TSINGHUA SCIENCE AND TECHNOLOGY

ISSN 1007-0214 17/32 pp695−707

DOI: 1 0 . 2 6 5 9 9 / T S T . 2 0 2 3 . 9 0 1 0 1 2 9
Volume 30, Number 2, April 2025

A Fall Detection Device Based on Single Sensor

Combined with Joint Features

Li Zhang*, Yu-An Liu*, Qiuyu Wang, Huilin Chen, Jingao Xu, and Danyang Li

Abstract: Accidental falls pose a significant threat to the well-being of the elderly, thus facilitating a quantum
leap in the field of fall detection technology. For fall detection, accurate identification of fall behavior is a key
priority. Our study proposes an innovative methodology to detect falls during activities of daily living (ADL), with
the objective of preventing further harm. Our design aims to achieve precise identification of falls by extracting
a variety of features obtained from the simultaneous acquisition of acceleration and angular velocity data using
a single sensor. To enhance detection accuracy and reduce false alarms, we establish a classifier based on the
joint acceleration and Euler angle feature (JAEF) analysis. With the aid of a support vector machine (SVM)
classifier, human activities are classified into eight categories: going upstairs, going downstairs, running,
walking, falling forward, falling backward, falling left, and falling right. In particular, we introduce a novel
approach to enhance the accuracy of fall detection algorithms by introducing the Equal Signal Amplitude
Difference method. Through experimental demonstration, the proposed method exhibits a remarkable
sensitivity of 99.25%, precision of 98.75%, and excels in classification accuracy. It is noteworthy that the
utilization of multiple features proves more effective than relying solely on a single aspect. The preliminary
findings highlight the promising applications of our study in the field of fall injury systems.

Key words: fall detection; support vector machine; wearable sensor; activity recognition

1 Introduction annual basis[2]. It is pertinent to note that falls can be

classified into four fundamental types, comprising
The phenomenon of falls represents a momentous
falling forward, falling backward, falling left, and
threat to the elderly and disabled population, often
falling right[3]. Clinical studies underscore the
acknowledged as the “fatal killer”[1]. Recent empirical importance of precise, rapid, and robust multi-
evidence from the Centers for Disease Control and directional fall detection. This aids clinicians in
Prevention reveals that no less than 25% of individuals promptly identifying the injured joint and minimizing
aged 65 and above encounter incidents of falling on an fall-related damage. Multi-directional data can shed
Li Zhang, Yu-An Liu, Qiuyu Wang, and Huilin Chen are with light on the most likely site of the initial head hit,
School of Mathematics, Hefei University of Technology, Hefei especially in cases of cerebral hemorrhage and brain
230009, China. E-mail: lizhang@hfut.edu.cn; yuanliu@ damage.
gmail.com; 2020111428@mail.hfut.edu.cn; 2021111448@mail. Therefore, the precise and expeditious identification
hfut.edu.cn. of falls occurring in multiple directions necessitates the
Jingao Xu and Danyang Li are with School of Software and
utilization of specific and efficacious techniques. We
also with BNRist, Tsinghua University, Beijing 100084, China.
E-mail: xujingao13@gmail.com; lidanyang1919@gmail.com.
studied numerous posture estimation-based or human
motion-induced improved methods in ambient signal-
* To whom correspondence should be addressed.
Manuscript received: 2023-04-20; revised: 2023-10-17; detecting systems for falls. Currently, most fall
accepted: 2023-10-29 detection systems can only determine the incidence of

© The author(s) 2025. The articles published in this open access journal are distributed under the terms of the
Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
 696 Tsinghua Science and Technology, April 2025, 30(2): 695−707

a fall, usually divided into two different categories. features collected by accelerometers and gyroscopes to
(1) Environmental device-based systems, like discover the fall. Wu and Xue[20] and Bourke et al.[21]
radar[4], microphone[5], radio-frequency devices[6], used the vertical velocity characteristics of the human
cameras[7], and multimodal approach[8], detect fall body in descending stage to detect descending, which
activity largely by the deployment of particular requires using data from accelerometers and
detection modules. The primary limitation of wearable gyroscopes to calculate vertical velocity. Gao et al.[22]
technology resides in its limited perspective. fixed four sensors to the waist, thigh, chest, and sides
Additionally, the use of cameras in this context raises of the body to detect falls. Nyan et al.[23] discovered
concerns about potential infringements on personal falls by evaluating data correlations between thigh and
privacy. waist. Wang et al.[24] saw and processed wireless signal
(2) Wearable technology captures both translational channel state information (CSI) data and identified
and rotational movements on the body through abnormal CSI sequences using local outlier factor
miniature sensors, enabling the detection of falls[9–11]. technology. Nevertheless, these methods of fall
Its portability and ubiquitous computing capabilities detection suffer from the following limitations: (1)
are notable advantages. Relying on thresholds to discern between falls and
To achieve exact fall detection, pose signals or activities of daily living (ADL) poses difficulties in
environmental signals are employed. Lai et al.[12] used adapting to dynamic fluctuations in the environment.
six accelerometers distributed throughout the body to (2) The utilization of numerous sensors to gather data
accurately measure various postures and identify introduces intricacy and reduces overall versatility.
accidental falling episodes. Nevertheless, this approach Conventional classification methods have been
lacks the capacity to determine the direction of descent. widely utilized in the domains of fall detection and
Wang et al.[13] proposed a real-time contactless fall activity recognition[25]. A neural network was proposed
detection system using common WiFi devices. The by Ref. [26] to recognize falls and non-falls. Yu
limitations of vision-based posture estimation methods et al.[27] developed a video image processing-based
lie in the constraints posed by flexibility and available online SVM algorithm to acknowledge falls. Shen
space. Furthermore, these methods often rely on et al.[28] developed a high-level fuzzy Petri net-based
individual scenarios and varying conditions. fall detection system. They placed the smartphone in
Recent studies have highlighted the efficacy of their thigh pocket for fall protection while studying.
wearable technology in the detection and recognition of Real-world situations can present particular challenges.
incidents involving falls. Lu et al.[14] created an energy- To exemplify, while walking, the positional
saving barometer with a maximum specificity of 98.0% relationship of a smartphone remains variable and
and a maximum sensitivity of 96.1% for detecting falls. showcases a stochastic characteristic. Hence, it requires
Montanini et al.[15] and de Quadros et al.[16] used smart the utilization of genuine training data to construct a
shoes with several sensors and a wristband, resilient mathematical model. The authors suggested a
respectively, to detect falls based on the threshold fall system for detecting falls based on several
detection approach. On the contrary, these fall classifiers[29]. The algorithm was developed using
detection methods require the extraction of intricate artificial neural networks (ANN), k-nearest neighbors
data attributes from a multitude of sensors, (KNN), radial basis functions (RBF), probabilistic
encompassing components such as accelerometers and principal component analyses (PPCA), and linear
gyroscopes. Moreover, these techniques require discriminant analyses (LDA). It is unsuitable for
significant allocation of training and computational wearable electronics. Regardless of the positive
resources. outcome, classification procedures are frequently time-
consuming. Researchers typically favor more
2 Related Work straightforward techniques for pre-impact fall detection
In the current detection method of falls before the systems. Tong et al.[30] proposed a hidden Markov
collision, Nyan et al.[17] discovered falls by analyzing model-based fall-prediction approach which can
the angle and angular velocity of the thigh in various anticipate 200−400 ms before impact. Liu and
falls and daily activities. Shi et al.[18], and Shan and Lockhart[31] used forecast classifier analysis to create a
Yuan[19] used support vector machine (SVM) to extract fall detection method before a crash. The average
 Li Zhang et al.: A Fall Detection Device Based on Single Sensor Combined with Joint Features 697

response time for the program to detect backward falls receives the streams of acceleration and angular
was 255 ms. velocity data to establish an enhanced training
By reason of the foregoing, this study seeks to framework. Based on this foundation, the data streams
explore the suitability of the SVM-based fall detection are segmented, features are extracted, and a fuzzy
system. To achieve dependable differentiation between query is performed on the angle feature matrix.
fall actions and ADLs, our focus lies on the Ultimately, the SVM undergoes training with the
construction of feature vectors, extraction of features, obtained results. To achieve a relatively accurate
and implementation of classification techniques. These prediction outcome, the user examines both the
approaches aim to optimize the accuracy of acceleration and angular velocity data collected from
identification. This paper is an extension of our the IMU within the system, transmitting them into the
conference paper accepted by MWSSH2022[32]. The SVM model. Should the system identify a fall incident,
following is a summary of the significant contributions: it promptly activates the user’s alarm device, ensuring
(1) We present a robust methodology for extracting timely care or emergency treatment for the elderly.
discerning features that enable differentiation among
various activities, utilizing the SVM to discriminate 3.1 Hardware
between falls and ADLs. Figure 2 shows the hardware for the fall detection
(2) We develop an innovative signal processing system includes a sensor (MPU6050), secured to the
technique to capture Euler angular data, which body with a bandage. Our research focuses on the most
undergoes meticulous filtering to enhance the general criterion of falls with backward, forward, left,
resolution of the extracted features. and right falls during ADLs. In the standing posture,
(3) We produce abundant investigations to angular velocity and acceleration values are near to
substantiate that an IMU device suffices to attain 0 °/s and 9.79 m/s2 after calibration. The module
exceptional precision in discriminating different possesses the capability to generate real-time data in a
motion patterns dynamic environment. A Bluetooth connection is
3 System Overview employed to transfer the sampled data to either a
personal computer or a smartphone, ensuring seamless
The system architecture is depicted in Fig. 1, communication.
showcasing the comprehensive framework. The SVM
3.2 Data preprocessing
receives training data using the features derived from
the IMU dataset. Concurrently, the user’s IMU For a fall detection system, the primary task of utmost
captures data across six axes, transmitting the importance is to extract appropriate features from the
processed features to the server. Initially, the user collected data in order to accurately characterize falling
records ADLs and fall events using the inertial sensor behavior. The distinction from the majority of recent
embedded within the system. Subsequently, the server studies, this paper adopts a machine learning approach.

Client side
Original Filter
Acceleration data
Query acceleration data
IMU Six axis database
Original Filter ZUPT
Gyroscope data Euler angle
Location-based smart applications

gyroscope data
Input

Server side
Acceleration data Segmentation
Fuzzy query
SVM model
Filter

of angle
Euler angle Feature extraction
Output

IMU DCM Dimension matrix

database Angle classifier
Quaternion update
SVM

Testing data
Filter

ZUPT algorithm Cross Accurate

Validation classification Predicted labels
Gyroscope data Training data

Fig. 1 Overview of system.

 698 Tsinghua Science and Technology, April 2025, 30(2): 695−707
 
 cos θ 0 − sin θ 
 
C12 =  0 1 0  (2)

sin θ 0 cos θ
 
 cos ψ sin ψ 0 
 
Cn1 =  − sin ψ cos ψ 0  (3)

0 0 1
An orthogonal matrix is used to transform two
Cartesian coordinate frameworks. Thus, it yields
( )−1 ( )T
Cbn = Cnb = Cnb (4)
 
 cos ψ cos θ C12 C13 
Fig. 2 IMU device.  
Cbn =  cos θ sin ψ C22 C23  (5)

− sin θ sin γ cos θ cos θ cos γ
The SVM’s training accuracy is significantly increased
in this paper by combining accelerations and Euler where the matrix Cbn is used to convert coordinates
angles as training features. Moreover, a zero-velocity from the B framework to the N framework, and
updating technique is used to obtain Euler angles. An C12 = sin γ sin θ cos ψ − cos γ sin ψ,
appropriate coordinate framework should be selected to C13 = sin γ sin ψ + cos γ sin θ cos ψ,
(6)
effectively describe the spatial motion state of the C22 = cos ψ sin γ + sin γ sin θ sin ψ,
carrier. Assume that Fig. 3 represents both the C23 = sin ψ sin θ cos γ − sin γ cos ψ
navigational coordinate framework (the N framework) Using the measurement from the IMU, the system’s
and the body coordinate framework (the B framework). attitude updating process involves calculating matrix
The fundamental rotations from the N framework to Cbn in real-time. The symbol ωnb represents the angular
the first rotational framework, the first rotational speed of the B framework in relation to the N system.
framework to the second rotational framework, and the The parts of ωnb in the B system are then listed as
follows:
second rotational framework to the B framework,
 b       
respectively, are denoted by the letters Cn1 , C12 , and C2b .  ωnbx   0   0   γ 
 b 
The coordinate transformation matrix, Cbn , from the N  ω  = C bC 2  0  + C b  θ  +  0  (7)
 nby  2 1   2    
ωbnbz −ψ 0 0
system to the B system is thus written as
  Then, the Euler angle differential equation is produced
 1 0 0 
 
C2b =  0 cos γ sin γ  (1) as follows:

0 − sin γ cos γ    −1  ωb 

 γ   1 0 − sin θ   nbx 
     b
 θ  =  0 cos γ sin γ cos θ   ωnby 
 (8)
ψ 0 − sin γ cos γ cos θ 
ωbnbz
Regarding ADLs, the relative positions of the three
Euler angular axes exhibit minimal variations.
However, during a falling event, notable changes in
these positions occur, making them distinguishable.
The Euler angle, therefore, serves as a discriminative
factor between falling actions and ADLs.
When the person falls four times during walking,
Fig. 4 depicts the change in the Euler angle. The
signals that the accelerometer and gyroscope need to be
cleaned of noise. Hence, averaging filters are employed
to attenuate noise present in the acceleration and Euler
Fig. 3 Transformation of sensor space angle position. angle signals, resulting in smoother and more refined
 Li Zhang et al.: A Fall Detection Device Based on Single Sensor Combined with Joint Features 699
6DOF animation (sample 10 305 of 10 305)
points, it can assist in the detection of quick activities
in shorter windows. For extended windows, it can
reduce interference more effectively, while it also
distorts the signal. Therefore, it is crucial to determine
the appropriate window size, evaluate sliding window
parameters, and reliably detect the impact of falling
Fig. 4 Pedestrians experienced falls while walking. behavior on recognition performance.
3.4 Features extraction algorithm
data. The acceleration and Euler angle values are Extraction of the proper features from the gathered data
transmitted over Bluetooth to a PC, and then recorded is crucial for accurate fall recognition. Figure 6 shows
by a recording application for analysis. the acceleration waveforms for each action. As
3.3 Windowing technique (Sliding window) apparent, each acceleration waveform possesses unique
characteristics. The time interval between each step
As mentioned earlier, the process of noise filtering was relatively longer for upstairs and downstairs, and
involves partitioning the accelerated data into several the change in wave amplitude was greater for
smaller segments, each with a predetermined size. To downstairs compared to upstairs. Running and walking
ensure minimal loss of data samples, a sliding window exhibited the briefest temporal intervals per step, with
approach is implemented, with a carefully chosen running further demonstrating a reduced inter-step time
overlapping ratio. This strategy helps maintain a high interval. However, the left, right, forward, and
recognition rate for activities. It is important to note backward falls are characterized by a step change in
that each action possesses distinct characteristics, acceleration in at least one direction compared to the
necessitating the scaling of the data window size in a other four movements, in addition to the different
tailored manner, thereby facilitating accurate directions and magnitudes between the four
identification of activity classes. Figure 5 depicts the movements of the fall. Figure 7 shows the Euler
data flow on acceleration under various windows. angular waveforms for each action. The main
Although it is less effective in suppressing interference differences between the waveforms for walking up and
Window=0 Window=20 Window=50
100 100 100
Acc (m/(0.01 s)2)

Acc (m/(0.01 s)2)

Acc (m/(0.01 s)2)

50 50 50

0 0 0

−50 −50 −50

−100 −100 −100

0 2000 4000 6000 8000 10 000 12 000 0 2000 4000 6000 8000 10 000 12 000 0 2000 4000 6000 8000 10 000 12 000
Time (0.01 s) Time (0.01 s) Time (0.01 s)

Window=100 Window=125 Window=180

100 100 100
Acc (m/(0.01 s)2)

Acc (m/(0.01 s)2)

Acc (m/(0.01 s)2)

50 50 50

0 0 0

−50 −50 −50

−100 −100 −100

0 2000 4000 6000 8000 10 000 12 000 0 2000 4000 6000 8000 10 000 12 000 0 2000 4000 6000 8000 10 000 12 000
Time (0.01 s) Time (0.01 s) Time (0.01 s)

Window=250 Window=320 Window=400

100 100 100
Acc (m/(0.01 s)2)

Acc (m/(0.01 s)2)

Acc (m/(0.01 s)2)

50 50 50

0 0 0

−50 −50 −50

−100 −100 −100

0 2000 4000 6000 8000 10 000 12 000 0 2000 4000 6000 8000 10 000 12 000 0 2000 4000 6000 8000 10 000 12 000
Time (0.01 s) Time (0.01 s) Time (0.01 s)

Fig. 5 Acceleration variation under different windows.

 700 Tsinghua Science and Technology, April 2025, 30(2): 695−707
Upstairs Downstairs Running Walking
20 20 20 20
X X X X
10 Y 10 Y 10 Y 10 Y
Z Z Z Z

0 0 0 0
Acc (m/s2)

Acc (m/s2)

Acc (m/s2)

Acc (m/s2)
−10 −10 −10 −10

−20 −20 −20 −20

−30 −30 −30 −30

−40 −40 −40 −40

−50 −50 −50 −50

0 200 400 600 800 0 200 400 600 800 0 200 400 600 800 0 200 400 600 800
Time (0.01 s) Time (0.01 s) Time (0.01 s) Time (0.01 s)

Forward fall Backward fall Left fall Right fall

20 20 20 20
X X X X
15 Y 15 Y 15 Y 15 Y
Z Z Z Z
10 10 10 10
5 5 5 5
Acc (m/s2)

Acc (m/s2)

Acc (m/s2)

Acc (m/s2)
0 0 0 0
−5 −5 −5 −5
−10 −10 −10 −10
−15 −15 −15 −15
−20 −20 −20 −20
0 200 400 600 800 0 200 400 600 800 0 200 400 600 800 0 200 400 600 800
Time (0.01 s) Time (0.01 s) Time (0.01 s) Time (0.01 s)

Fig. 6 Acceleration variation for each axis in different actions.

Upstairs Downstairs Running Walking

3 3 3 3
Yaw Yaw Yaw Yaw
Pitch Pitch Pitch Pitch
2 Roll 2 Roll 2 Roll 2 Roll

1 1 1 1
Angle (r/s)

Angle (r/s)

Angle (r/s)

0 0 0 Angle (r/s) 0

−1 −1 −1 −1

−2 −2 −2 −2

−3 −3 −3 −3
0 200 400 600 800 0 200 400 600 800 0 200 400 600 800 0 200 400 600 800
Time (0.01 s) Time (0.01 s) Time (0.01 s) Time (0.01 s)

Forward fall Backward fall Left fall Right fall

5 5 5 5
Yaw Yaw Yaw Yaw
4 Pitch 4 Pitch 4 Pitch 4 Pitch
Roll Roll Roll Roll
3 3 3 3
2 2 2 2
Angle (r/s)

Angle (r/s)

Angle (r/s)

Angle (r/s)

1 1 1 1
0 0 0 0
−1 −1 −1 −1
−2 −2 −2 −2
−3 −3 −3 −3
−4 −4 −4 −4
−5 −5 −5 −5
0 200 400 600 800 0 200 400 600 800 0 200 400 600 800 0 200 400 600 800
Time (0.01 s) Time (0.01 s) Time (0.01 s) Time (0.01 s)

Fig. 7 Euler angle variation for each axis in different actions.

down stairs, running and walking are frequency and Within this work, a novel type of feature is
amplitude. However, the main difference between the introduced with the primary objective of enhancing
waveforms of left, right, forward and backward falls is precision during the training process. We extract
the step. In a word, the variations of the triaxial acceleration and Euler angle features, respectively, and
acceleration and Euler angular amplitude of these eight then put them into an SVM. In order to identify
movements exhibit different forms over time. appropriate characteristics to distinguish falls from
Therefore, we propose a feature method based on equal ADL, we analyzed the characteristics of the different
signal amplitude differences. activities. As previously mentioned, during normal
 Li Zhang et al.: A Fall Detection Device Based on Single Sensor Combined with Joint Features 701

activities such as going stairs or walking, the data described below:

curves are smooth with small fluctuations. Instead, ( )
F = F1, sum , F2, sum , F3, sum , . . . , F N, sum (13)
during fall events, the data fluctuations are volatile.
Therefore, we adopt a novel features extraction where N represents total samples.
method, equational signal magnitude variation Prior to SVM training and prediction, we normalize
(ESMV), to reflect the data fluctuations. The ESMV the feature vectors to ensure that all feature values fall
feature is defined as follows: within the [0, 1] range. These specifics are provided:
(y )
i+1 − yi y = (ymax − ymin ) ∗ (x − xmin ) / (xmax − xmin ) + ymin (14)
ESMV = arctan (9)
∆t where the values of each column vector in F are
where the sample value yi is the i -th sample, and ∆t is represented by the biggest and smallest element values,
the sample time difference. respectively, by xmax and xmin . Assign ymax and ymin
For all training data from categories 1 to 8, where values of 1 and 0, respectively.
categories 1 to 4 are ADLs, and categories 4 to 8 are Figures 8 and 9 show the data of acceleration and
fall activities, acceleration and Euler angles are Euler angle features, respectively. In the controlled
extracted as features for the SVM classifier. In this activity, except for the high degree of distinction
section, we establish classifiers by using angles. between the running and walking features, a small
Through extensive experiments, we find that the best
portion of the eigenvalues between similar actions
experimental results are obtained by setting nine
(e.g., up and down stairs) are more distinct, and most
classifiers, which are −90 degrees, −70 degrees, −50
of the eigenvalues are close, which can easily lead to
degrees, −30 degrees, −10 degrees, 10 degrees, 30
confusion. Figure 10 shows the data for the joint
degrees, 50 degrees, 70 degrees, and 90 degrees. Every
acceleration and Euler angle features (JAEFs), and
training sample’s acceleration feature matrix can be
since there are fewer eigenvalues that differ for a single
written as F A :
( )′ feature, Fig. 10 combines the eigenvalues of both
F A = A x , Ay , Az = features. It is clear from Fig. 10 that there is a higher
 
 a x,1 a x,2 · · · a x,9  degree of differentiation between the combined
  (10)
 ay,1 ay,2 · · · ay,9  acceleration and Euler angle features compared to the
az,1 az,2 · · · az,9 method using only a single feature, thus improving the
where A x , Ay , and Az represent the x , y , and z axes of
acceleration, respectively; a x,i , ay,i , and az,i indicate the
number of ESMVs belonging to each classifier,
respectively.
Value of feature

30
Each training sample’s Euler angle feature matrix is
Right fall
20
written as F E : Left fall
Backward fall
( )′ 10
Forward fall
F E = E x , Ey , Ez = 0 Walking
  0 Running
 e x,1 e x,2 · · · e x,9  5 10 Downstairs
  (11) Sequence
15 20 Upstairs
 ey,1 ay,2 · · ·
25
ey,9  s

ez,1 ez,2 · · · ez,9

Fig. 8 Employing acceleration features.
where E x , Ey , and Ez represent the x , y , and z axes of
Euler angle, respectively; e x,i , ey,i , and ez,i indicate the
number of ESMVs belonging to each classifier,
respectively.
After the feature selection, the feature vectors of each
Value of feature

40
Right fall
training sample are expressed as follows: Left fall
( ) 20 Backward fall
Fsum = F A′ F B′ = Forward fall
( ) (12) 0 Walking
Running
Ax Ay Az E x Ey Ez 0 5 10 Downstairs
15 20 Upstairs
Sequence 25
s
All eight action samples’ feature vectors are
combined into one feature matrix in the manner Fig. 9 Employing Euler angle features.
 702 Tsinghua Science and Technology, April 2025, 30(2): 695−707

∑
m
1 ∑∑
m m
L(w, b, α) = αi − αi α j y i y j x i x j (19)
i=1
2 i=1 j=1

∑
m
Value of feature

40
Right fall
αi yi = 0, αi ⩾ 0, i = 1, 2, . . . , m (20)
Left fall i=1
20 Backward fall
Forward fall
Walking
After solving α , according to Eq. (18), we can
0
Running
0 10 Downstairs
further obtain the values of w , and further find b , and
20 30
Sequence 40 Upstairs
s 50 then get the following model:
Fig. 10 Employing JAEF features. ∑
m
f (x) = wT x + b = αi yi xiT x + b (21)
i=1
classification accuracy.
When it comes to tackling the small sample, The Karush-Kuhn-Tucker (KKT) conditions for the
nonlinear, and high dimensional pattern recognition above process are given as

problem, the SVM classifier exhibits numerous distinct 
αi ⩾ 0,



advantages. The primary principle of the SVM is to 

yi f (xi ) ⩾ 1 − ξi ,



(22)
perform some nonlinear mapping on the input vector to 
αi (yi f (xi ) − 1 + ξi ) = 0,



transform it into a high-dimensional feature space. logi ⩾ 0, µi ξi = 0
It is worth mentioning that the SVM is essentially a
Moreover, using Lagrange theory and quadratic
regularized minimization problem, as shown following:
programming strategies to solve the minimization
1∑ 2 ∑
l l problem. To model a real-world scenario for an internet
min(ω) = ω +C ξi (15) application in the suggested architecture, we generate a
ξ 2 i=1 i i=1
 l  feature matrix from the processed accelerations and
∑  Euler angles, and put it into SVM classification for
yi  ωi ϕ (xi ) + b ⩾ 1 − ξi ∀i = 1, 2, . . . , l (16)
continuous training, so as to obtain a better training
i=1
framework. Then, the frame is extracted and the real-
where ξi is the slack variable and C stands for the
time motion data of the elderly is processed and
penalty component. Furthermore, in order to avoid the
transmitted to the model of the SVM classifier through
explicit definition of the non-linear mapping, the kernel Bluetooth to judge whether the elderly’s activity is
function is introduced. falling or daily life activities.
The Lagrange function is established as
∑m 4 Expertmental Study
1
L(w, b, α, ξ, µ) = ∥w∥2 + C ξi +
2 i=1 4.1 Experiment setup
(17)
∑
m ( ( )) ∑
m
Next, we will introduce the experimental process in a
αi 1 − ξi − yi wT xi + b − µi ξ i
real scenario. Figure 11 shows the experimental
i=1 i=1
scenario, which is on the 17th floor of Building B of
where αi ⩾ 0 , µi ⩾ 0 are Lagrange multipliers.
the Science Education Building at Hefei University of
Let the partial derivative of L(w, b, α, ξ, µ) with
respect to w , b , α be zero, it yields
 ∑



m


 w = αi yi xi ,



Restroom
Elevator




i=1 Cargo elevator Staircase
∑ m



(18)


 αi yi = 0,






i=1
C = α i + µi Room

Substituting Eq. (18) into Eq. (17), we have

Fig. 11 Experimental areas.
 Li Zhang et al.: A Fall Detection Device Based on Single Sensor Combined with Joint Features 703
 
Technology. We conducted a lot of experiments in the  λ11 m1 λ12 m1 ··· λ1C m1 
 λ m λ22 m2 ··· λ2C m2 
laboratory, hall, and corridor. Additionally, falling left,  21 2 
CM =  .. .. .. ..  (24)
falling right, running, walking, falling ahead, falling  . . . . 
 
backward, and climbing and descending stairs were λC1 mC λC2 mC ··· λCC mC
taking into account. Besides, the 15 volunteers aged 20 which is the Hadamard (elementwise) product of two
to 27 years old, with heights ranging from 161 cm to matrices with the following expression as
188 cm and weights ranging from 45 kg to 80 kg, carry    
 λ11 λ12 ... λ1C   m1 m1 ... m1 
out various activities. They are each in great health and  λ λ22 ... λ2C   m m2 ... m2 
 21   2 
do not have any physical ailments that might affect  .. .. .. ..  ◦  .. .. .. ..  (25)
 . . . .   . . . . 
how they move.    
λC1 λC2 ... λCC mC mC ... mC
To imitate activities that are similar to those carried
out by seniors, they had to mimic the actions older The confusion matrix can be expressed as in the
adults take in the video clips. For the walking trials and binary case, when C = 2, the classes are present as
[ ]
fall trials, a subject completed each type of trial m11 m12
CM ≡ (26)
50 times. The walking trials consisted of a minimum of m21 m22
two full gait cycles. Throughout the walking trials, the One of the classes is typically referred to as the
comprehensive sequence of activities, including “Positive class”, and the other as the “Negative class”.
running, walking, ascending, and descending stairs, is Therefore, using this new terminology, the confusion
meticulously captured in the experimental data. matrix can now be represented as follows:
Throughout the fall trials, each person performed 50 [ ]
mPP mPN
falls in the forward, backward, left, and right CM ≡ (27)
mNP mNN
directions. At the same height, subjects landed on
where the elements of this matrix mPP means “True
mattresses. Every reliable fall test result must have at
Positive (TP)”; mPN means “False Negative (FN)”;
least two complete walking motion data. Nearly 400
mNP means “False Positive (FP)”; and mNN means
experimental trials were conducted overall.
“True Negative (TN)”.
A division was made within the experimental trials,
Consider a dataset D = {d1 , d2 , . . . , dm } with m
creating a training subset and a testing subset. The
elements, where dk is the k -th element. The total
training subset consisted of the complete set of
number of positive mP and negative mN elements in D
experimental data obtained from eight subjects, while
is equal to the total number of elements, that is,
the remaining information from the other seven mP + mN = m . Furthermore, it is also true that the
subjects was utilized for testing purposes. number of elements correctly classified in class P
4.2 Quality criteria ( mPP ), and the number of elements misclassified in that
class P ( mPN ), adds up to the number of elements in the
As an effective way to represent classification findings,
positive class ( mP ), that is, mPP + mPN = mP . Similarly,
this study focuses on indicators based on the confusion
it can be stated that mNP + mNN = mN . The confusion
matrix,
matrix can therefore be written as
  [ ]
 m11 m12 ... m1C 
 m  mPP mP − mPP
 21 m22 ... m2C  CM = (28)
CM ≡  . .. .. ..  (23) mN − mNN mNN
 .. . . . 
  This is also formulable using the ratios as
mC1 mC2 ... mCC [ ]
λPP mP λPN mP
The expression represents the number of elements CM = =
λNP mN λNN mN
actually belonging to the i -th class but that are [ ] (29)
λPP mP (1 − λPP ) mP
identified as belonging to the j -th class. In the context (1 − λNN ) mN λNN mN
of our research, it is better to describe the term mi j in
terms of the total number of items mi belonging to the Additionally, use eP and eN to represent the total
number of items in D that are assessed to be positive
i -th class. By denoting λi j as the ratio mi j /mi , it yields
(despite their true class) and negative, respectively,
 704 Tsinghua Science and Technology, April 2025, 30(2): 695−707

Upstairs
shown as
Downstairs

eP = mPP + mNP = λPP mP + (1 − λNN ) mN (30) Running

True class
Walking
Forward fall
eN = mNN + mPN = λNN mN + (1 − λPP ) mP (31)
Backward fall
which means eP + eN = m . Figure 12 presents a Left fall
Right fall
summary of the confusion matrix definitions.
4.3 Experiment results
rs rs g g ll ll ll ll
ai stai nin lkin d fa d fa ft fa t fa
We conduct three comparable experiments utilizing st n a r r h
Up own Ru W rwa kwa Le Rig
D Fo Bac
three different sets of features: accelerations alone,
Predicted class
Euler angles alone, and accelerations and Euler angles
together. Results showed that the accuracy of Fig. 14 Confusion matrix for fall activities and ADLs
recognition can be considerably increased by using employing Euler angle features.
accelerations and Euler angles as characteristics.
Upstairs
Figure 13 shows the confusion matrix for fall activities Downstairs
and ADLs, employing the acceleration features. Running
True class Walking
Figure 14 shows the confusion matrix for fall activities
Forward fall
and ADLs, employing Euler angle features. Figure 15 Backward fall
shows the confusion matrix for fall accidents and Left fall

ADLs, employing joint the acceleration and Euler Right fall

angle features. The confusion matrix demonstrates that

the chosen features function well in identifying the
rs rs g g ll ll ll ll
ai stai nin lkin d fa d fa ft fa t fa
eight different sorts of activities. st n a r r h
Up own Ru W rwa kwa Le Rig
D Fo Bac

Predicted class

Fig. 15 Confusion matrix for fall activities and ADLs

employing JAEF features.

Figures 16–18 show the comparison among equal-

signal amplitude difference feature method, statistical
feature method (SF)[33], and threshold method (TM)[34]
in terms in precision, recall, and F1-score, respectively.
To begin with, it can be seen from the figure that the
Fig. 12 Confusion matrix for binary classification.
traditional threshold-based method is significantly
Upstairs lower than our proposed method as well as the
Downstairs
statistical feature-based method in precision, recall, and
Running
True class

Walking 100 ESMV

SF
Forward fall 95
TM
Backward fall
90
Precision (%)

Left fall
85
Right fall
80

75

rsrs g g ll ll ll ll 70
ai ai nin lkin d fa d fa ft fa t fa
st st n a r r h
Up own Ru W rwa kwa Le Rig rs rs ing ing fall fall fall fall
D Fo Bac ai ai
st st nn alk Left ight ard ard
Up own Ru W R orw kw
Predicted class D F Bac

Category
Fig. 13 Confusion matrix for fall activities and ADLs
employing acceleration features. Fig. 16 Precision of different methods.
 Li Zhang et al.: A Fall Detection Device Based on Single Sensor Combined with Joint Features 705

100 ESMV 120

110 Only A
SF OnlyE
95 100 A&E
TM
90
90
80
Recall (%)

Precision (%)
85 70
60
80 50
40
75 30
20
70
10
ai
rs rs ing ing fall fall fall fall
ai irs irs ll ll ll ll
st st nn alk Left ight ard ard a a ing kin
g fa fa fa fa
Up own Ru W R orw kw st st nn al rd r d ft ht
D F Bac Up wn Ru W wa wa Le Ri
g
r
Do Fo ck
Ba
Category Categories

Fig. 17 Recall of different methods. Fig. 19 Comparison chart of detection precision.

1.00 ESMV 120
SF 110 Only A
0.95 OnlyE
TM 100 A&E
0.90 90
F1-score (%)

80

Sensitivity (%)
0.85 70
60
0.80 50
40
0.75
30
0.70 20
10
l ll ll ll
ai
rs irs ing ing fal fa fa fa
st nsta unn alk eft ght ard ard rs rs ng g fa
ll
fa
ll
fa
ll
fa
ll
p
U ow W L i ai ai ni kin ft
R R orw kw st st n al r d rd ht
D F Bac Up n
Ru W wa wa Le Ri
g
ow r ck
D Fo Ba
Category
Categories

Fig. 18 F1-score of different methods. Fig. 20 Comparison chart of detection sensitivity.

F1-score. Next, according to data results, although the The experimental results demonstrate that our method
statistical feature-based method has higher accuracy for exhibits excellent performance in fall detection. By
forward fall, backward fall, left-side fall, and right-side extracting multiple features, including combined
fall, there is no clear distinction between up and down acceleration and Euler angle features, our classifier is
stairs, running, and walking. To summarize, we find able to accurately identify fall behaviors. Compared to
that the proposed feature method significantly traditional methods, our approach shows significant
outperforms the statistical feature method and the improvements in sensitivity, precision, and
threshold method in terms of accuracy, recall, and F1- classification accuracy. This method demonstrates
scores for the same dataset. good performance and has the potential for wide
Human activities can be divided into eight groups application in fall injury systems. We believe that this
using the SVM classifier. The results demonstrate that research will make important contributions to the
the approach is capable of accurately differentiating health and safety of the elderly and provide valuable
between various fall and ADLs kinds. Figures 19 and references for future related studies.
20 compare the multi-feature-based method with two
5 Conclusion
single-feature-based methods in precision and
sensitivity. According to the results, the method using a The present study devises and assesses a fall detection
single Euler angle feature and a single acceleration system for detecting pre-impact falls. This system
feature produces unsatisfactory results. However, the leverages data concerning acceleration and angular
multi-feature method clearly outperforms the single- velocity to extract relevant features. Following the
feature methods. selection of the classifying components, the SVM
Through experimental verification, the method classifier is employed to categorize the data accurately.
proposed in this paper has been proven to be effective. Drawing upon the results of feature selection, the
We conducted a series of experiments to evaluate the incorporation of acceleration and angular velocity data
performance of this method in detecting falls in the proves to be pivotal in the classification of activities.
elderly and compared it with other existing methods. The experimental findings indicate that utilizing
 706 Tsinghua Science and Technology, April 2025, 30(2): 695−707

multiple features for fall detection yields an average algorithms for acoustic fall detection using a microsoft
sensitivity surpassing 96%. The combination of kinect, IEEE Trans. Biomed. Eng., vol. 61, no. 3, pp.
745–755, 2013.
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E. Gambi, A footwear-based methodology for fall
This work was supported by the National Natural Science
detection, IEEE Sens. J., vol. 18, no. 3, pp. 1233–1242,
Foundation of China (No. 61972131), and the National 2017.
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Li Zhang received the BS degree in Yu-An Liu received the MS degree in

applied mathematics from Anhui Normal control science and engineering from
University, Wuhu, China, in 1999, and the Anhui University of Technology,
MS and PhD degrees in computational Ma’anshan, China, in 2022. He is currently
mathematics and computer science and working toward the PhD degree in
technology from Hefei University of mathematics from Hefei University of
Technology, Hefei, China, in 2004 and Technology, Hefei, China. His current
2009, respectively. From 2012 to 2013, she research interests include networked
was a postdoctoral researcher in computer science and control system and Internet of Things.
technology at Arizona State University, Phoenix, AZ, USA. She
is currently a professor with School of Mathematics, Hefei Huilin Chen received the BS degree in
University of Technology. Her current research interests include applied mathematics from Anqing Normal
indoor localization, mobile computing, and Internet of Things. University, Anqing, China, in 2021. She is
currently pursuing the master’s degree
Qiuyu Wang received the BS degree in with School of Mathematics, Hefei
applied mathematics from Anqing Normal University of Technology. Her research
University, Anqing, China, in 2019, and interests include the Internet of Things.
the ME degree from School of
Mathematics, Hefei University of
Technology. Her research interests include Danyang Li received the BE degree in
the Internet of Things. School of Software from Yanshan
University in 2019 and the ME degree in
School of Software from Tsinghua
Jingao Xu received the BE degree from University in 2022. He is currently
School of Software, Tsinghua University, pursuing the PhD degree in School of
in 2017, and the PhD degree from School Software, Tsinghua University. His
of Software, Tsinghua University, in 2022. research interests include Internet of
He is currently a postdoctoral researcher in Things and mobile computing.
School of Software, Tsinghua University.
His research interests include the mobile
computing, edge computing, wireless
localization, visual SLAM systems, and drone-based
applications.