A smart phone-based pocket fall accident detection, positioning, and rescue system.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2328593, IEEE Journal of Biomedical and Health Informatics

A SMART PHONE-BASED POCKET FALL ACCIDENT DETECTION, POSITIONING AND RESCUE SYSTEM Lih-Jen Kau, Member, IEEE, and Chih-Sheng Chen

ABSTRACT We propose in this paper a novel algorithm as well as architecture for the fall accident detection and corresponding wide area rescue system based on a smart phone and the third generation (3G) networks. To realize the fall detection algorithm, the angles acquired by the electronic compass (ecompass) and the waveform sequence of the triaxial accelerometer on the smart phone are used as the system inputs. The acquired signals are then used to generate an ordered feature sequence and then examined in a sequential manner by the proposed cascade classifier for recognition purpose. Once the corresponding feature is verified by the classifier at current state, it can proceed to next state; otherwise, the system will reset to the initial state and wait for the appearance of another feature sequence. Once a fall accident event is detected, the user’s position can be acquired by the global positioning system (GPS) or the assisted GPS (A-GPS), and sent to the rescue center via the 3G communication network so that the user can get medical help immediately. With the proposed cascaded classification architecture, the computational burden and power consumption issue on the smart phone system can be alleviated. Moreover, as we will see in the experiment that a distinguished fall accident detection accuracy up to 92% on the sensitivity and 99.75% on the specificity can be obtained when a set of 450 test actions in nine different kinds of activities are estimated by using the proposed cascaded classifier, which justifies the superiority of the proposed algorithm. Index Terms— Fall detection, Smart phone, triaxial accelerometer, Electronic compass, Cascade classifier, Support vector machine, GPS System, 3G network I. INTRODUCTION Fall accident has been the major cause of injury to the elderly in recent years. To protect the elderly from the injury of fall accident events or to give an immediate assistance to the elderly after the occurrence of a fall accident event, many researches have been devoted to the design of a fall detection algorithm and system [1]-[27]. Among all the currently proposed algorithms, the fall detection system can be roughly divided into two Manuscript received Dec. 23 2013; revised April 14, 2014; accepted May 23, 2014. Lih-Jen Kau is with the Department of Electronic Engineering, National Taipei University of Technology, Taipei 10608, Taiwan (e-mail: [email protected]). Chih-Sheng Chen is with Realtek, Hsinchu 30078, Taiwan (e-mail: [email protected]).

categories [1]-[4], namely, environmental monitoring-based [5][14], and wearable sensor-based systems [15]-[27]. As for the environmental monitoring-based systems, typically used sensors such as cameras [5]-[9], acoustic sensors (e.g., microphone array) [10], radar and infrared sensors [11][12], pressure sensors [13], or accelerometer for vibration detection [14] are placed in a predefined space or environment to monitor the activities of the elderly as well as the occurrence of a fall accident event. Compared to the type of wearable sensor-based system, the environmental monitoring-based fall detection system is more comfortable to the elderly since there is no need of wearing any module. However, the environmental monitoringbased system can only function in a predefined environment where it is installed. Moreover, the protection of the private matters for the elderly is another problem and contention is usually discussed with the environmental monitoring-based system [1]-[4]. With the advances of integrated circuit technologies in micro electro-mechanical systems (MEMS), the inertial and posture sensors, e.g., the triaxial accelerometer and gyroscope, can be made very compact in its dimension and easy to be embedded in portable devices. Based on this reason, many wearable sensorbased fall detection systems have been proposed recently [15][27]. For wearable sensor-based fall detection systems, some of which employ the use of a single triaxial accelerometer as the system input [15]-[19], while most of them apply the use of multiple sensors [20]-[27]. Among the algorithms that use multiple sensors, multiple triaxial accelerometers [20][21] or a triaxial accelerometer in conjunction with a gyroscope [22]-[25] is usually applied. In certain multiple sensor-based systems, even the atmospheric air pressure (or barometric pressure) sensor [25][26] or a surface electromyography (SEMG) sensor [27] are used to assist the triaxial accelerometer in discriminating the the posture as well as the motion of the elderly. Unlike the environmental monitoring-based systems that can function only in a predefined space, the wearable sensorbased fall detection systems can function in a larger area. However, most of the wearable sensor-based fall detection systems are made of a self-designed circuit module that should be placed and fastened around certain position, e.g., the chest or the waist, of the user [15]-[27]. Therefore, the necessity of wearing an additional sensor module can cause the elderly feel uncomfortable and lead to certain degree of inconvenience. In addition, how to address the current position of the elderly when a fall accident event occurs is a problem to be solved in wearable sensor-based fall detection systems. Moreover, the

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power consumption burden is another issue that should be treated carefully in mobile devices as well as in wearable sensor-based fall detectors. In order to monitor the status of the elderly and to locate the user’s position when a fall accident event is detected, some of the algorithms propose the use of a ZigBee sensor network to communicate between the fall detector that is with the elderly and the monitoring center [17]-[19]. However, to locate the user’s position with Zigbee sensor network, a set of so-called reference nodes should be placed in advance. Moreover, the range that can be addressed is also quite limited due to the transmission distance of Zigbee and the placement of reference nodes. Therefore, to locate the user’s current position with the use of a Zigbee sensor network is not suitable for wide area applications. Aimed to design a compact fall accident detector, we propose in this paper a pocket-based fall accident detector that uses a smart phone as the platform of the system. The triaxial accelerometer as well as the electronic compass (ecompass) will be used as the sensors to generate primitive input signals. In general, the fall accident recognition accuracy can not be satisfactory without the aids of a sophisticated classification algorithm. However, the use of a sophisticated classifier means an increased computational complexity which is not suitable to be used in wearable sensor-based devices. Therefore, we apply in this paper the use of an electronic compass to assist in discriminating real fall events from normal activities so that the unsatisfactory false positive rates among accelerometrybased fall detection devices can be improved. The acquired input signals will be processed by the proposed algorithm to generate a feature sequence based on the order of appearance, and then the features in the sequence will be examined by the proposed cascaded classifier (or state machine) in a sequential manner. The state machine can proceed to next state only if the corresponding feature is verified by the current state classifier; otherwise it resets to the initial state and waits for the appearance of the first feature in the sequence. In the proposed cascaded classifier scheme, the last state is composed of a support vector machine (SVM) in which more computations are required for higher order feature extraction and recognition. To speed up the efficiency of classification process, the early states are composed of simple and important features which allows a large number of negative samples to be quickly excluded from being regarded as a fall event. Those complex features are then placed in later states. With the cascaded architecture, the fall detection efficiency can be significantly enhanced. In addition to the cascaded classifier architecture, the global positioning system (GPS) or the assisted GPS (A-GPS) will be used to acquire the user’s current position, and the longitude and latitude will be sent to the coordination center via the 3G communication network if a fall accident event is detected. This way, the coordination center can know the user’s position exactly. Moreover, the detailed position can also be shown on the screen of the coordination center with electronic maps, e.g., Google map, so that the user can get medical help immediately. Meanwhile, the system will send out a loud sound as a warning signal so that people nearby can notice this fall accident

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Fig. 1. Architecture of the proposed fall accident detection and rescue system. Falling

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Fig. 2. Scenario of using the smart phone-based pocket fall accident detector. event and provide assistance to the user immediately. With the proposed algorithm and architecture, the computational and the power consumption burden can be quite alleviated since we check each fall accident feature sequentially and reset to the initial state once any one of the feature in the state machine is not verified. Since we also use the angle acquired by the electronic compass to assist in discriminating a fall down event, the user just put the smart phone in their pocket (as in Fig. 2), which is easy to carry with. Moreover, the proposed system can locate the user and communicate with the coordination center in a wide area as long as the 3G network is available, which facilitates the daily activities of the elderly. The rest of the paper is organized as follows. Section II gives an overview on the architecture of the proposed pocket fall accident detection system. The process of signal acquisition and features selection are given in section III. The high frequency characteristic of the acquired signal with the inertial sensor (triaxial accelerometer) when a fall accident event occurs will be analyzed in section IV. Section V address the extraction of higher order features and its fusion with the support vector machine (SVM). The integrated fall detection system will be given in section VI. Experimental results of the proposed approach and comparisons to existing state-of-the-art fall detection algorithms can be addressed in section VII. Finally, a concluding remark is given in Section VIII. II. SYSTEM OVERVIEW The architecture of the proposed fall accident detection and rescue system is shown in Fig. 1. As can be seen in Fig. 1, the



III. SIGNAL ACQUISITION AND FEATURES SELECTION In this section, the signal acquisition as well as the feature selection process will be introduced. It is noted that most of the smart devices are equipped with certain kinds of inertia detectors, e.g., the triaxial accelerometer (also known as GSensor), the electronic compass, or the gyroscope, so that the orientation of the device can be recognized by its operating system. Considering the availability, we use the triaxial accelerometer (G-Sensor) and the electronic compass as the major sensors for input signal acquisition and generation in the proposed system. III-A. The triaxial Accelerometer In this paper, the outputs of the triaxial accelerometer will be sampled periodically as the input signals of the proposed system with a frequency of 150Hz. The sampled signal is a three-dimensional data sequence, i.e., [ax [n], ay [n], az [n]]. To simplify the dimension of the sampled signal, we apply in this

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proposed system is mainly composed of three blocks: the smart phone-based pocket fall accident detector, the coordination center, and the rescue center which is composed of the hospitals nearby or the first-aid stations. As can be seen in the part of smart phone-based pocket fall accident detector (Fig. 1), the triaxial accelerometer and the ecompass will be used to acquire the posture of motion activities for the elderly. In the proposed system, the inclusion of the ecompass is to acquire the tilt angle, i.e., pitch, of the smart phone. This is because when the elderly is suffering a fall accident event, the smart phone in the user’s pocket also tends to lie down, and the pitch angle is usually small. Actually, the work of acquiring the pitch angle of the smart phone can also be accomplished by using a gyroscope which provides the angular acceleration information of the smart phone [29]. However, the gyroscope is only available in higher grade smart phones. On the contrary, the ecompass is available in most of the smart phones. Furthermore, the tilt angle (pitch angle) of the smart phone can be estimated by using the ecompass in conjunction with the triaxial accelerometer. We therefore decide to use the ecompass for the estimation of pitch angle so that the proposed algorithm can be applied for most of the smart phone systems. We also list in Fig. 1 the tools and algorithms that are used for the analysis and detection of a fall event. Fig. 2 shows a scenario of placing the smart phon-based fall accident detector in the pocket of the elderly. As can be seen in Fig. 1 and Fig. 2, a loud sound as a warning signal will be sent out once a fall accident event is detected, and then the longitude and latitude, i.e., the current position, of the elderly will be transmitted to the coordination center via the 3G network. The coordination center is composed of an emergency signal handling program module which is used to receive the current position and important personal information of the elderly. The received longitude and latitude can then be integrated and displayed with an electronic map, e.g., Google map.

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Fig. 3. S[n] sequence with 300 data samples under a fall event. (a) Sequence obtained with the detector fastened on the chest. (b) Sequence obtained by placing the detector in the pocket. paper the use of the one-dimensional signal magnitude vector (SMV) S[n] as below [28]. (1) S[n] = a2x [n] + a2y [n] + a2z [n], where n is the sample index, ax [n], ay [n] and az [n] are the gravitation values along the x-axis, y-axis, and z-axis, respectively (as in Fig. 6). To illustrate the signal sampling strategy as well as the features that will be used in the proposed system, we show in Fig. 3.(a) a typical sequence of the SMV signal (i.e., S[n]) under a fall event with 300 samples. The sequence in Fig. 3.(a) is obtained with the smart phone fastened around the chest of the user. As can be seen in Fig. 3.(a), there is a significant signal drop below 1G around the 50th data sample. Actually, this is due to the fact that when the user is suffering a fall accident event, the body will quickly drops toward the ground, and results in a weightless state temporarily. During this short period of time, the triaxial accelerometer will produce an S[n] value typically smaller than 0.6G. At the instant just when the body hits the ground heavily, the triaxial accelerometer can produce an S[n] value larger than 1.8G. After that, the user will stay motionless for a short time, and the triaxial accelerometer will produce a slowly varying sequence of S[n] around 1G. In this paper, the moment at which the value of S[n] is equal to 0.6G (i.e., the 50th data sample in Fig. 3.(a)) will be used as the reference point for the sampling of the S[n] sequence. That is, the 50 and 250 data samples just before and after the reference point will be recorded by the proposed system to form a sequence of 300 samples. The 300 samples will be sent to the proposed state machine and examined by the proposed algorithm to check if the features of a fall accident event can be satisfied in a sequential manner. Moreover, the appearance of an S[n] value smaller than 0.6G and greater than 1.8G, as well as the slowly varying waveform of S[n] value in Fig. 3.(a) will be used as the first three characteristics or features, i.e., the first three state, of the proposed system. It should be noted that the use of an S[n] sequence in Fig. 3.(a) is just for explanation convenience. In the proposed fall detection system, the smart phone, i.e., the fall detector, is placed in the user’s pocket so that the elderly won’t feel uncomfortable. However, as the smart phone is placed in the



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of the S[n] between different kinds of activities. As can be seen in Fig. 4, the first two features that are used for the fall accident event detection, i.e., S[n] ≤ 0.6G and S[n] ≥ 1.8G, can also be easily satisfied in all the eight kinds of normal (d) Go upstairs (c) Sit down activities, as indicated by the circles in Fig. 4. In other words, the first two conditions for the fall event recognition can be regarded as necessary conditions, but not sufficient. Therefore, we have to find more features to distinguish a fall event from normal activities. We notice that the S[n] sequence still varies frequently and the amplitude variance of S[n] is large after the appearance of the second feature (the instant that S[n] ≥ 1.8G) in most of the continuous motion activities, e.g., run, walk, jump, go upstairs, go downstairs. However, the amplitude variation of S[n] is much smaller in the case of a fall event (e) Go downstairs (f) Tread than that in continuous motion activities after the appearance of the second feature (Fig. 3.(b)). This observation is very helpful and will be used as the third feature of the proposed system so that normal activities with continuous motion can be excluded from being regarded as possible candidate of fall events. To further illustrate the difference on the pattern of S[n] between a fall event and that of continuous motion activities, we show in Fig. 5 the S[n] sequences of a fall event and that of a running activity simultaneously. As can be seen in Fig. 5.(a), (g) Jump (h) Wavering the phone up and downthe amplitude variation of the S[n] after the appearance of the second feature (the instant that S[n] ≥ 1.8G) is much smaller than that of a running activity. Actually, the slowly varying Fig. 4. The waveform sequence of S[n] for eight different kinds characteristic of the S[n] sequence is due to the temporarily of activities. motionless status after the fall event. We find in our experiments that the sequence of S[n] varies slowly around 1G after the appearance of the second feature, and the standard deviation σ user’s pocket without any constraint, the smart phone can of the last 50 data samples in the S[n] sequence is found to be vibrate as long as the elderly is in active. For this, we show smaller than 0.1 during a fall event. Therefore, the third feature in Fig. 3.(b) a segment of S[n] with 300 samples obtained by can be examined by first calculating the standard deviation σ placing the smart phone in the pocket (as in Fig. 2) under a of the last 50 samples in S[n] sequence as below. fall event. As can be seen in Fig. 3.(b), the sequence of S[n] obtained by placing the smart phone in the pocket varies more 300 1 frequently than that in Fig. 3.(a) due to vibrations. Nevertheless, (S[n] − S¯50 )2 , (2) σ= the first three features can still be easily observed in Fig. 3.(b). 50 n=251 We further show in Fig. 4 the sequences of S[n] when the smart phone is placed in the pocket for eight kinds of where S¯50 is the average of the last 50 samples of S[n] normal activities, including run, walk, sit down, going upstairs, sequence. We then check if the standard deviation σ is smaller going downstairs, tread, jump, and wavering the smart phone than a predefined threshold 0.1. If so, the third feature satisfies up and down, so that we can know the waveform difference the state machine condition, and we proceed to next state for 1

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III-B. The Electronic Compass and Device Orientation In this paper, the pitch angle acquired by the electronic compass is used to assist in discriminating real fall events from normal activities. The coordinate convention of the triaxial accelerometer and the orientation definition of the electronic compass are shown in Fig. 6.(a) and Fig. 6.(b) respectively [29]. It should be noted that the electronic compass should be used in company with the triaxial accelerometer, where the triaxial accelerometer is used to regulate and compensate the actual angle obtained. With the aids of information acquired by the magnetic field sensor as well as the gravity sensor, a so-called 3×3 rotation matrix can be obtained by using the function “getRotationMatrix” in android-based systems, and then the rotation matrix will be used as the input of the function “getOrientation” to get the orientation of the smart phone, i.e., the angle of azimuth, pitch and roll. It is noted that the azimuth

rotates around the Z-axis, the pitch rotates around the X-axis, and the roll rotates around the Y -axis [29]. The pitch, which indicates the angle between the Y -axis and the ground will be selected as the fourth feature of the proposed algorithm. This is because when the user is suffering a fall accident event, the smart phone in the user’s pocket also tends to lie down, and the pitch angle is usually small and around zero. This characteristic can be best observed in Fig. 7.(a), where we show a pitch sequence with 300 samples when the user is suffering a fall accident event. For comparison purpose, we also show in Fig. 7.(b) to Fig. 7.(d) the pitch sequences of three kinds of normal activities including jump, running, and tread. As can be seen in the tail of the sequence in Fig. 7.(a), the absolute value of the pitch angle is much smaller than that of the transient state and that in Fig. 7.(b) to Fig. 7.(d). Based on this observation, the fourth feature in this paper is determined by checking if the average pitch angle of the last 15 samples, i.e., the 286th to the 300th data samples, in Fig. 7.(a) is smaller than a predefined threshold. In this paper, the threshold is selected to be 50, and we find it works very well as we will see in the experiments. IV. HIGH FREQUENCY CHARACTERISTIC ANALYSIS OF A FALL EVENT So far, we have defined the first four features that can be applied for the recognition of a fall accident event between normal activities. However, we find in our experiments that some of the normal activities, e.g., sit down and the behavior of wavering the smart phone up and down, is also possible in generating an S[n] sequence or pitch sequence similar to that of a fall accident event. The behavior of wavering the smart phone up and down can take place when the user is in a short-term



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Fig. 10. The magnitude response of the proposed high-pass filter. running activity and with the smart phone held in his or her hand. The behavior of wavering the smart phone is a special scenario since the smart phone is designed to be placed in the user’s pocket. However, this behavior do take place frequently in our daily life. Therefore, we have to find more useful features that can be used for distinguishing a fall accident event from normal activities like sit down and phone wavering. To do this, we analyze and compare the frequency components (spectrum) of the S[n] sequence under a fall accident event with that of normal activities like sit down and smart phone wavering. As the S[n] and pitch sequence of wavering the smart phone and that of a sit down activity are quite similar, the case of wavering the smart phone will be used for explanation and compared with a fall accident event for simplicity. The spectrums of the S[n] sequence under a fall event and that of wavering the smart phone are shown in Fig. 8.(a) and Fig. 8.(b) respectively. In order that the high frequency energy can be observed in a more clear manner, we also show in Fig. 8.(c) and Fig. 8.(d) the plot of Fig. 8.(a) and Fig. 8.(b) in log scale respectively. As can be seen in Fig. 8, we find that most of the frequency components of normal activities are less than 50Hz. On the contrary, frequency components higher than 50Hz can be detected when the user is suffering a fall accident event, meaning that energy in high-frequency part would be helpful and can be used in the classification process. IV-A. High-pass Filtering of the S[n] Signal To extract the high frequency characteristic of the S[n] sequence, a high-pass filter with finite impulse response (FIR filter) is designed in this paper. The specification of the de-

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Fig. 11. Time and frequency domain response of the S[n] sequence after the proposed high-pass filter. (a) Time domain response of the high-pass filtered S[n] sequence under a fall event. (b) Time domain response of the high-pass filtered S[n] sequence by wavering the smart phone. (c) Spectrum of (a). (d) Spectrum of (b). signed high-pass filter is listed as below and shown in Fig. 9 simultaneously [30]. • • • •

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According to these parameters, we implement an 84th order high-pass FIR filter in this paper [30]. The magnitude response of the proposed high-pass FIR filter is shown in Fig. 10. With the proposed filter, we can get a high-pass filtered signal, SHP F [n], of the S[n]. To highlight the difference on the high frequency characteristic between a fall event and normal activities, the response of the S[n] sequence under a fall event and that of obtained by wavering the smart phone up and down are shown in Fig. 11.(a) and Fig. 11.(b) respectively. To verify the effectiveness of the designed high-pass FIR filter, the spectrum (i.e., the frequency distribution) of Fig. 11.(a) and Fig. 11.(b) are shown in Fig. 11.(c) and Fig. 11.(d) respectively. We can see in Fig. 11.(c) and Fig. 11.(d) that the low frequency components of the S[n] sequence obtained under a fall event and that by wavering the smart phone up and down can be attenuated successfully after the filtering process. Moreover, we notice in Fig. 11.(c) and Fig. 11.(d) that the high frequency energy (higher than 50Hz) of a fall event is larger than that of wavering the smart phone (the largest strength is 4dB for fall accident and 1.4dB for phone wavering). Based



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Fig. 14. Time domain sequences of the triaxial accelerometer generated by wavering the smart phone up and down. (a) The S[n] sequence. (b) The ax [n] sequence. (c) The ay [n] sequence. (d) The az [n] sequence.

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Fig. 13. Time domain sequences generated by the triaxial accelerometer under a fall event. (a) The S[n] sequence. (b) The ax [n] sequence. (c) The ay [n] sequence. (d) The az [n] sequence. on this observation, we then take absolute value on the 300 amplitudes of the high-pass filtered S[n] sequence, i.e., take absolute value on SHP F [n] sequence, and then the absolute amplitudes of the 300 samples are summed up to get one of the components that will be used in the fifth feature. IV-B. Discrete Wavelet Transform (DWT) In addition to the use of a high-pass filter, we also apply the use of discrete wavelet transformation (DWT) so that the high frequency details of a fall accident event can be easily observed. Compared to short-time Fourier Transform (STFT), which employs a windowed fast Fourier transform (FFT) of fixed time and frequency resolution, the wavelet transform offers superior temporal resolution of the high frequency components and scale resolution of the low frequency components [31]-[33]. Based on its characteristic of providing a very good trade-off between temporal and frequency resolution simultaneously, the DWT has been widely applied to the field of signal processing, and

in particular, is ever used for the gait analysis of the elderly and patients with Parkinson’s disease [34]. The block diagram of a DWT analysis filter bank is shown in Fig. 12. To simplify the computational complexity, the Harr wavelet will be chosen for the transformation in this paper [33]. In DWT analysis filter bank, an input sequence ax [n] is first convolved with the low-pass filter g[n] and high-pass filter h[n] (as in Fig.12) respectively, and then the filtered sequences are down sampled by a factor of 2 to get the approximation and detail coefficients of the original sequence. When the discrete Haar wavelet transformation is used, the approximation coefficients aax [n] and the detail coefficients adx [n] of a sequence ax [n] can be calculated efficiently as in (3) and (4), respectively. [33]. 1 aax [n] = √ (ax [2n] + ax [2n + 1]); 2

(3)

1 adx [n] = √ (ax [2n] − ax [2n + 1]); 2

(4)

As we are paying attention to the high frequency characteristic of a fall event in this paper, we apply the Harr wavelet analysis filter bank to the ax [n], ay [n] and az [n] (i.e., sequences generated by the triaxial accelerometer), and get the part of detail coefficients, i.e., the adx [n], ady [n] and adz [n] in Fig. 12, of the filter bank in a similar manner as that in (4). Before we introduce how the DWT can be applied for the recognition of a fall event, we shown in Fig. 13 and Fig. 14 respectively the sequences generated by the triaxial



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(a) Detail coefficients of S[n]. (b) adx [n] by phone wavering.

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(c) ady [n] by phone wavering. (d) adz [n] by phone wavering.

Fig. 15. Detail coefficients after the Haar wavelet transform under a fall event. (a) The detail coefficients of S[n]. (b) The adx [n] sequence. (c) The ady [n] sequence. (d) The adz [n] sequence.

Fig. 16. Detail coefficients of the triaxial accelerometer after the Haar wavelet transform by wavering the smart phone up and down. (a) The detail coefficients of S[n]. (b) The adx [n] sequence. (c) The ady [n] sequence. (d) The adz [n] sequence.

accelerometer, i.e., S[n], ax [n], ay [n], and az [n], under a fall event and that by wavering the smart phone up and down, all with a segment of 300 data samples. Besides, the detail coefficients of the sequences in Fig. 13 and Fig. 14 after the discrete Haar wavelet analysis filter bank are shown in Fig. 15 and Fig. 16 respectively. As can be seen in Fig. 12 (the discrete wavelet filter analysis bank), there is an operation of down sample by 2 after the high-pass (h[n]) and low-pass filter (g[n]) respectively. Therefore, the length of the detail coefficient sequences after the discrete wavelet analysis filter bank will become 150 as can be seen in Fig. 15 and Fig. 16. We notice that the largest amplitude (in absolute value) among the detail coefficients of S[n] between a fall event (Fig. 15.(a)) and that of wavering the smart phone (Fig. 16.(a)) are around 0.26 (under a fall event) and 0.21 (phone wavering) respectively. The diversity on the largest amplitude is not remarkable. However, when we compare the detail coefficients, i.e., adx [n], ady [n], and adz [n], of a fall event and that of wavering smart phone in a separation manner, we can find a significant diversity on the largest amplitude between the two kinds of activities. Actually, we find the largest amplitude in Fig. 15.(b) to Fig. 15.(d), are 0.32 (adx [n]), 0.38 (ady [n]), and 0.48 (adz [n]) respectively, and that in Fig. 16.(b) to Fig. 16.(d) are 0.052 (adx [n]), 0.058 (ady [n]), and 0.22 (adz [n]) respectively. Obviously, the diversity on the detail coefficients of the ax [n], ay [n], and az [n], can be used for the recognition of a fall accident event from normal activities. In this paper, the largest amplitude in each of the three detail coefficient

Kernel Function:Linear Kernel 11 0 (training) 0 (classified) 1 (training) 1 (classified)

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Fig. 17. Training and classification result of the SVM. sequences will be picked out, and then the absolute values of the three amplitudes are summed up together to get the second component of the fifth feature. This value together with the energy strength just obtained in subsection IV-A by summing up the 300 amplitudes of the high-pass filtered S[n] sequence constitutes the fifth feature (a two-dimensional vector) of the proposed classification system. V. SUPPORT VECTOR MACHINE (SVM) The support vector machine (SVM), a supervised learning algorithm, is widely applied in the field of machine learning



S[n]>0.6G

Table I. The support vectors, corresponding weights and bias of the proposed SVM. wi -0.4348 0.0061 0.2377 0.1911

xi 8.2241 4.4865 7.7041 7.8150

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l1 = max (|adx [n]|) + max ((|ady [n]|) + max ((|adz [n]|) , (5) n

n

where n = 1 . . . 150, adx [n], ady [n], and adz [n] are the detail coefficients of ax [n], ay [n], and az [n] respectively by using a discrete Haar wavelet analysis filter bank in subsection IV-B. Moreover, the second component l2 (i.e., Label2) of the feature vector is given according to the following equation. l2 =

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|SHP F [n]| ,

(6)

n=1

where SHP F [n] is the result by convolving the S[n] with the proposed high-pass filter defined in subsection IV-A. Based on (5) and (6), we can construct a two-dimensional feature vector T x = (l1 , l2 ) , and this two-dimensional feature vector x will be processed by the designed support vector machine (SVM) (as in (7)) to recognize if the elderly is suffering a fall accident event. n y = (w1 x1 +w2 x2 +· · ·+wn xn )·x+b = wi xi ·x+b, (7) i=1

where x1 , x2 , ..., xn are 2×1 support vectors, n is the number of support vectors, w1 , w2 , ..., wn are the weights corresponding to individual support vectors, b is the bias, and y indicates the result of classification. To find the support vectors, the bias, as well as the weights corresponding to individual support vectors, a set with 63 positive feature vectors (i.e., the case of a fall accident event) and 60 negative feature vectors are used for the training of the SVM [35][36][37]. The process for finding the optimal support vectors is performed via the Matlab function “svmtrain”. In addition, the set of feature vectors will be randomly divided into two groups, one for training and the other for test, by using the Matlab function “crossvalind” before the training process. After an off-line training process, a set of support vectors with linear decision boundary can be obtained. The classification result of the training process is shown in Fig. 17, and the number of support vectors is found to be 4, i.e., n = 4, after the

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