falls of the elderly always lead to serious health issues as the decline of their physical fitness . fracture is the most common injury in fall of an elderly and there is also a certain possibility to get coma , brain trauma , and paralysis . at most fall situations , the fall process is the main source of injury because of the high impact . but sometimes the late medical salvage may worsen the situation . that means the faster the salvage comes , the less risk the elderly will face . mems ( microelectro mechanical systems ) sensors have simplified the design and implementation of sensor system . location based service ( lbs ) makes it more convenient to locate the elderly in health monitoring . beside these cameras are distributed at limited space to offer pictures or videos of human activities to implement fall detection algorithm . external supports such as motion sensors could be used to enhance computer vision based fall detection method , and a data fusion algorithm can operate the validation and correlation among the two subsystems to raise robust performance of fall detection . these computer based methods work effectively in indoor environment , but they are hard to realize in outdoor environment as the deployment of cameras is always limited . there are several kinds of detection methods which differ in constitution of motion sensors and detection algorithms . a single triaxial accelerometer can provide object 's accelerations in three directions which include the influence of gravity . the influence of gravity or dynamic acceleration is available by using a low pass filter or a high pass filter . some kinds of angular movement information can also be calculated based on the relationship between acceleration components and their vector sum . a triaxial magnetometer can detect magnetic strength in three directions , and it can also provide angular motion information in the horizontal plane . but the environment magnetic field may disturb the geomagnetic field which reduces the reliability of the magnetometer outputs , for instance , in some steel structure architecture or near some objects with strong electromagnetism . as angular information can also be extracted from accelerometer measurements , a state space filter such as the kalman filter is a commonly used technique to combine angular motion information . beside these , sensors such as barometer can also assist pure motion sensors at human gait recognition . but , in fact , using more sensors means more power consumption , and it is a challenge to design a proper algorithm to fuse different kinds of sensors . a single triaxial accelerometer is quite enough for human fall detection as sufficient information could be extracted from its measurements . besides this , the accelerometer coordinate does not have to be fixed if only the magnitude of sum vector is needed , and that is quite convenient for wearable application . in this paper , a fall detection system based on a wearable device is developed . the hardware and software realization of the device is mainly based on a single triaxial accelerometer and gps / gsm module . the device uses an efficient fall detection algorithm with less resource and power consumption , which means that it is a proper design for outdoor application . then it will get the elderly 's geographic position and send fall alarm short message to caregivers . so the elderly who has fallen can get timely help to minimize the negative influence . information like linear movements ( e.g. , displacement , velocity , and acceleration ) and angular movements ( e.g. , angle , angular velocity , and angular acceleration ) could be obtained directly or indirectly . beside these , frequency domain parameters could be extracted from basic sensor measurements by techniques such as fft and wavelet [ 11 , 12 ] . for single triaxial accelerometer application , accelerations and derived angular parameters could be used as recognition features . fall detection algorithm design according to the recognition feature , fall detection algorithms are classified as threshold based and machine learning based . for threshold based method , threshold of recognition feature is set by the designer before application which makes the algorithm have rapid response and less resource consumption . but the choice of threshold needs both rigorous schemes and adequate experiments . for machine learning based design , the classification of fall and normal activities is available with the assistance of technologies such as support vector machine ( svm ) and neural network [ 14 , 15 ] . machine learning assistance may enhance system robustness to some extent , but its algorithm design is always high computing resource consumed which limits its application in wearable device . as the compact wearable device requires low power consumption and a single triaxial accelerometer could provide effective information , threshold based fall detection algorithm will be used in this system . algorithm used in this fall alarm system when a real fall happens , collision between human 's body and ground will produce obvious peak value at the sum acceleration a which has magnitude as 
 ( 1)a = ax2+ay2+az2 , 
 where ax , ay , and az present accelerometer measurements of three axes . the system uses the sum acceleration as the first step to distinguish high intensity movements from others . but normal motions such as jumping or sitting also produce peak values , which mean that additional detection features are required . as human 's motion has low acceleration , it is feasible to get gravity component in each axis by using a low pass filter . if gravity components could be separated before and after human 's fall , then it is possible to calculate the rotation angle of accelerometer coordinate in 3d space , which is also equivalent to the rotation angle of gravity vector relative to fixed coordinate . quaternion is an effective tool to describe rotation movement in human 's gait change which also includes falling . a quaternion could be described as 
 ( 2)q = q0+q1i+q2j+q3k 
 which has magnitude as 
 ( 3)q = q02+q12+q22+q32 . unit quaternion which has magnitude q = 1 can be described as 
 ( 4)q = cos2+sin2qxi+sin2qyj+sin2qzk. as shown in figure 3 , rotation angle of q equals . the rotation axis is orthogonal to the rotation plane and its direction is in accordance with right hand screw rule . qx , qy , and qz are three components of the unit vector which describes the orientation of the quaternion at the fixed coordinate . besides rotation movement , quaternion can also describe a vector in 3d space , such as the gravity vector g which could be described as a quaternion 
 ( 5)g=0+gxi+gyj+gzk.gx , gy , and gz are three components of g which has quaternion magnitude as 
 ( 6)g = gx2+gy2+gz2=g . a unit quaternion q is used to describe human 's falling movement , which can also be divided into three rotation quaternions q1 , q2 , and q3 to simplify the calculation as shown in figure 4 . with the help of gravity vector information before and after human 's falling movement as shown in figure 3 , these three separated quaternions are all available . q 
 1 could be expressed as 
 ( 7)q1=cos12+sin12sini+sin12cosj 
 which has rotation angle and rotation axis information as 
 ( 8)1=arctangbefore , zgbefore , x2+gbefore , y2,sin=gbefore , ygbefore , x2+gbefore , y2,cos=gbefore , xgbefore , x2+gbefore , y2 . quaternion q2 can be calculated as 
 ( 9)q2=cos22+sin22k 
 which has rotation angle as 
 ( 10)2=arctan2gafter , ygafter , xarctan2gbefore , ygbefore , x . quaternion q3 is 
 ( 11)q3=cos32+sin32sini+sin32cosj 
 with rotation angle and rotation axis information as 
 ( 12)3=arctangafter , zgafter , x2+gafter , y2,sin=gafter , ygafter , x2+gafter , y2,cos=gafter , xgafter , x2+gafter , y2 . then the rotation of the fall movement can be expressed by quaternion multiplication as 
 ( 13)gafter = qgbeforeq=q3q2q1gbeforeq1q2q3 , 
 where q=q0-q1i -- q2j -- q3k- is the conjugate quaternion of q. quaternion algebra is normally implemented based on basic matrix algebra . quaternion multiplication used above could be realized by matrix multiplication as 
 ( 14)qgbefore = mq0gbefore , xgbefore , ygbefore , z = q0q1q2q3q1q0q3q2q2q3q0q1q3q2q1q00gbefore , xgbefore , ygbefore , z . the whole rotation quaternion can also be decomposed as 
 ( 15)q = q3q2q1=mq3mq2q1.q1 , q2 , and q3 are all available based on gravity information before and after the falling movement . at last , it is possible to get four elements of quaternion q by the equation above and the rotation angle  could be calculated as 
 ( 16)=2arctanq12+q22+q32q0 . when an object is falling , magnitude of  will approach 90 which is also a character different from most normal activities . the wearable device will be mounted on human 's waist at first to reflect the motion of human body closely , and the device will record gbefore while the elderly is standing still . there is no special requirement of the device orientation but only keep stationary during the wear . athreshold means the threshold of sum acceleration magnitude and tthreshold means the threshold of oscillation time duration after the break of athreshold . when measurements in three different axes have been acquired , the sum acceleration |a| will be calculated . when a real fall happens , sum acceleration will reach peak value of |a|  athreshold . in a real falling , the fluctuation of acceleration will stop in time duration tthreshold and then the sum acceleration is |a|  g as the elderly will lie on the ground . then the acceleration a is recorded as gafter . , the system will consider it as a fall if the rotation angle ||  90. ti 's 16 bits mcu msp430f1611 is used to control the whole system and imply the detection algorithm . the measurement range of accelerometer could be set at 2  g , 4  g , 8  g , or 16 g , and the maximal sampling rate is 3.2  khz . as human 's activities are normally at low frequency bands , 100  hz is a proper sampling rate for human fall detection . there is an inner digital filter in adxl345 which could weaken noise and reduce the burden of digital signal processing in mcu to some extent . the measurements will be sent through iic ( interintegrated circuit ) bus communication between the sensor and the mcu . sim908 can offer gps and gsm service on serial port communication with mcu , and it can also work in low power mode . each hardware component of the wearable device is working under low voltage and the detection algorithm does not need complex calculation resource , so the power consumption of the whole device is quite low . a 1200  mah , 3.7  v polymer lithium battery is quite enough to provide the need of the wearable device for a couple of days . hardware structure of the detection device is shown in figure 6 , and the pcb board prototype is shown in figure 7 . one of them is the software design in wearable device , and the other is in the caregiver 's handset . after initialization of the system , gbefore would be extracted from acceleration measurements by using a low pass filter when the elderly is standing . if a fall has been detected , the wearable device will locate the user and send alarm short message to caregivers immediately . if the user withdraws the alarm by pressing a button manually , the device will get back to fall detection state and a short message will be sent to inform the caregivers . there is a url ( universal resource locator ) which links to a web map in the alarm short message . the fall location information will be highlighted on a web map when the caregiver opens this link . system test of the fall detection system has been conducted based on the system design described above . the sampling rate of accelerometer is set at 100  hz and the measurement range is 16  g with a maximum precision of 4  mg . mcu will read raw measurements from sensor 's inner fifo and apply the detection algorithm . the test objects are three different volunteers at the ages of 23 , 42 , and 60 , respectively . based on analysis of these volunteers ' experiment data , athreshold and tthreshold are set as 2  g and 2  s , respectively . in order to get g when standing and lying after the fall , sum acceleration a which has magnitude between ( 1  0.3 )  g and ( 1 + 0.3 )  g will be considered as gbefore and gafter . considering that the tilt of the ground or the lying posture of the elderly may affect the rotation angle , rotation angle  between ( 90  30) and ( 90 + 30) will infer that the elderly has fallen . system test contains five kinds of activities of daily living ( i.e. , walking , jumping , squatting , sitting , and resting ) and four kinds of fallings ( i.e. , forward , backward , leftward , and rightward ) . each kind of motion has been repeated 20 times on each volunteer , and the detection results of the proposed algorithm and an acceleration threshold based algorithm   are listed in table 1 . the sensitivity and specificity [ 21 , 22 ] of the proposed system can be got from the test data in table 1 . test results of acceleration threshold based algorithm show lower sensitivity and specificity at 91.6% and 88.7% , respectively . figure 9 shows the accelerations in different kinds of fallings which all trigger the fall alarm correctly and the corresponding rotation angles are 91.9 , 100.5 , 104.7 , and 114.1. 
 figure 10 shows acceleration during activity of lying down and resting which has rotation angle of 117.0 and similar waveform to falling , but the peak acceleration is much lower . they all do not have rotation about 90 ; even some of the peak values are quite high , so the fall alarm has not been triggered . an alarm sms ( short message service ) containing a map url has been received by the handset as shown in figure 12 when a fall has been detected . clicking the url will open a map in web browser on which the fall location will be displayed accurately as shown in figure 13 . this paper developed a fall detection system based on a single triaxial accelerometer based wearable device . there is no special requirement of the device 's mounting orientation because the algorithm does not claim the axes of accelerometer to be fixed strictly . the system has low power consumed hardware design and highly efficient algorithm which could extend the service time of the wearable device . as normal activity of resting also has similar rotation as falling , it may trigger fall alarm when the body hits ground heavily . so the choice of athreshold is quite important to distinguish falling from heavily lying activity . sufficient sample number collected from subjects with different age and gender will improve the reliability and robustness of the threshold . beside these , technologies such as svm and neural network are considerable to seek out a proper classification method based on the features used in this system .
fall detection is a major challenge in the public healthcare domain , especially for the elderly as the decline of their physical fitness , and timely and reliable surveillance is necessary to mitigate the negative effects of falls . 
 this paper develops a novel fall detection system based on a wearable device . 
 the system monitors the movements of human body , recognizes a fall from normal daily activities by an effective quaternion algorithm , and automatically sends request for help to the caregivers with the patient 's location .