-Tag plane ocientation -Tag arrany sotacioa 0 02 50 10 15 20 slation erro (c)Translation erro (d)Rotation error Tag array rotation 00 350 l50 20 350 Heavy multisnath ion betwee t盖different(f Rotation roith论erent tag-(Translation error wit通 Heavy multi-path Light multi-path (e)Translation error different (h)Rotation error with different tag-antenna distances antenna distances multi-path environments mult-path environments Fig.12.Evaluating the translation error and the rotation error with different settings. we can calculate the theoretical phase values based on the Different actual tag positions in the GCS,which are further used to spin tramework OptiTrack as arr可s calculate the phase change A0..In regard to the coordinate transformation,since the direction from the antenna to the tag RFID 3 tags array is calculated as Va =Ci/C in the GCS,which should Reader represent the same vector with the estimated direction vector V in the LCS,we simply transform the coordinate of the tag array from the LCS to the GCS based on Va and Tag array labeled antenna tennis racket E.3D Orientation Estimation After determining the position of the tag array,we estimate Fig.11.Experimental setup. the rotation angle of the tag array,which corresponds to the to evaluate the performance of our system in the 3D motion rotating angle around the estimated direction vector Va in the tracking.The initial posture is known by default.For each spe- GCS.The basic idea is to compare the calculated mismatching cific setting,we move the tag array along one coordinate axis directions m.i with the theoretical mismatching directions with the distance of 50cm to evaluate the tracking accuracy of m.,which are calculated based on the model in Section IV-B. the translation,and rotate the tag array around one coordinate Specifically.we can calculate the rotation angle Ao as: axis with the angle of 90 to evaluate the tracking accuracy of the rotation.Particularly,we use two metrics to judge the w Om.i-Om.i accuracy:the translation error refers to the difference between (14) =1 the ground-truth translation and the estimated translation,and Then,according to the rotation angle Ao and the estimated the rotation error refers to the angle difference between the antenna-tag direction Va,we rotate the tag array around Va ground-truth rotation and the estimated rotation.We use the with the angle of Ao.After the rotation,we can finally OptiTrack system to capture the ground-truth of the translation get the position and orientation of the tag array.Therefore, and rotation with the high-speed camera. by connecting the consecutive windows,we can track the B.Overall Performance of 3D Motion Tracking translation and the rotation of the tag array in the 3D space. Our solution can accurately track the translation with the VI.PERFORMANCE EVALUATION average error of 13.6cm and track the rotation with the average error of 8.3.We first show the overall tracking A.Experimental Setup accuracy of our system with the CDF in Fig.12(a)and We have implemented a system prototype with the ImpinJ Fig.12(b).For the translation error in Fig.12(a),the Y- R420 Speedway RFID reader and the Laird PA9-12 linearly axis outperforms the other two axes in tracking the movement polarized antenna.As shown in Fig.11,we design a spin of the tag array,because the translation along the Y-axis framework,which can continuously spin the antenna around leads to more distinctive phase change compared with the the spin axis and interrogate the tags simultaneously.The translation along the X-axis or Z-axis.Overall,more than antenna spins 4 rounds per second in our system.We design 80%experiment results achieve the translation error within three kinds of the tag array deployment with different numbers 14.5cm along the X-axis,5.8cm along the Y-axis and 13.4cm of tags,i.e.,3,4 and 5,which separates the endpoints between along the Z-axis.For the rotation error in Fig.12(b),the tag adjacent tags to reduce the mutual interference.During the array rotation achieves less than 4.8 error for 80%results, experiments,we vary the number of tags,the distance between which is 6.2 smaller than the rotation error of the tag plane. the tag array and the antenna,and the multi-path environment The accuracy of the tag array rotation is based on the RSSI 80 10 20 30 40 50 60 Translation error (cm) 0 0.2 0.4 0.6 0.8 1 CDF X-asix Y-axis Z-axis Combined (a) Overall translation error 0 5 10 15 20 25 30 Rotation error (°) 0 0.2 0.4 0.6 0.8 1 CDF Tag plane orientation Tag array rotation (b) Overall rotation error 3 4 5 Number of tags 0 5 10 15 20 Translation error (cm) X-asix Y-axis Z-axis (c) Translation error 3 4 5 Number of tags 0 5 10 15 20 25 Rotation error ( °) Tag plane orientation Tag array rotation (d) Rotation error 150 250 350 Translation between tag and antenna (cm) 0 5 10 15 20 Translation error (cm) X-asix Y-axis Z-axis (e) Translation error with different tag-antenna distances 150 250 350 Translation between tag and antenna (cm) 0 5 10 15 20 25 Rotation error ( °) Tag plane orientation Tag array rotation (f) Rotation error with different tag￾antenna distances Heavy multi-path Light multi-path 0 5 10 15 20 Translation error (cm) X-asix Y-axis Z-axis (g) Translation error with different multi-path environments Heavy multi-path Light multi-path 0 5 10 15 20 25 Rotation error ( °) Tag plane orientation Tag array rotation (h) Rotation error with different multi-path environments Fig. 12. Evaluating the translation error and the rotation error with different settings. we can calculate the theoretical phase values based on the actual tag positions in the GCS, which are further used to calculate the phase change ∆θbi,j . In regard to the coordinate transformation, since the direction from the antenna to the tag array is calculated as Vbd = Cbj/|Cbj | in the GCS, which should represent the same vector with the estimated direction vector Vb 0 d in the LCS, we simply transform the coordinate of the tag array from the LCS to the GCS based on Vbd and Vb 0 d . E. 3D Orientation Estimation After determining the position of the tag array, we estimate the rotation angle of the tag array, which corresponds to the rotating angle around the estimated direction vector Vbd in the GCS. The basic idea is to compare the calculated mismatching directions φbm,i with the theoretical mismatching directions φm,i, which are calculated based on the model in Section IV-B. Specifically, we can calculate the rotation angle ∆φ as: ∆φ = 1 N X N i=1  φm,i − φbm,i . (14) Then, according to the rotation angle ∆φ and the estimated antenna-tag direction Vbd, we rotate the tag array around Vbd with the angle of ∆φ. After the rotation, we can finally get the position and orientation of the tag array. Therefore, by connecting the consecutive windows, we can track the translation and the rotation of the tag array in the 3D space. VI. PERFORMANCE EVALUATION A. Experimental Setup We have implemented a system prototype with the ImpinJ R420 Speedway RFID reader and the Laird P A9-12 linearly polarized antenna. As shown in Fig. 11, we design a spin framework, which can continuously spin the antenna around the spin axis and interrogate the tags simultaneously. The antenna spins 4 rounds per second in our system. We design three kinds of the tag array deployment with different numbers of tags, i.e., 3, 4 and 5, which separates the endpoints between adjacent tags to reduce the mutual interference. During the experiments, we vary the number of tags, the distance between the tag array and the antenna, and the multi-path environment Spin￾antenna Linearly polarized antenna RFID Reader WiFi Spin axis OptiTrack � � � � Spin axis Tag array labeled tennis racket 3 tags 5 tags 4 tags Spin framework Different tag arrays Fig. 11. Experimental setup. to evaluate the performance of our system in the 3D motion tracking. The initial posture is known by default. For each spe￾cific setting, we move the tag array along one coordinate axis with the distance of 50cm to evaluate the tracking accuracy of the translation, and rotate the tag array around one coordinate axis with the angle of 90◦ to evaluate the tracking accuracy of the rotation. Particularly, we use two metrics to judge the accuracy: the translation error refers to the difference between the ground-truth translation and the estimated translation, and the rotation error refers to the angle difference between the ground-truth rotation and the estimated rotation. We use the OptiTrack system to capture the ground-truth of the translation and rotation with the high-speed camera. B. Overall Performance of 3D Motion Tracking Our solution can accurately track the translation with the average error of 13.6cm and track the rotation with the average error of 8.3 ◦ . We first show the overall tracking accuracy of our system with the CDF in Fig. 12(a) and Fig. 12(b). For the translation error in Fig. 12(a), the Y - axis outperforms the other two axes in tracking the movement of the tag array, because the translation along the Y -axis leads to more distinctive phase change compared with the translation along the X-axis or Z-axis. Overall, more than 80% experiment results achieve the translation error within 14.5cm along the X-axis, 5.8cm along the Y -axis and 13.4cm along the Z-axis. For the rotation error in Fig. 12(b), the tag array rotation achieves less than 4.8 ◦ error for 80% results, which is 6.2 ◦ smaller than the rotation error of the tag plane. The accuracy of the tag array rotation is based on the RSSI 8