一N=1,0.0) N=0,10 -V=1,0.0m =087,05.01 N=050.870) V05,-0.87.0 Antenna V=0.87,050 Tag array 2 N=05.087.0 N=(-087,050 -V=0.87-0.5,0 V=0.5.0870 N=-l.00m plane V=0.1.m Y 2 0 2 1 2 Fig.7.Antenna direction estimation based on tag array tion m when we vary normal vec-tion m when we vary relative di- elevation angle and the deflection angle.Therefore,when we tor Nt.Vd =(0,1,0) rection Vd,N:(0,1,0) deploy more than three tags in the tag array,we can generate Fig.6.Mismatching direction om V.S.rotation offset 6. at least three pairs of phase difference to accurately estimate (8).As shown in Fig.6,when the normal vector of the tag the antenna direction Va.which is further used to estimate the array plane N:is orthogonal to antenna-tag direction Va,m movements of the tag array in Section V-D. is always 0,because the projections of the tag P:with different rotation offsets o share the same direction.Beyond that,the V.SYSTEM DESIGN A.Overview mismatching directionom is almost monotonically changing with the rotation offset o,indicting the possibility to estimate The major objective of our work is to track the 3D motion of 6 from the detected om.Besides,for the tag with the same the tag array labeled objects with the new antenna deployment, rotation offset 6,the mismatching direction om varies a little i.e.,Spin-antenna.By spinning the linearly polarized antenna, with either Ne or Va,which is caused by the small orientation we can not only extract the most distinctive signal features change during the projection.Since the real calculatedom due to the linear polarization;but also sufficiently suppress fluctuates due to the noise,it is difficult to accurately estimate the ambient signal interference.Fig.8 shows the system either Va or N:based on the tiny change ofm. overview of Spin-antenna.We take as input both the RSSI C.Modeling Phase Difference of Tag Array with Spin-antenna and the phase stream.First,Preprocessing segments the signals Different from the RSSI pattern,which is more sensitive into separated windows,calculates the mismatching directions to the rotation offset 6,the phase value is more sensitive to and calibrates the phase based on the RSSI variation,which the translation of the tag array,which is corresponding to the produces the distinctive signal features.Then,Relative Di- rection Estimation uses the phase model in Section IV-C to antenna-tag direction and the orientation of the tag array plane. Therefore,we build a phase-based model with the tag array to estimate the relative direction of the antenna based on the estimate the direction of the signal source.As shown in Fig.7. calibrated phase values.After that,Coordinate Transforma- instead of using the Global Coordinate System(GCS),we use tion transforms the relative direction of antenna in the local the Local Coordinate System (LCS)of the tag array,and set coordinate system to the global coordinate system based on the center of the tag array to the origin.The coordinate of each the positions of the tag array in the previous window.Based tag is preset based on the deployment of the tag array.When on the transformed positions of the tag array,3D Orientation the antenna,i.e..the signal source,transmits the RF-signal to Estimation finally estimates the rotation of the tag array based on the mismatching directions.Therefore,with the position the tag array,the incident angle can be represented as a unit direction vector V.We use the prime symbol to represent the and the orientation of the tag array in the consecutive window, vectors in the LCS.The RF-signal traverses different distances we can estimate the corresponding translation and the rotation of the tag array,which are used to calibrate the 3D motion to reach each tag Ti in Fig.7.If we use To as a reference tag, then the difference of the transmitting distance between T;and tracking in the following windows. To is: Mismatching RSSI/Phase stream Calibrated △d,o=V.0Va (9) directions phase Preprocessing Here,Vio is the vector from Toto Ti in the LCS.Eq. 3D (9)calculates the length of the projection of vector Vo orientation Coordinate Relative direction transformation along the direction V.which is actually the difference of estimation estimation the transmitting distance.In the RFID system,the difference Translation/Rotation of the transmitting distance can be calculated from the phase estimation difference of corresponding tags as: △90=4r△40 Fig.8.System overview of Spin-antenna mod 2 (10) 入 B.Preprocessing where A0i.o=0i-0o calculates the phase difference between In this section,we preprocess the raw phase/RSSI signals T;and 7o.and A is the wavelength.Therefore,we can estimate to extract the most distinctive signal features.Particularly,we the vector of the incident angle V based on the measured segment the signals into separated windows based on the cycle phase difference A0io and the preset tag array deployment of the spinning framework,then estimate the mismatching Vo V is represented with two angle parameters,i.e.,the directions from the RSSI variation.and calibrate the phase 60 1 2 3 (radian) -2 0 2 4 m (radian) N t=(1,0,0) N t=(0.87,0.5,0) N t=(0.5,0.87,0) N t=(0,1,0) N t=(-0.5,0.87,0) N t=(-0.87,0.5,0) N t=(-1,0,0) (a) Variation of mismatching direc￾tion φm when we vary normal vec￾tor Nt, Vd = (0, 1, 0) 0 1 2 3 (radian) -2 0 2 4 m (radian) Vd=(0,-1,0) Vd=(0.5,-0.87,0) Vd=(0.87,-0.5,0) Vd=(1,0,0) Vd=(0.87,0.5,0) Vd=(0.5,0.87,0) Vd=(0,1,0) (b) Variation of mismatching direc￾tion φm when we vary relative di￾rection Vd, Nt = (0, 1, 0) Fig. 6. Mismatching direction φm V.S. rotation offset δ. (8). As shown in Fig. 6, when the normal vector of the tag array plane Nt is orthogonal to antenna-tag direction Vd, φm is always 0, because the projections of the tag Pt with different rotation offsets δ share the same direction. Beyond that, the mismatching direction φm is almost monotonically changing with the rotation offset δ, indicting the possibility to estimate δ from the detected φm. Besides, for the tag with the same rotation offset δ, the mismatching direction φm varies a little with either Nt or Vd, which is caused by the small orientation change during the projection. Since the real calculated φm fluctuates due to the noise, it is difficult to accurately estimate either Vd or Nt based on the tiny change of φm. C. Modeling Phase Difference of Tag Array with Spin-antenna Different from the RSSI pattern, which is more sensitive to the rotation offset δ, the phase value is more sensitive to the translation of the tag array, which is corresponding to the antenna-tag direction and the orientation of the tag array plane. Therefore, we build a phase-based model with the tag array to estimate the direction of the signal source. As shown in Fig. 7, instead of using the Global Coordinate System (GCS), we use the Local Coordinate System (LCS) of the tag array, and set the center of the tag array to the origin. The coordinate of each tag is preset based on the deployment of the tag array. When the antenna, i.e., the signal source, transmits the RF-signal to the tag array, the incident angle can be represented as a unit direction vector V 0 d . We use the prime symbol to represent the vectors in the LCS. The RF-signal traverses different distances to reach each tag Ti in Fig. 7. If we use T0 as a reference tag, then the difference of the transmitting distance between Ti and T0 is: ∆di,0 = V 0 i,0 · V 0 d . (9) Here, V 0 i,0 is the vector from T0 to Ti in the LCS. Eq. (9) calculates the length of the projection of vector V 0 i,0 along the direction V 0 d , which is actually the difference of the transmitting distance. In the RFID system, the difference of the transmitting distance can be calculated from the phase difference of corresponding tags as: ∆θi,0 = 4π∆di,0 λ mod 2π, (10) where ∆θi,0 = θi−θ0 calculates the phase difference between Ti and T0, and λ is the wavelength. Therefore, we can estimate the vector of the incident angle V 0 d based on the measured phase difference ∆θi,0 and the preset tag array deployment V 0 i,0 . V 0 d is represented with two angle parameters, i.e., the � � � Antenna � �& �' �) * Tag array plane ∆�',& �',& * Fig. 7. Antenna direction estimation based on tag array. elevation angle and the deflection angle. Therefore, when we deploy more than three tags in the tag array, we can generate at least three pairs of phase difference to accurately estimate the antenna direction V 0 d , which is further used to estimate the movements of the tag array in Section V-D. V. SYSTEM DESIGN A. Overview The major objective of our work is to track the 3D motion of the tag array labeled objects with the new antenna deployment, i.e., Spin-antenna. By spinning the linearly polarized antenna, we can not only extract the most distinctive signal features due to the linear polarization; but also sufficiently suppress the ambient signal interference. Fig. 8 shows the system overview of Spin-antenna. We take as input both the RSSI and the phase stream. First, Preprocessing segments the signals into separated windows, calculates the mismatching directions, and calibrates the phase based on the RSSI variation, which produces the distinctive signal features. Then, Relative Di￾rection Estimation uses the phase model in Section IV-C to estimate the relative direction of the antenna based on the calibrated phase values. After that, Coordinate Transforma￾tion transforms the relative direction of antenna in the local coordinate system to the global coordinate system based on the positions of the tag array in the previous window. Based on the transformed positions of the tag array, 3D Orientation Estimation finally estimates the rotation of the tag array based on the mismatching directions. Therefore, with the position and the orientation of the tag array in the consecutive window, we can estimate the corresponding translation and the rotation of the tag array, which are used to calibrate the 3D motion tracking in the following windows. RSSI/Phase stream Preprocessing Relative direction estimation 3D orientation estimation Translation/Rotation estimation Mismatching directions Calibrated phase Coordinate transformation Fig. 8. System overview of Spin-antenna. B. Preprocessing In this section, we preprocess the raw phase/RSSI signals to extract the most distinctive signal features. Particularly, we segment the signals into separated windows based on the cycle of the spinning framework, then estimate the mismatching directions from the RSSI variation, and calibrate the phase 6