This article has been accepted for inclusion in a future issue of this journal.Content is final as presented,with the exception of pagination IEEE/ACM TRANSACTIONS ON NETWORKING general-purpose tags,which are EPC C1G2 standards compli- Z◆4Y ant.We attach five RFID tags to the five fingers of a glove,one tag per finger,as shown in Figure 2(b).In performing multi- P(X,0,) finger micromovements,we let the RFID reader continuously 08i0,0,0) interrogate these tags and obtain RF signals from each tag via three antennas. Operation Plane 口0' A.3D Positioning Model p-0,0,h (x,y,-h) When the human subject performs the multi-touch gesture in the air with the tagged fingers,he/she usually performs the Fig.3.The position of the tag P on the operation plane. following two kinds of movement:1)Large-range movement: the human subject performs the movement with fairly large range in the 3-dimensional space,such as swipe left/right and punch.The moving range is usually greater than half of the wave length (i.e.,about 17cm)so that the phase changes of the RFID tags exceed a complete period.2)Small-range micromovement:the human subject performs the movement with very small range in the 3-dimensional space,such as zoom in/out,rotate left/right,and flick.The moving range is less than half of the wave length(i.e.,about 17cm)so that the 10 phase changes of the RFID tags does not exceed a complete X axis period. Fig.4.The hyperbola:the intersection between the conical surface and the Therefore,for the large-range movement,since the phase operation plane. change exceeds a complete period,it is neither accurate nor necessary to recognize the movement by phase changes. Instead,we can leverage the 3D positioning method to effec- as (,y,-h).Thus POll =vx2 +2+h2.Since the angle tively recognize the large-range movement.For the small- ∠POP'=a,then range micromovement,since the position change of the tagged ‖PO=IPOll cosa. (1) fingers is rather small (it is usually less than 5cm).thus we rely on the phase changes to recognize the small-range micromove- Hence,as P'Ol =Eq.(1)is equivalent to ment.Nevertheless,the phase changes of the micromovement l=Vx2+y2+h2.cosa. (2) also depends on the exact position of the tagged fingers.For example,the phase changes of the same type of micromove- Therefore, ment may vary to a certain extent when it is performed at sin2a·x2-cos2a·y2=h2.cos2a. different positions of the 3-dimensional space.In summary, (3) 3D positioning is essential in recognizing both the large-range It implies that the feasible solution of P on the operational and small-range movement. plane is a hyperbola.We further illustrate the above conclu- Suppose we can build a 3D coordinate system according to sion with an example as shown in Fig.4.Since the angle the operation plane,as shown in Fig.3.The antenna pair is POP'=a,and OP'is collinear with the X-axis,so the deployed along the X-axis,while the origin O is set to the possible trace of P in the 3-dimensional space can be denoted center of the antenna pair.The X-axis and Y-axis are mutually as a conical surface originated from the point O.When the orthogonal and parallel to the operation plane,and the Z-axis conical surface intersects with the operation plane,the possible is orthogonal to the operation plane.Assume that a specified trace of P forms a hyperbola on the operation plane. tag is denoted as a point P=(,y,z)on the operation plane, Suppose the human subject is performing the micromove- the projection of the point P on the X-axis is P.As in ment on the same operation plane,more or less.That is conventional operations of multi-touch in the air,the tagged to say,the distance h between the operation plane and the fingers of the human subjects are separated with a fairly large antenna plane keeps almost constant.As we deploy two mutu- distance (e.g.,150cm~200cm)to the three antennas,whereas ally orthogonal antenna pairs along the X-axis and Y-axis, the antennas are separated with a limited distance (e.g.,20cm respectively,then,according to the two antenna pairs,the ~30cm)to each other,thus we can leverage the Angle of feasible solutions of the tag's position can be estimated as two Arrival(AoA)method to figure out the direction of the tag in hyperbolas intersecting on the operation plane.Thus,we can the 3D space.Then,according to the AoA method,we can estimate the position of the tag by computing the intersections estimate the angle between OP and OP/as a.Assume that of the two hyperbolas.Fig.5 shows an example of positioning the projection of the origin O on the operation plane is O', the tag by computing the intersections between two hyperbolas then the distance between the antenna plane and the operation on the operation plane.Here,the antennas are separated with a plane is h=OO'l=-z.Therefore,the coordinate of horizontal/vertical distance of 20cm,and the distance between O'is (0,0,-h),the coordinate of P can be also denoted the operation plane and the antenna plane is set to 100cm.This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4 IEEE/ACM TRANSACTIONS ON NETWORKING general-purpose tags, which are EPC C1G2 standards compli￾ant. We attach five RFID tags to the five fingers of a glove, one tag per finger, as shown in Figure 2(b). In performing multi- finger micromovements, we let the RFID reader continuously interrogate these tags and obtain RF signals from each tag via three antennas. A. 3D Positioning Model When the human subject performs the multi-touch gesture in the air with the tagged fingers, he/she usually performs the following two kinds of movement: 1) Large-range movement: the human subject performs the movement with fairly large range in the 3-dimensional space, such as swipe left/right and punch. The moving range is usually greater than half of the wave length (i.e., about 17cm) so that the phase changes of the RFID tags exceed a complete period. 2) Small-range micromovement: the human subject performs the movement with very small range in the 3-dimensional space, such as zoom in/out, rotate left/right, and flick. The moving range is less than half of the wave length (i.e., about 17cm) so that the phase changes of the RFID tags does not exceed a complete period. Therefore, for the large-range movement, since the phase change exceeds a complete period, it is neither accurate nor necessary to recognize the movement by phase changes. Instead, we can leverage the 3D positioning method to effec￾tively recognize the large-range movement. For the small￾range micromovement, since the position change of the tagged fingers is rather small (it is usually less than 5cm), thus we rely on the phase changes to recognize the small-range micromove￾ment. Nevertheless, the phase changes of the micromovement also depends on the exact position of the tagged fingers. For example, the phase changes of the same type of micromove￾ment may vary to a certain extent when it is performed at different positions of the 3-dimensional space. In summary, 3D positioning is essential in recognizing both the large-range and small-range movement. Suppose we can build a 3D coordinate system according to the operation plane, as shown in Fig.3. The antenna pair is deployed along the X-axis, while the origin O is set to the center of the antenna pair. The X-axis and Y -axis are mutually orthogonal and parallel to the operation plane, and the Z-axis is orthogonal to the operation plane. Assume that a specified tag is denoted as a point P = (x, y, z) on the operation plane, the projection of the point P on the X-axis is P . As in conventional operations of multi-touch in the air, the tagged fingers of the human subjects are separated with a fairly large distance (e.g., 150cm∼200cm) to the three antennas, whereas the antennas are separated with a limited distance (e.g., 20cm ∼30cm) to each other, thus we can leverage the Angle of Arrival (AoA) method to figure out the direction of the tag in the 3D space. Then, according to the AoA method, we can estimate the angle between OP and OP as α. Assume that the projection of the origin O on the operation plane is O , then the distance between the antenna plane and the operation plane is h = OO = −z. Therefore, the coordinate of O is (0, 0, −h), the coordinate of P can be also denoted Fig. 3. The position of the tag P on the operation plane. Fig. 4. The hyperbola: the intersection between the conical surface and the operation plane. as (x, y, −h). Thus P O = x2 + y2 + h2. Since the angle ∠POP = α, then P O = P O · cos α. (1) Hence, as P O = |x|, Eq.(1) is equivalent to |x| = x2 + y2 + h2 · cos α. (2) Therefore, sin2 α · x2 − cos2 α · y2 = h2 · cos2 α. (3) It implies that the feasible solution of P on the operational plane is a hyperbola. We further illustrate the above conclu￾sion with an example as shown in Fig.4. Since the angle ∠POP = α, and OP is collinear with the X-axis, so the possible trace of P in the 3-dimensional space can be denoted as a conical surface originated from the point O. When the conical surface intersects with the operation plane, the possible trace of P forms a hyperbola on the operation plane. Suppose the human subject is performing the micromove￾ment on the same operation plane, more or less. That is to say, the distance h between the operation plane and the antenna plane keeps almost constant. As we deploy two mutu￾ally orthogonal antenna pairs along the X-axis and Y -axis, respectively, then, according to the two antenna pairs, the feasible solutions of the tag’s position can be estimated as two hyperbolas intersecting on the operation plane. Thus, we can estimate the position of the tag by computing the intersections of the two hyperbolas. Fig.5 shows an example of positioning the tag by computing the intersections between two hyperbolas on the operation plane. Here, the antennas are separated with a horizontal/vertical distance of 20cm, and the distance between the operation plane and the antenna plane is set to 100cm.