning”
algorithm is used combined with the real-time acceleration correction on angular
velocity: According to the previous gravity unit vector and the gravity unit vector
obtained by this measurement, the cross-product of two is obtained for correcting
angular velocity. Then, quaternion (q 0 , q 1 , q 2 , q 3 ) is updated according to
“Runge–Kutta of the first order,” so that the triaxial rotation angles “t x ”, “t y ”, and
“t z ” relative to the heaven and earth coordinate system are [9, 10]:
t x ¼ a sin À2 Ã q 1 Ã q 3 þ 2 Ã q 0 Ã q 2
ð
Þ Ã 57:3
ð3Þ
t y ¼ a tan 2 2 Ã q 2 Ã q 3 þ 2 Ã q 0 Ã q 1 ; À2 Ã q 1 Ã q 1 À 2 Ã q 2 Ã q 2 þ 1
ð
Þ Ã 57:3
ð4Þ
tz ¼ a tan 2 2 Ã q 1 q 2 þ 2 Ã q 0 q 3 ; À2 Ã q 2 q 2 À 2 Ã q 3 q 3 þ 1
ð
Þ Ã 57:3
ð5Þ
Table 1. Three-dimensional data in different scenes
Design of Elderly Fall Detection Based on XGBoost
49