Za directions.Therefore,it is essential to build a body coordinate system (BCS)to depict the limb movements in a consistent approach by reference to the human body. In regard to the body coordinate system.we set the vector corresponding to the heading direction of the human subject to represent the 2o axis.For the horizontal plane which is Yw orthogonal to the Z axis,we set the vector which is parallel Yg to the physical plane of the body to represent the X axis,and (a)The relationships between WCS (b)The relationships between GCS set the vector which is perpendicular to the physical plane of and GCS and BCS the body to represent the Yo axis.Fig.2(b)shows the three axes Fig.2.The relationship between different coordinate systems (X,Yo,Zo)of BCS and the three axes (Xg:Ya Zg)of GCS the Butterworth filter [4])in the watch coordinate system. in regard to the physical plane of the human body,respectively. Moreover,according to the magnetic measurements from the Considering that the human subject can perform the activity magnetometer,we can extract the magnetic force as a vector with different orientations of the physical plane of the body. m in the watch coordinate system.Then,we can build a e.g.,standing on the floor or lying on the floor,in all situations, global coordinate system (GCS)based on the gravity direction we can transform any inertial measurement from the GCS to and magnetic direction in the watch coordinate system.The BCS by also using the direction cosine representation.The procedure is as follows:After we obtain the gravity vector orientation of the body coordinate system relative to the global g,we derive its opposite value and normalize this vector as coordinate system is specified by a 3 x 3 rotation matrix C' Zg=g we then set this vector zg to represent the global in which each column is a unit vector along one of the global Zgaxis as it is in the opposite direction of the gravitational coordinate axes specified in terms of the body coordinate axes. acceleration and it is perpendicular to the horizontal plane. A vector quantity vo defined in GCS is equivalent to the vector After computing the cross product y =g x m,we obtain v=C'.v defined in BCS.In this way,we can transform any a vector y that is perpendicular to the plane determined by inertial measurement from the GCS to the BCS.In Section IV. the two distinct but intersecting lines corresponding to g we will introduce the approach to compute the rotation matrix and m.We normalize this vector as ya= 前·Since the C',by leveraging two signal gestures. vector y is on the horizontal plane,we set this vector ya In regard to the activities where the physical plane of the to represent the global Ya-axis.After that,by computing the human body is continuously changing,e.g.,sit-ups,we can set cross product x=gxy,we obtain a vector x that is orthogonal the initial physical plane of the human body as the reference to the plane determined by the two distinct but intersecting body coordinate system.In this way,each of the following lines corresponding to g and y.We normalize this vector as inertial measurements are measured in terms of the reference xg=to represent the global Xg-axis..Fig.2(a)further body coordinate system shows the relationship between the three axes(x,y and z) of WCS and the three axes (xgy and zg)of GCS. B.Modeling the Human Motion with Meta-Activity To quantify the orientation difference between the watch Each complex activity,e.g.,dumbbell side raise and bent- coordinates and global coordinates,we use the direction cosine over dumbbell laterals,is performed with a large range of representation [5].In the direction cosine representation,the movement.So it can be decomposed into a series of small- orientation of the global coordinate relative to the watch range movements which are sequentially performed over time. coordinate system is specified by a 3 x 3 rotation matrix C, Therefore,we leverage the term meta-activities to denote these in which each column is a unit vector along one of the watch small-range movements.Each meta-activity is defined as a unit coordinate axes specified in terms of the global coordinate movement with logically the minimal granularity in regard to axes.A vector quantity ve defined in the watch coordinate the moving range.We can define the whole set of complex system is equivalent to the vector v=C.v defined in the activities as a set C.and the whole set of meta-activities as a global coordinate system.In this way,we are able to transform set M.Then,according to the above definition,each complex any inertial measurement v from WCS to the corresponding activity cC can be depicted as a series of meta-activities, inertial measurement vg in GCS.During the human motion,i.e.,ci=(mj,...,mj),where mjE M. the directions of g and m are continuously updated in WCS 1)Angle Profiles:In regard to the activity sensing,due to track the three axes of GCS,so as to further update the to the differences in human-specific characters such as the rotation matrix C in a real-time approach. height,arm length,and moving behavior,different human 2)From Global Coordinate System to Body Coordinate subjects may perform the same activity with different speeds System:During the human motion,the human subject may and amplitudes.This causes nonnegligible deviations among be facing any arbitrary direction in regard to the global the inertial measurements of the same activities in both time coordinate system.Hence,although we can derive the inertial domain and space domain.Therefore,the meta-activity should measurement of limb movements in GCS,these measurements be depicted in a scalable approach,such that the activity may not be consistent with each other even if they belong sensing scheme can be tolerant to the variances in the limb to the same activity,due to the differences in the facing movements.However,traditional inertial measurements suchXw Yw Zw Zg Xg Yg (a) The relationships between WCS and GCS Zg(Zb) Yb Xb G Yg Xg ! ! Watch (b) The relationships between GCS and BCS Fig. 2. The relationship between different coordinate systems the Butterworth filter [4]) in the watch coordinate system. Moreover, according to the magnetic measurements from the magnetometer, we can extract the magnetic force as a vector m in the watch coordinate system. Then, we can build a global coordinate system (GCS) based on the gravity direction and magnetic direction in the watch coordinate system. The procedure is as follows: After we obtain the gravity vector g, we derive its opposite value and normalize this vector as zg = −g kgk , we then set this vector zg to represent the global Zg-axis as it is in the opposite direction of the gravitational acceleration and it is perpendicular to the horizontal plane. After computing the cross product y = g × m, we obtain a vector y that is perpendicular to the plane determined by the two distinct but intersecting lines corresponding to g and m. We normalize this vector as yg = y kyk . Since the vector yg is on the horizontal plane, we set this vector yg to represent the global Yg-axis. After that, by computing the cross product x = g×y, we obtain a vector x that is orthogonal to the plane determined by the two distinct but intersecting lines corresponding to g and y. We normalize this vector as xg = x kxk to represent the global Xg-axis.. Fig. 2(a) further shows the relationship between the three axes (xw, yw and zw) of WCS and the three axes (xg, yg and zg) of GCS. To quantify the orientation difference between the watch coordinates and global coordinates, we use the direction cosine representation [5]. In the direction cosine representation, the orientation of the global coordinate relative to the watch coordinate system is specified by a 3 × 3 rotation matrix C, in which each column is a unit vector along one of the watch coordinate axes specified in terms of the global coordinate axes. A vector quantity vw defined in the watch coordinate system is equivalent to the vector vg = C · vw defined in the global coordinate system. In this way, we are able to transform any inertial measurement vw from WCS to the corresponding inertial measurement vg in GCS. During the human motion, the directions of g and m are continuously updated in WCS to track the three axes of GCS, so as to further update the rotation matrix C in a real-time approach. 2) From Global Coordinate System to Body Coordinate System: During the human motion, the human subject may be facing any arbitrary direction in regard to the global coordinate system. Hence, although we can derive the inertial measurement of limb movements in GCS, these measurements may not be consistent with each other even if they belong to the same activity, due to the differences in the facing directions. Therefore, it is essential to build a body coordinate system (BCS) to depict the limb movements in a consistent approach by reference to the human body. In regard to the body coordinate system, we set the vector corresponding to the heading direction of the human subject to represent the Zb axis. For the horizontal plane which is orthogonal to the Zb axis, we set the vector which is parallel to the physical plane of the body to represent the Xb axis, and set the vector which is perpendicular to the physical plane of the body to represent the Yb axis. Fig. 2(b) shows the three axes (Xb, Yb, Zb) of BCS and the three axes (Xg, Yg, Zg) of GCS in regard to the physical plane of the human body, respectively. Considering that the human subject can perform the activity with different orientations of the physical plane of the body, e.g., standing on the floor or lying on the floor, in all situations, we can transform any inertial measurement from the GCS to BCS by also using the direction cosine representation. The orientation of the body coordinate system relative to the global coordinate system is specified by a 3 × 3 rotation matrix C’, in which each column is a unit vector along one of the global coordinate axes specified in terms of the body coordinate axes. A vector quantity vg defined in GCS is equivalent to the vector vb = C’·vg defined in BCS. In this way, we can transform any inertial measurement from the GCS to the BCS. In Section IV, we will introduce the approach to compute the rotation matrix C’, by leveraging two signal gestures. In regard to the activities where the physical plane of the human body is continuously changing, e.g., sit-ups, we can set the initial physical plane of the human body as the reference body coordinate system. In this way, each of the following inertial measurements are measured in terms of the reference body coordinate system. B. Modeling the Human Motion with Meta-Activity Each complex activity, e.g., dumbbell side raise and bent￾over dumbbell laterals, is performed with a large range of movement. So it can be decomposed into a series of small￾range movements which are sequentially performed over time. Therefore, we leverage the term meta-activities to denote these small-range movements. Each meta-activity is defined as a unit movement with logically the minimal granularity in regard to the moving range. We can define the whole set of complex activities as a set C, and the whole set of meta-activities as a set M. Then, according to the above definition, each complex activity ci ∈ C can be depicted as a series of meta-activities, i.e., ci = hmj1 , · · · , mjk i, where mj ∈ M. 1) Angle Profiles: In regard to the activity sensing, due to the differences in human-specific characters such as the height, arm length, and moving behavior, different human subjects may perform the same activity with different speeds and amplitudes. This causes nonnegligible deviations among the inertial measurements of the same activities in both time domain and space domain. Therefore, the meta-activity should be depicted in a scalable approach, such that the activity sensing scheme can be tolerant to the variances in the limb movements. However, traditional inertial measurements such