IEEE TRANSACTIONS ON MOBILE COMPUTING,VOL.XX,NO.XX,2020 14 OptiTrack Movement tags Touch tag the eraser.The multi-path propagation mainly comes from the RF-signal reflection from the human hand.It is observed that as the number of tags increases,the translation error 5 monotonically decreases for the light multi-path situation, 11g 9.5cm because phase samplings from more tags help reduce the es- 2四640 timation error;For the heavy multi-path situation,the trans- Router 9.48cm lation error does not monotonically decrease,sometimes it RFID Reader Linear Region even slightly increases,because the phase samplings from Non-linear Region some tags become outliers due to the multi-path from the hand,further increasing the estimation error.Besides,as the Fig.20.The experimental setup moving distance gradually increases from 0~3cm to 6~9cm, 9 PERFORMANCE EVALUATION the translation error monotonically increases,because the 9.1 Experimental Setup translation error should be mainly linear to the moving distance.Nevertheless,the average translation errors are all We built RF-Dial using an ImpinJ R420 reader,two Laird less than 1cm for the light multi-path situation,and less than S9028 RFID antennas and a board eraser with multiple tags, 2cm for the heavy multi-path situation.Fig.21(b)shows i.e.,AZ9629 tags as movement tags,and E51 AZ9640/ the translation error for the non-linear region in the heavy AZ9662 as the touch tag.For the rigid motion tracking,as multi-path situation.It is observed that the translation error shown in Fig.20,we deployed two antennas around a table for the non-linear region is a bit larger than the one for in a mutually orthogonal manner.The two antennas are the linear region,nevertheless,very close performance is separated about 0.8m away from the table,and the antennas achieved for the two regions.It implies that our solution is and the table are at the same height of 0.8m.The size of the able to efficiently tackle the translation estimation in both board eraser is 13x5.5cm2,and we designed three layouts the linear region and non-linear region.The above solu- of the tag array with different numbers of tags,i.e.,2,4, tions all used the movement calibration method,we further 6.We operated the tagged board eraser on the table within evaluated the performance for the movement calibration the range of 100x50cm2,including the linear region and method.Fig.21(c)shows the translation error with/without non-linear region.For the touch gesture detection,only one calibration in the heavy multi-path situation.The number antenna is required in theory.According to Observation 3,the of tags is 4,and the translation is randomly selected from RSSI deviation is insensitive to the angle below 45.Consid- 0~9cm.It is observed that the calibrated solution can further ering that the board eraser can be with any rotation on the reduce 44%and 47%of the translation error,respectively,for table and there are one orthogonally deployed antenna pair, the linear region and non-linear region. we select the antenna whose polarization angle relative to the tag is smaller to collect data for analysis.We tested three 9.2.2 Evaluate the rotation error kinds of linear tags as touch tag,including E51/AZ9640/ To evaluate the rotation error of the rigid transformation,we AZ9662.OptiTrack was used to provide the ground truth. set the central point of the eraser as the rotation center,and rotated the eraser around the center with a random angle 9.2 Evaluation of Rigid Motion Tracking from 0 to 30.We randomly selected 100 samples with We first evaluated the performance in tracking the motion of different rotation angles,,i.e,010°，1020°，and2030° translation and rotation.We respectively used two metrics Fig.21(d)shows the rotation error with different multi-path to evaluate the performance in tracking accuracy,i.e.,the effect in the linear region.the results are very similar to the translation error and rotation error.The translation error refers translation error for different multi-path situations.The av- to the difference between the ground-truth translation and erage rotation errors are all less than 2.2 for the light multi- the estimated translation,which is measured in the unit path situation,and less than 6 for the heavy multi-path of cm.The rotation error refers to the difference between situation.Fig.21(e)shows the rotation error for the non- the ground-truth rotation and the estimated rotation,which linear region in the heavy multi-path situation.The rotation is measured in the unit of degree.We evaluated the per- error for the nonlinear region is a bit larger than the linear formance by varying the following factors:1)the number region,nevertheless,very close performance is achieved for of tags in the tag array,2)the moving distance of the the two regions.It implies that our solution can efficiently tagged object,3)the light multi-path and heavy multi-path tackle the rotation in both regions.The above solutions situations,and 4)the linear region and non-linear region. all used the calibration method,we further evaluated the performance for the calibration method.Fig.21(f)shows the 9.2.1 Evaluate the translation error rotation error with/without calibration in the heavy multi- To evaluate the translation error of the rigid transformation, path situation.The number of tags is 4,and the rotation we selected a start point and moved the tagged eraser to is randomly selected from 0~30.It is observed that the an end point with only translation.We randomly selected calibrated solution can further reduce 25%and 26%of the 100 samples with different moving distances,i.e.,0~3cm, rotation error for the linear region and non-linear region. 3~6cm,and 6~9cm.Fig.21(a)shows the translation error with different multi-path effect in the linear region.Here 9.2.3 Macro benchmark of rigid motion tracking the light multi-path situation refers to the situation where We further compare RF-Dial with the state-of-art absolute the user does not hold the eraser,whereas the heavy multi-localization-based solution (AbsLoc),which is also adopted path situation refers to the situation where the user holds in Tagball [16].For AbsLoc,we estimated the absoluteIEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. XX, NO. XX, 2020 14 11cm 11cm 5.5cm 11cm 5.5cm RFID Antenna Pair RFID Reader Tagged Object Linear Region Non-linear Region 2 tags 4 tags 6 tags WiFi Router OptiTrack Movement tags Touch tag AZ9640 AZ9662 E51 9.5cm 9.48cm 7cm 1.7cm 0.8cm 0.8cm Fig. 20. The experimental setup 9 PERFORMANCE EVALUATION 9.1 Experimental Setup We built RF-Dial using an ImpinJ R420 reader, two Laird S9028 RFID antennas and a board eraser with multiple tags, i.e., AZ9629 tags as movement tags, and E51 / AZ9640 / AZ9662 as the touch tag. For the rigid motion tracking, as shown in Fig. 20, we deployed two antennas around a table in a mutually orthogonal manner. The two antennas are separated about 0.8m away from the table, and the antennas and the table are at the same height of 0.8m. The size of the board eraser is 13×5.5cm2 , and we designed three layouts of the tag array with different numbers of tags, i.e., 2, 4, 6. We operated the tagged board eraser on the table within the range of 100×50cm2 , including the linear region and non-linear region. For the touch gesture detection, only one antenna is required in theory. According to Observation 3, the RSSI deviation is insensitive to the angle below 45◦ . Consid￾ering that the board eraser can be with any rotation on the table and there are one orthogonally deployed antenna pair, we select the antenna whose polarization angle relative to the tag is smaller to collect data for analysis. We tested three kinds of linear tags as touch tag, including E51 / AZ9640 / AZ9662. OptiTrack was used to provide the ground truth. 9.2 Evaluation of Rigid Motion Tracking We first evaluated the performance in tracking the motion of translation and rotation. We respectively used two metrics to evaluate the performance in tracking accuracy, i.e., the translation error and rotation error. The translation error refers to the difference between the ground-truth translation and the estimated translation, which is measured in the unit of cm. The rotation error refers to the difference between the ground-truth rotation and the estimated rotation, which is measured in the unit of degree. We evaluated the per￾formance by varying the following factors: 1) the number of tags in the tag array, 2) the moving distance of the tagged object, 3) the light multi-path and heavy multi-path situations, and 4) the linear region and non-linear region. 9.2.1 Evaluate the translation error To evaluate the translation error of the rigid transformation, we selected a start point and moved the tagged eraser to an end point with only translation. We randomly selected 100 samples with different moving distances, i.e., 0∼3cm, 3∼6cm, and 6∼9cm. Fig. 21(a) shows the translation error with different multi-path effect in the linear region. Here the light multi-path situation refers to the situation where the user does not hold the eraser, whereas the heavy multi￾path situation refers to the situation where the user holds the eraser. The multi-path propagation mainly comes from the RF-signal reflection from the human hand. It is observed that as the number of tags increases, the translation error monotonically decreases for the light multi-path situation, because phase samplings from more tags help reduce the es￾timation error; For the heavy multi-path situation, the trans￾lation error does not monotonically decrease, sometimes it even slightly increases, because the phase samplings from some tags become outliers due to the multi-path from the hand, further increasing the estimation error. Besides, as the moving distance gradually increases from 0∼3cm to 6∼9cm, the translation error monotonically increases, because the translation error should be mainly linear to the moving distance. Nevertheless, the average translation errors are all less than 1cm for the light multi-path situation, and less than 2cm for the heavy multi-path situation. Fig. 21(b) shows the translation error for the non-linear region in the heavy multi-path situation. It is observed that the translation error for the non-linear region is a bit larger than the one for the linear region, nevertheless, very close performance is achieved for the two regions. It implies that our solution is able to efficiently tackle the translation estimation in both the linear region and non-linear region. The above solu￾tions all used the movement calibration method, we further evaluated the performance for the movement calibration method. Fig. 21(c) shows the translation error with/without calibration in the heavy multi-path situation. The number of tags is 4, and the translation is randomly selected from 0∼9cm. It is observed that the calibrated solution can further reduce 44% and 47% of the translation error, respectively, for the linear region and non-linear region. 9.2.2 Evaluate the rotation error To evaluate the rotation error of the rigid transformation, we set the central point of the eraser as the rotation center, and rotated the eraser around the center with a random angle from 0 ◦ to 30◦ . We randomly selected 100 samples with different rotation angles, i.e., 0∼10◦ , 10∼20◦ , and 20∼30◦ . Fig. 21(d) shows the rotation error with different multi-path effect in the linear region. the results are very similar to the translation error for different multi-path situations. The av￾erage rotation errors are all less than 2.2◦ for the light multi￾path situation, and less than 6◦ for the heavy multi-path situation. Fig. 21(e) shows the rotation error for the non￾linear region in the heavy multi-path situation. The rotation error for the nonlinear region is a bit larger than the linear region, nevertheless, very close performance is achieved for the two regions. It implies that our solution can efficiently tackle the rotation in both regions. The above solutions all used the calibration method, we further evaluated the performance for the calibration method. Fig. 21(f) shows the rotation error with/without calibration in the heavy multi￾path situation. The number of tags is 4, and the rotation is randomly selected from 0∼30◦ . It is observed that the calibrated solution can further reduce 25% and 26% of the rotation error for the linear region and non-linear region. 9.2.3 Macro benchmark of rigid motion tracking We further compare RF-Dial with the state-of-art absolute localization-based solution (AbsLoc), which is also adopted in Tagball [16]. For AbsLoc, we estimated the absolute