Spin-Antenna - 3D Motion Tracking for Tag Array Labeled Objects via Spinning Antenna

Spin-Antenna:3D Motion Tracking for Tag Array Labeled Objects via Spinning Antenna Chuyu Wang,Lei Xie,Keyan Zhang,Wei Wang,Yanling Bu,Sanglu Lu State Key Laboratory for Novel Software Technology,Nanjing University,China Email:{chuyu,Ixie,ww,sanglu}@nju.edu.cn,{yanling,koye@smail.nju.edu.cn Abstract-Nowadays,the growing demand for the 3D human- computer interaction(HCD has brought about a number of novel Spinning linearly polarized antenna approaches,which achieve the HCI by tracking the motion of dif- ferent devices,including the translation and the rotation.In this paper,we propose to use a spinning linearly polarized antenna to track the 3D motion of a specified object attached with the passive RFID tag array.Different from the fixed antenna-based 3D motion Linear solutions,which suffer from the unavoidable signal interferences polarization at some specific positions/orientations,and only achieve the good performance in some feasible sensing conditions,our spinning antenna-based solution seeks to sufficiently suppress the ambient signal interferences and extracts the most distinctive features, by actively spinning the antenna to create the optimal sensing Fig.1.Use the spinning antenna to track the 3D motion of tagged object. condition.Moreover,by leveraging the matching/mismatching smartphone,reconstruct the gesture trace based on the inertial property of the linearly polarized antenna,i.e.,in comparison measurement data from the accelerometer and the gyroscope, to the circularly polarized antenna,the phase variation around the matching direction is more stable,and the RSSI variation which suffer from the limited battery life and the high cost of in the mismatching direction is more distinctive,we are able to hardwares.Moreover,some specific sensors with the accurate find more distinctive features to estimate the position and the sensing capability are relatively heavy,leading to uncomfort- orientation.We build a model to investigate the RSSI and the able user experience.Recently,the sensorless methods,such as phase variation of the RFID tag along with the spinning of the WiFi and RFID-based sensing,have been widely investigated antenna,and further extend the model from a single RFID tag to an RFID tag array.Furthermore,we design corresponding to design novel HCI schemes.In particular,due to the low- solutions to extract the distinctive RSSI and phase values from cost and the light-weight properties,the RFID system has the RF-signal variation.Our solution tracks the translation of the enabled brand-new solutions for the motion tracking and the tag array based on the phase features,and the rotation of the gesture recognition [4.8,9,11,15],by attaching the RFID tag array based on the RSSI variation.The experimental results tags on the HCI devices.However,most of the previous work show that our system can achieve an average error of 13.6cm in the translation tracking,and an average error of 8.3 in the tracks the motion of the tagged object only in the 2D space rotation tracking in the 3D space which do not consider the orientation variation of the tagged I.INTRODUCTION object in the 3D space.Tagyro [13]tracks the orientation of Nowadays,the 3D human-computer interaction (HCl)has a tagged object via multiple antennas.however.it is not able become a brand-new approach to allow the users to interact to track the absolute translation of the object simultaneously. with the computer via natural 3D gestures.Conventionally, Tag-compass [7]estimates the orientation of one tag based the users perform the gestures with a specific device,while on multiple spinning antennas,however,it is based on the both the position and the orientation of this device are contin- precondition that the tagged object is deployed in a specified uously tracked to generate the corresponding gestures for the 2D plane.Different from these work,we need to track the interaction.Such interaction style can get rid of the constraint motion of the tag array in the 3D space with six degrees from traditional interaction devices,e.g.,the keyboard and the of freedom,including the translation and rotation,which has mouse,which only work in the 2D space,and provide more remained unresolved so far. comfortable user experience and accurate operation,when In this paper,we propose a novel RFID-based approach interacting in the 3D space. to track the 3D motion of the tagged object by continuously The state-of-art HCI approaches mainly fall into three spinning the linearly polarized antenna.Specifically,we attach categories,i.e.,the computer vision (CV)-based approaches, a tag array onto the specified object with multiple tags in sensor-based approaches,and sensorless approaches.The CV-different orientations,and extract the distinctive signal features based approaches,e.g.,Microsoft Kinect,use the features from based on the spinning antenna to track the 3D motion of captured images to perform the motion tracking and gesture the tagged object,including the translation and the rotation. recognition,which are easy to be affected by either the poor Realizing that the fixed antenna-based solutions in the previous light condition or the object occlusion in the non-line-of- work usually suffer from the unavoidable signal interferences sight condition.Sensor-based approaches,e.g.,IMU in the at some specific positions/orientations,and only achieve good

Spin-Antenna: 3D Motion Tracking for Tag Array Labeled Objects via Spinning Antenna Chuyu Wang, Lei Xie, Keyan Zhang, Wei Wang, Yanling Bu, Sanglu Lu State Key Laboratory for Novel Software Technology, Nanjing University, China Email: {chuyu, lxie, ww, sanglu}@nju.edu.cn, {yanling, koye}@smail.nju.edu.cn Abstract—Nowadays, the growing demand for the 3D human￾computer interaction (HCI) has brought about a number of novel approaches, which achieve the HCI by tracking the motion of dif￾ferent devices, including the translation and the rotation. In this paper, we propose to use a spinning linearly polarized antenna to track the 3D motion of a specified object attached with the passive RFID tag array. Different from the fixed antenna-based solutions, which suffer from the unavoidable signal interferences at some specific positions/orientations, and only achieve the good performance in some feasible sensing conditions, our spinning antenna-based solution seeks to sufficiently suppress the ambient signal interferences and extracts the most distinctive features, by actively spinning the antenna to create the optimal sensing condition. Moreover, by leveraging the matching/mismatching property of the linearly polarized antenna, i.e., in comparison to the circularly polarized antenna, the phase variation around the matching direction is more stable, and the RSSI variation in the mismatching direction is more distinctive, we are able to find more distinctive features to estimate the position and the orientation. We build a model to investigate the RSSI and the phase variation of the RFID tag along with the spinning of the antenna, and further extend the model from a single RFID tag to an RFID tag array. Furthermore, we design corresponding solutions to extract the distinctive RSSI and phase values from the RF-signal variation. Our solution tracks the translation of the tag array based on the phase features, and the rotation of the tag array based on the RSSI variation. The experimental results show that our system can achieve an average error of 13.6cm in the translation tracking, and an average error of 8.3 ◦ in the rotation tracking in the 3D space. I. INTRODUCTION Nowadays, the 3D human-computer interaction (HCI) has become a brand-new approach to allow the users to interact with the computer via natural 3D gestures. Conventionally, the users perform the gestures with a specific device, while both the position and the orientation of this device are contin￾uously tracked to generate the corresponding gestures for the interaction. Such interaction style can get rid of the constraint from traditional interaction devices, e.g., the keyboard and the mouse, which only work in the 2D space, and provide more comfortable user experience and accurate operation, when interacting in the 3D space. The state-of-art HCI approaches mainly fall into three categories, i.e., the computer vision (CV)-based approaches, sensor-based approaches, and sensorless approaches. The CV￾based approaches, e.g., Microsoft Kinect, use the features from captured images to perform the motion tracking and gesture recognition, which are easy to be affected by either the poor light condition or the object occlusion in the non-line-of￾sight condition. Sensor-based approaches, e.g., IMU in the ! Spin axis Linear polarization Spinning linearly polarized antenna 3D motion Tag array " # Fig. 1. Use the spinning antenna to track the 3D motion of tagged object. smartphone, reconstruct the gesture trace based on the inertial measurement data from the accelerometer and the gyroscope, which suffer from the limited battery life and the high cost of hardwares. Moreover, some specific sensors with the accurate sensing capability are relatively heavy, leading to uncomfort￾able user experience. Recently, the sensorless methods, such as WiFi and RFID-based sensing, have been widely investigated to design novel HCI schemes. In particular, due to the low￾cost and the light-weight properties, the RFID system has enabled brand-new solutions for the motion tracking and the gesture recognition [4, 8, 9, 11, 15], by attaching the RFID tags on the HCI devices. However, most of the previous work tracks the motion of the tagged object only in the 2D space, which do not consider the orientation variation of the tagged object in the 3D space. Tagyro [13] tracks the orientation of a tagged object via multiple antennas, however, it is not able to track the absolute translation of the object simultaneously. Tag-compass [7] estimates the orientation of one tag based on multiple spinning antennas, however, it is based on the precondition that the tagged object is deployed in a specified 2D plane. Different from these work, we need to track the motion of the tag array in the 3D space with six degrees of freedom, including the translation and rotation, which has remained unresolved so far. In this paper, we propose a novel RFID-based approach to track the 3D motion of the tagged object by continuously spinning the linearly polarized antenna. Specifically, we attach a tag array onto the specified object with multiple tags in different orientations, and extract the distinctive signal features based on the spinning antenna to track the 3D motion of the tagged object, including the translation and the rotation. Realizing that the fixed antenna-based solutions in the previous work usually suffer from the unavoidable signal interferences at some specific positions/orientations, and only achieve good 1

performance in some feasible sensing conditions,our spin- In this paper,we make three main contributions as follows. ning antenna-based solution seeks to sufficiently suppress the 1)To the best of our knowledge,we are the first to thoroughly ambient signal interferences and extracts the most distinctive investigate the characteristics of the spinning linearly polarized features,by actively spinning the antenna to create the optimal antenna in the RFID system,with empirical studies and sensing condition.We build a model to investigate the received building models,which further facilitate the motion tracking signal strength indicator(RSSI)and phase variation along with in the 3D space.2)We propose to leverage the tag array the spinning of the antenna.Besides,we further extend the with different tag orientations for the 3D motion tracking, model of a single tag to the tag array,which investigates the e and build corresponding models to derive the translation and relationship between the RF-signal features and the posture of the rotation based on the RSSI and the phase extracted from the tag array,including the position and the orientation.Based the spinning linearly polarized antenna.3)We implement a on the above model,we design corresponding solutions to prototype system of a spinning antenna with the COTS RFID extract the distinctive RSSI and phase values from the RF- and evaluate its performance in the real environment.The signal variation.Our solution tracks the translation of the experiments show that our system can achieve an average tag array according to the extracted phase features,and the accuracy of 13.6cm in the translation tracking,and an average rotation of the tag array according to the extracted RSSI accuracy of 8.3 in the rotation tracking in the 3D space. variation.In this way,we are able to accurately track the II.RELATED WORK motion of tagged object in the 3D space.Fig.1 gives a Computer Vision-based Approach.Based on the accurate illustration of our spinning antenna-based solution by attaching captured images and videos,the CV-based approaches are the tag array onto the tennis racket. widely used to track the motion or recognize the gesture There are two key challenges to address in this paper.The of either objects or human subjects [3,5].However,these first challenge is to accurately estimate the 3D motion of the approaches are easily affected by the poor light condition or tag array,including the translation and the rotation,which has the object occlusion in the non-line-of-sight (NLOS)condition. six degrees of freedom.Since the change of any degree of In contrast,we leverage the RFID technology,which uses the freedom usually leads to the variation of all signal features backscatter communication to read the passive RFID tags,so including the RSSI and phase,it is conventionally impractical that our system has no requirements of the light condition. to efficiently figure out the exact motion state from the com- Sensor-based Approach.Built-in sensors in wearable de- plex state space.To address this challenge,we spin the linearly vices,e.g.,the accelerometer and the gyroscope,can be uti- polarized antenna to continuously interrogate the tag array for lized to reconstruct the gesture trace [12,14.16].For example, the motion tracking.By leveraging the matching/mismatching ArmTrack [10]proposes to track the posture of the entire arm property of the linearly polarized antenna,i.e.,in comparison solely relying on the smartwatch.However,the motion sensors to the circularly polarized antenna,the phase variation around in wearable devices have limited battery life and high cost,and the matching direction is more stable,and the RSSI variation the tracking accuracy is relatively low due to the noise of the in the mismatching direction is more distinctive,we are able measurement data.Some specific sensors with high accuracy to find more distinctive features to estimate the orientation and sensing capability are too heavy to provide comfortable user position.Moreover,by actively spinning the antenna,we can experience.In contrast,we attach a paper-like passive tag array effectively create the optimal sensing conditions and extract onto the target to track the 3D motion,which is battery-free, the distinctive signal features including the RSSI and the low-cost,light-weight and portable. phase,to perform the accurate tracking of the 3D motion. RFID-based Approach.Recently,several studies have pro- The second challenge is to tackle the variation of signal posed to utilize the RFID technique to track the motion of features when spinning the antenna,and use these features tagged objects [1,6,9,11,15,17].Wang et al.[11]track to derive six degrees of freedom for the tag array,since the moving tagged finger in a 2D plane with multiple fixed the relationship between the signal feature variations and the antennas.Shangguan et al.[9]track the 2D moving trace of 3D motion with the spinning linearly polarized antenna has the tagged object to obtain user feedbacks with only one fixed never been sufficiently investigated before.To address this antenna.These solutions focus on tracking the moving trace challenge,we conduct empirical studies and learn that,during in the 2D space,but they are not suitable for the orientation the spinning process,the RSSI is reduced to the minimum tracking in the 3D space.Tagyro [13]tracks the 3D orientation when the linear polarization of the antenna is mismatching the of a tagged objects based on the phase differences of the tags tag orientation,and the phase keeps stable around the matching via multiple antennas.Liu et al.[7]leverage multiple spinning direction of the antenna.Furthermore,we build a model to linearly polarized antenna to estimate the 3D orientation of one depict the relationship between the signal feature variations tag in a specified 2D plane.However,these methods only can and the matching/mismatching direction of the antenna-tag tracks the 3D orientation and are unable to track the absolute pair.We further extend the model to the tag array.Based on translation of the object in the 3D space simultaneously. this model,according to the distinctive RSSI variation.we use Different from the prior work,we focus on tracking the rigid the mismatching direction of each antenna-tag pair to estimate motion of the tag array in the 3D space via only one spinning the rotation of the tag array,and use the stable phase features linear polarized antenna,including both the translation and the to estimate the translation of the tag array rotation.which has remained unresolved so far. 2

performance in some feasible sensing conditions, our spin￾ning antenna-based solution seeks to sufficiently suppress the ambient signal interferences and extracts the most distinctive features, by actively spinning the antenna to create the optimal sensing condition. We build a model to investigate the received signal strength indicator (RSSI) and phase variation along with the spinning of the antenna. Besides, we further extend the model of a single tag to the tag array, which investigates the relationship between the RF-signal features and the posture of the tag array, including the position and the orientation. Based on the above model, we design corresponding solutions to extract the distinctive RSSI and phase values from the RF￾signal variation. Our solution tracks the translation of the tag array according to the extracted phase features, and the rotation of the tag array according to the extracted RSSI variation. In this way, we are able to accurately track the motion of tagged object in the 3D space. Fig.1 gives a illustration of our spinning antenna-based solution by attaching the tag array onto the tennis racket. There are two key challenges to address in this paper. The first challenge is to accurately estimate the 3D motion of the tag array, including the translation and the rotation, which has six degrees of freedom. Since the change of any degree of freedom usually leads to the variation of all signal features including the RSSI and phase, it is conventionally impractical to efficiently figure out the exact motion state from the com￾plex state space. To address this challenge, we spin the linearly polarized antenna to continuously interrogate the tag array for the motion tracking. By leveraging the matching/mismatching property of the linearly polarized antenna, i.e., in comparison to the circularly polarized antenna, the phase variation around the matching direction is more stable, and the RSSI variation in the mismatching direction is more distinctive, we are able to find more distinctive features to estimate the orientation and position. Moreover, by actively spinning the antenna, we can effectively create the optimal sensing conditions and extract the distinctive signal features including the RSSI and the phase, to perform the accurate tracking of the 3D motion. The second challenge is to tackle the variation of signal features when spinning the antenna, and use these features to derive six degrees of freedom for the tag array, since the relationship between the signal feature variations and the 3D motion with the spinning linearly polarized antenna has never been sufficiently investigated before. To address this challenge, we conduct empirical studies and learn that, during the spinning process, the RSSI is reduced to the minimum when the linear polarization of the antenna is mismatching the tag orientation, and the phase keeps stable around the matching direction of the antenna. Furthermore, we build a model to depict the relationship between the signal feature variations and the matching/mismatching direction of the antenna-tag pair. We further extend the model to the tag array. Based on this model, according to the distinctive RSSI variation, we use the mismatching direction of each antenna-tag pair to estimate the rotation of the tag array, and use the stable phase features to estimate the translation of the tag array. In this paper, we make three main contributions as follows. 1) To the best of our knowledge, we are the first to thoroughly investigate the characteristics of the spinning linearly polarized antenna in the RFID system, with empirical studies and building models, which further facilitate the motion tracking in the 3D space. 2) We propose to leverage the tag array with different tag orientations for the 3D motion tracking, and build corresponding models to derive the translation and the rotation based on the RSSI and the phase extracted from the spinning linearly polarized antenna. 3) We implement a prototype system of a spinning antenna with the COTS RFID and evaluate its performance in the real environment. The experiments show that our system can achieve an average accuracy of 13.6cm in the translation tracking, and an average accuracy of 8.3 ◦ in the rotation tracking in the 3D space. II. RELATED WORK Computer Vision-based Approach. Based on the accurate captured images and videos, the CV-based approaches are widely used to track the motion or recognize the gesture of either objects or human subjects [3, 5]. However, these approaches are easily affected by the poor light condition or the object occlusion in the non-line-of-sight (NLOS) condition. In contrast, we leverage the RFID technology, which uses the backscatter communication to read the passive RFID tags, so that our system has no requirements of the light condition. Sensor-based Approach. Built-in sensors in wearable de￾vices, e.g., the accelerometer and the gyroscope, can be uti￾lized to reconstruct the gesture trace [12, 14, 16]. For example, ArmTrack [10] proposes to track the posture of the entire arm solely relying on the smartwatch. However, the motion sensors in wearable devices have limited battery life and high cost, and the tracking accuracy is relatively low due to the noise of the measurement data. Some specific sensors with high accuracy sensing capability are too heavy to provide comfortable user experience. In contrast, we attach a paper-like passive tag array onto the target to track the 3D motion, which is battery-free, low-cost, light-weight and portable. RFID-based Approach. Recently, several studies have pro￾posed to utilize the RFID technique to track the motion of tagged objects [1, 6, 9, 11, 15, 17]. Wang et al. [11] track the moving tagged finger in a 2D plane with multiple fixed antennas. Shangguan et al. [9] track the 2D moving trace of the tagged object to obtain user feedbacks with only one fixed antenna. These solutions focus on tracking the moving trace in the 2D space, but they are not suitable for the orientation tracking in the 3D space. Tagyro [13] tracks the 3D orientation of a tagged objects based on the phase differences of the tags via multiple antennas. Liu et al. [7] leverage multiple spinning linearly polarized antenna to estimate the 3D orientation of one tag in a specified 2D plane. However, these methods only can tracks the 3D orientation and are unable to track the absolute translation of the object in the 3D space simultaneously. Different from the prior work, we focus on tracking the rigid motion of the tag array in the 3D space via only one spinning linear polarized antenna, including both the translation and the rotation, which has remained unresolved so far. 2

III.EMPIRICAL STUDY We conduct empirical studies to investigate the RF-signal features of the spinning antenna,by using an RFID reader,a ntenna circularly polarized antenna,a linearly polarized antenna and LInear polarization a passive UHF RFID tag.The experiment setup is shown in Fig.2.For the global coordinate system (GCS),the origin O 1a2 B is set to the center of the antenna,the Z-axis is vertically 100cm straight up,the Y-axis is along the spin axis,and the GCS Polarization angle Spin axis is a right-hand system.Specifically,for the linearly polarized antenna,the polarization angle,denoted as o,is defined as the Fig.2.Empirical study setup. incline angle between the X-axis and the linear polarization phase values,and more sensitive orientation information based plane.The polarization direction is defined as the direction on the distinctive RSSI variation.Thus,we prefer the linearly of intersection between the linear polarization plane and the polarized antenna in our work. antenna plane.For simplicity,we use the polarization angle to B. RSSI Variation Pattern of Linearly Polarized Antenna indicate the spin angle of the antenna during the spinning,i.e., Observation 2.For the linearly polarized antenna,the mis- when the linear polarization plane of the antenna is vertical matching direction,corresponding to the minimum RSSI value, as the blue plane in Fig.2.the polarization angle is 900,and is more distinctive for the estimation of the tag orientation the spin angle equals 90.As a dipole,the tag is regarded as than the matching direction,corresponding to the maximum a line and depicted with the 3D orientation of the line. RSSI value.We move the tag from position A (0,200,0)to A.Signal Features between Different Antennas position B(-100,200,0)with the same orientation,and spin Observation 1.During the spinning process,in comparison the linearly polarized antenna to interrogate the tag,the results to the circularly polarized antenna,the phase variation of are plotted in Fig.3(c).By comparing Fig.3(c)with Fig.3(b). the linearly polarized antenna is more stable,and the RSSI it is found that the two RSSI variation patterns of the tag at variation of the linearly polarized antenna is more distinctive. different positions share the similar shape,consisting of two As shown in Fig.2,we put a tag at position A(0,200,0), arches,but they have quite different absolute values.The peak which is parallel to the XZ-plane with the included angle of the arch refers to the perfectly matching polarization direc- against the X-axis (or Z-axis)of 60(or 30),then spin tion with the tag orientation,called the matching direction,and the circular/linearly polarized antenna around the Y-axis to the valley of the arch refers to the mismatching polarization interrogate the tag,separately.We compare the RF-signal direction with the tag orientation,called the mismatching variation of the tag from the circularly polarized antenna with direction.The mismatching direction in Fig.3(b)is 153, that from the linearly polarized antenna,and plot the results which is almost orthogonal to the tag orientation when the in Fig.3(a)and Fig.3(b).It is found that the phase value tag is at position A.But the mismatching direction changes to from the circularly polarized antenna is linearly changing with 166 in Fig.3(c).It indicates that even if the tag orientation is the antenna spinning,while that from the linearly polarized unchanged,the mismatching direction will change according antenna almost keeps unchanged.For the circularly polarized to the position of the tag.Moreover,as shown in Fig.3(c),the antenna,the polarization direction rotates electronically,which RSSI values are similar around the matching direction,while can be regarded as the summation of multiple RF-signals with they are more distinctive around the mismatching direction. different polarization directions and initial phase values.The Hence,we use the mismatching direction to estimate the tag matches the RF-signal with the same polarization direction tag orientation instead of the matching direction,which is to harvest the maximum energy,thus,the phase value of the relatively difficult to deduce. tag changes during the spinning.For the linearly polarized C.Phase Variation Pattern of Linearly Polarized Antenna antenna,it has only one polarization direction with one initial Observation 3.For the linearly polarized antenna,the phase value,so the phase value of the tag is independent phase value keeps stable when the polarization direction of the of the spinning angle and keeps stable.Besides,the RSSI antenna matches the tag orientation perfectly;and the phase values from the two types of antennas are both changing value fluctuates when the polarization direction mismatches periodically with the spinning antenna,but the RSSI variation the tag orientation due to the multi-path effect.We place range from the linearly polarized antenna is much larger,i.e., the tag at position A vertically or horizontally,i.e.,the tag 23dB larger than that from the circularly polarized antenna. orientation is along the Z-axis or the X-axis,and spin the For the circularly polarized antenna,the RSSI reduction is linearly polarized antenna to interrogate the tags with different due to the different antenna gains along different directions. orientations,respectively.We conduct the experiments in an For the linearly polarized antenna,the RSSI reduction is due open lobby,where the antenna is at the height of 150cm and to the mismatch of the linear polarization direction with the 500cm away from the surrounding walls,so the horizontal tag orientation,which leads to large energy loss and causes multi-path effect is relatively smaller than the vertical one more distinctive RSSI variation.Therefore,compared to the As shown in Fig.3(d),the phase value of the vertical tag circularly polarized antenna,the linearly polarized antenna can almost keeps unchanged,while that of the horizontal tag provide more reliable position information based on the stable changes to a certain extent,especially when the tag orientation 3

III. EMPIRICAL STUDY We conduct empirical studies to investigate the RF-signal features of the spinning antenna, by using an RFID reader, a circularly polarized antenna, a linearly polarized antenna and a passive UHF RFID tag. The experiment setup is shown in Fig. 2. For the global coordinate system (GCS), the origin O is set to the center of the antenna, the Z-axis is vertically straight up, the Y -axis is along the spin axis, and the GCS is a right-hand system. Specifically, for the linearly polarized antenna, the polarization angle, denoted as φ, is defined as the incline angle between the X-axis and the linear polarization plane. The polarization direction is defined as the direction of intersection between the linear polarization plane and the antenna plane. For simplicity, we use the polarization angle to indicate the spin angle of the antenna during the spinning, i.e., when the linear polarization plane of the antenna is vertical as the blue plane in Fig. 2, the polarization angle is 90◦ , and the spin angle equals 90◦ . As a dipole, the tag is regarded as a line and depicted with the 3D orientation of the line. A. Signal Features between Different Antennas Observation 1. During the spinning process, in comparison to the circularly polarized antenna, the phase variation of the linearly polarized antenna is more stable, and the RSSI variation of the linearly polarized antenna is more distinctive. As shown in Fig. 2, we put a tag at position A (0, 200, 0), which is parallel to the XZ-plane with the included angle against the X-axis (or Z-axis) of 60◦ (or 30◦ ), then spin the circular/linearly polarized antenna around the Y -axis to interrogate the tag, separately. We compare the RF-signal variation of the tag from the circularly polarized antenna with that from the linearly polarized antenna, and plot the results in Fig. 3(a) and Fig. 3(b). It is found that the phase value from the circularly polarized antenna is linearly changing with the antenna spinning, while that from the linearly polarized antenna almost keeps unchanged. For the circularly polarized antenna, the polarization direction rotates electronically, which can be regarded as the summation of multiple RF-signals with different polarization directions and initial phase values. The tag matches the RF-signal with the same polarization direction to harvest the maximum energy, thus, the phase value of the tag changes during the spinning. For the linearly polarized antenna, it has only one polarization direction with one initial phase value, so the phase value of the tag is independent of the spinning angle and keeps stable. Besides, the RSSI values from the two types of antennas are both changing periodically with the spinning antenna, but the RSSI variation range from the linearly polarized antenna is much larger, i.e., 23dB larger than that from the circularly polarized antenna. For the circularly polarized antenna, the RSSI reduction is due to the different antenna gains along different directions. For the linearly polarized antenna, the RSSI reduction is due to the mismatch of the linear polarization direction with the tag orientation, which leads to large energy loss and causes more distinctive RSSI variation. Therefore, compared to the circularly polarized antenna, the linearly polarized antenna can provide more reliable position information based on the stable z � � � Linear polarization Antenna � � Tag � � Polarization angle Spin axis Fig. 2. Empirical study setup. phase values, and more sensitive orientation information based on the distinctive RSSI variation. Thus, we prefer the linearly polarized antenna in our work. B. RSSI Variation Pattern of Linearly Polarized Antenna Observation 2. For the linearly polarized antenna, the mis￾matching direction, corresponding to the minimum RSSI value, is more distinctive for the estimation of the tag orientation than the matching direction, corresponding to the maximum RSSI value. We move the tag from position A (0, 200, 0) to position B (−100, 200, 0) with the same orientation, and spin the linearly polarized antenna to interrogate the tag, the results are plotted in Fig. 3(c). By comparing Fig. 3(c) with Fig. 3(b), it is found that the two RSSI variation patterns of the tag at different positions share the similar shape, consisting of two arches, but they have quite different absolute values. The peak of the arch refers to the perfectly matching polarization direc￾tion with the tag orientation, called the matching direction, and the valley of the arch refers to the mismatching polarization direction with the tag orientation, called the mismatching direction. The mismatching direction in Fig. 3(b) is 153◦ , which is almost orthogonal to the tag orientation when the tag is at position A. But the mismatching direction changes to 166◦ in Fig. 3(c). It indicates that even if the tag orientation is unchanged, the mismatching direction will change according to the position of the tag. Moreover, as shown in Fig. 3(c), the RSSI values are similar around the matching direction, while they are more distinctive around the mismatching direction. Hence, we use the mismatching direction to estimate the tag orientation instead of the matching direction, which is relatively difficult to deduce. C. Phase Variation Pattern of Linearly Polarized Antenna Observation 3. For the linearly polarized antenna, the phase value keeps stable when the polarization direction of the antenna matches the tag orientation perfectly; and the phase value fluctuates when the polarization direction mismatches the tag orientation due to the multi-path effect. We place the tag at position A vertically or horizontally, i.e., the tag orientation is along the Z-axis or the X-axis, and spin the linearly polarized antenna to interrogate the tags with different orientations, respectively. We conduct the experiments in an open lobby, where the antenna is at the height of 150cm and 500cm away from the surrounding walls, so the horizontal multi-path effect is relatively smaller than the vertical one. As shown in Fig. 3(d), the phase value of the vertical tag almost keeps unchanged, while that of the horizontal tag changes to a certain extent, especially when the tag orientation 3

Phase fluctuation Weak Stable pha muti-pat业 Stable pha to mull山-pah direction. 00 00 100 200 300 100 200 0 100 200 300 Spinning direction() Spinning direction() Spinming direction() pinning (a)RF-signal from the circularly po-(b)RF-signal from the linearly polar-(c)RF-signal from the linearly polar-(d)Phase measurement when a tag is larized antenna of a tag at (0,200,0)ized antenna of a tag at (0,200,0)ized antenna of a tag at(-100,200.0)vertically/horizontally deployed Fig.3.Results of the empirical study mismatches the polarization direction of the antenna.When the tag orientation mismatches the polarization direction of Tangent the antenna,the received signal power of the tag is relatively plane Tangent small,thus,the multi-path signal will affect the received plane signal and change the phase value.For the horizontal tag, the mismatching direction is corresponding to the vertical Antenna Spin polarization direction,thus,the tag suffers from the larger axis vertical multi-path effect from the ground.For the vertical P tag,the mismatching direction of polarization is horizontal. (a)Modeling in the uplink (b)Modeling in the downlink Since the horizontal multi-path effect is relatively smaller,the Fig.4.Polarization modeling of a single tag. corresponding phase change is not distinct.As a result,the orientation of the long side of the tag,which is represented horizontal tag suffers larger multi-path effect than the vertical by the elevation angle B and the deflection angle yy as shown tag according to the phase measurement.It indicates that the in Fig.4.Hence,the unit vector of the tag orientation is phase values around the matching direction are more accurate. V:=[t,Ut=[cos B cos7,cos Bsin y,sin BT. D.Summary Polarization loss factor calculation.In the communication system.the Received Signal Strength Indicator (RSSI)is Above all,we get the following three key findings.First,the calculated as:R=10x log(PRx).Theoretically,the received linearly polarized antenna can capture the more stable phase power PRx is calculated as:PRx Prxh(dt)Gp,where value and distinctive RSSI variation compared to the circularly polarized antenna.Thus,it is more suitable to use linearly Prx is the transmit power.h(dt)represents the path loss factor in the communication,which can be calculated based polarized antenna to estimate the position with the phase value on the Friis equation [2,7].Gp presents the polarization loss and estimate the orientation with the RSSI variation.Second. factor (PLF)[7],which calculates the matching coefficient for the linearly polarized antenna,the mismatching direction between the polarization direction of the antenna and the tag based on the RSSI variation is more distinctive to estimate the orientation in the RFID system.Since the change of the PLF tag orientation compared to the matching direction.Third,for value Gp is caused by the linear polarization change when the the linearly polarized antenna,the phase around the matching antenna is spinning,we focus on investigating the variation of direction is more stable than the phase around the mismatching PLF with different linear polarizations.In theory,G includes direction,indicating that we can calibrate the phase value by the signal loss of both the uplink Gp.u and the downlink Gp.d removing the noisy phase around the mismatching direction. in RFID communications,i.e.,Gp Gp.uGp,d.According to IV.MODELING the radar principle,the amount of the energy received by the In this section,we build the models to describe the relation- object,e.g.,the tag,is dependent on the reflective area of the ships between the signal features and the position/orientation object,which is the Radar Cross Section(RCS)[2].Similarly of the tag,which are further used to depict the translation and in the RFID system,we can project the polarized signal on the rotation of the object. the tag to calculate the reflective area in both the uplink and the downlink,which is the corresponding PLF. A.Modeling RSSI Pattern of a Single Tag with Spin-antenna For the uplink transmission,the linearly polarized antenna As shown in Fig.4,in the Global Coordinate System(GCS). scatters the signal to the spherical surface in the ambient space the linearly polarized antenna is located at the origin O,and as shown in Fig.4(a).The projection of the linear polarization spins around the Y-axis.We define the polarization angle at the tag position with the polarization angle is: as o,i.e.,the polarization direction is offset the X-axis by P。=MVo (1) in the XZ-plane.The polarization vector is defined as Here,M is the transforming matrix to project the vector Vo V=[cos,0,sin,which is the unit vector pointing to onto the tangent plane of the spherical surface.Since Va is the polarization angle The tag is deployed at a distance the normal vector of the tangent plane,M is calculated as: of dt away from the antenna,and the antenna-tag direction [1-x -Tdyd -Tdzd is Va =[rd,yd,zd]T,which is a unit vector pointing from 1-yi -Yd2d (2) the antenna to the tag.The tag orientation is defined as the -Tdzd -Ydzd 1-2

0 100 200 300 Antenna direction (°) -70 -60 -50 -40 RSSI (dBm) 0 1 2 3 4 5 6 Phase (radian) 5dB Linearly changing phase Spinning direction (a) RF-signal from the circularly po￾larized antenna of a tag at (0, 200, 0) 0 100 200 300 Antenna direction (°) -70 -60 -50 -40 RSSI (dBm) 0 1 2 3 4 5 6 Phase (radian) Stable phase 28dB Matching direction Mismatching direction Spinning direction 153 (b) RF-signal from the linearly polar￾ized antenna of a tag at (0, 200, 0) 0 100 200 300 Antenna direction (°) -70 -60 -50 -40 RSSI (dBm) 0 1 2 3 4 5 6 Phase (radian) Matching direction Mismatching direction 16dB Phase fluctuation Spinning direction 166 (c) RF-signal from the linearly polar￾ized antenna of a tag at (−100, 200, 0) 0 100 200 300 Antenna direction (°) 0 1 2 3 4 5 6 Phase (radian) Horizontal tag Vertical tag Stable phase Phase change due to multi-path Weak multi-path Obvious multi-path Matching direction Mismatching direction Spinning direction (d) Phase measurement when a tag is vertically/horizontally deployed Fig. 3. Results of the empirical study. mismatches the polarization direction of the antenna. When the tag orientation mismatches the polarization direction of the antenna, the received signal power of the tag is relatively small, thus, the multi-path signal will affect the received signal and change the phase value. For the horizontal tag, the mismatching direction is corresponding to the vertical polarization direction, thus, the tag suffers from the larger vertical multi-path effect from the ground. For the vertical tag, the mismatching direction of polarization is horizontal. Since the horizontal multi-path effect is relatively smaller, the corresponding phase change is not distinct. As a result, the horizontal tag suffers larger multi-path effect than the vertical tag according to the phase measurement. It indicates that the phase values around the matching direction are more accurate. D. Summary Above all, we get the following three key findings. First, the linearly polarized antenna can capture the more stable phase value and distinctive RSSI variation compared to the circularly polarized antenna. Thus, it is more suitable to use linearly polarized antenna to estimate the position with the phase value and estimate the orientation with the RSSI variation. Second, for the linearly polarized antenna, the mismatching direction based on the RSSI variation is more distinctive to estimate the tag orientation compared to the matching direction. Third, for the linearly polarized antenna, the phase around the matching direction is more stable than the phase around the mismatching direction, indicating that we can calibrate the phase value by removing the noisy phase around the mismatching direction. IV. MODELING In this section, we build the models to describe the relation￾ships between the signal features and the position/orientation of the tag, which are further used to depict the translation and the rotation of the object. A. Modeling RSSI Pattern of a Single Tag with Spin-antenna As shown in Fig. 4, in the Global Coordinate System (GCS), the linearly polarized antenna is located at the origin O, and spins around the Y -axis. We define the polarization angle as φ, i.e., the polarization direction is offset the X-axis by φ in the XZ-plane. The polarization vector is defined as Vφ = [cos φ, 0,sin φ] T , which is the unit vector pointing to the polarization angle φ. The tag is deployed at a distance of dt away from the antenna, and the antenna-tag direction is Vd = [xd, yd, zd] T , which is a unit vector pointing from the antenna to the tag. The tag orientation is defined as the � � � � � � �' Tangent plane �' Tag � � � �* Antenna Tangent plane Spin axis �* �+ � Tag �' (a) Modeling in the uplink � � � � � � �' Tangent plane �' Tag � � � �* Antenna Tangent plane Spin axis �* �+ � Tag �' (b) Modeling in the downlink Fig. 4. Polarization modeling of a single tag. orientation of the long side of the tag, which is represented by the elevation angle β and the deflection angle γ as shown in Fig. 4. Hence, the unit vector of the tag orientation is Vt = [xt, yt, zt] T = [cos β cos γ, cos β sin γ,sin β] T . Polarization loss factor calculation. In the communication system, the Received Signal Strength Indicator (RSSI) is calculated as: R = 10×log(PRX). Theoretically, the received power PRX is calculated as: PRX = PTXh(dt)Gp, where PTX is the transmit power. h(dt) represents the path loss factor in the communication, which can be calculated based on the Friis equation [2, 7]. Gp presents the polarization loss factor (PLF) [7], which calculates the matching coefficient between the polarization direction of the antenna and the tag orientation in the RFID system. Since the change of the PLF value Gp is caused by the linear polarization change when the antenna is spinning, we focus on investigating the variation of PLF with different linear polarizations. In theory, Gp includes the signal loss of both the uplink Gp,u and the downlink Gp,d in RFID communications, i.e., Gp = Gp,uGp,d. According to the radar principle, the amount of the energy received by the object, e.g., the tag, is dependent on the reflective area of the object, which is the Radar Cross Section (RCS) [2]. Similarly in the RFID system, we can project the polarized signal on the tag to calculate the reflective area in both the uplink and the downlink, which is the corresponding PLF. For the uplink transmission, the linearly polarized antenna scatters the signal to the spherical surface in the ambient space as shown in Fig. 4(a). The projection of the linear polarization at the tag position with the polarization angle φ is: Pφ = MVφ. (1) Here, M is the transforming matrix to project the vector Vφ onto the tangent plane of the spherical surface. Since Vd is the normal vector of the tangent plane, M is calculated as: M =   1 − x 2 d −xdyd −xdzd −xdyd 1 − y 2 d −ydzd −xdzd −ydzd 1 − z 2 d   . (2) 4

Then,based on the vector projection P and the tag orientation Vt.the PLF in the uplink is calculated as Gp.=PV2 Actually,the PLF represents the magnitude of the projection of Tag array plane the polarization vector P along the tag orientation Vt.which Antenn reflects the reflective area of the tag [2,7]. For the downlink transmission,given the orientation of the Spin axis tag Vt as shown in Fig.4(b),which is the polarization direction of the dipole tag,the projected polarization vector Pt at the antenna position is calculated similar to Eq.(1)as: Fig.5.Polarization modeling of a tag array. Pt=(xt,p,班，p2t,p)=MVt (3) difference.Therefore,the differences of om between adjacent Since the linearly polarized antenna is a patch antenna,it can tags are also maximized,which provides the maximum dis- be regarded as a panel to receive the signal backscattered from crimination.Since the antenna-tag directions Va are similar the tag [7],while the tag only receives the matching signal of for different tags in the tag array,we consider all tags are its orientation.Therefore,different from the uplink PLF,the deployed at the same position with different orientations. downlink PLF is the projection of P:on the antenna plane, Definition of the tag array orientation.Basically,the 3D i.e..the XZ-plane,which is Gp.d=.p+2.Based on orientation is usually expressed with three angles,e.g.,the the PLF in the uplink and the downlink,we can calculate Euler angles.For simplicity,we decompose the three angles the theoretical RSSI change based on the PLF,and use it to of the orientation of the tag array into two parts.1)The calculate the mismatching directions in Section V-B. incline orientation represents the orientation of the tag array Mismatching direction.As investigated in the empirical plane,which is denoted as the unit normal vector of the plane study,we try to use the mismatching direction to estimate the N=[n,.It is determined by two angles.2)The tag orientation.The mismatching direction,denoted as om,is rotation offset represents the rotation angle of the tag array defined as the spin angle of the antenna,when the projection inside the plane.Without loss of generality,we randomly of antenna polarization is orthogonal to the tag direction,i.e., choose a labeled tag To in the tag array and use the angle PL Vt,and the RSSI value reaches its minimum value. difference 6 from the reference orientation to represent it.The Based on the orthogonal relationship,Po.V:=0,which is reference orientation is defined from the unit normal vector expanded as: Nt as: (MV。).Vt=0. (4) T Then,we can deduce the mismatching direction m as: Vr= -In 21 ,0 (6 tann=-r4-zau跳-zaa4 V品+乐'√品+ (5) which is a unit vector along the intersecting line between the TdzdTt yazayt -(1-z3)zi XY plane and the tag plane as shown in Fig.5.Then,we can where V:=[t,yt,T is the tag orientation vector.Accord- use the tuple [N,6}to define the orientation of the tag array. ing to Eq.(5),both the tag orientation V:and the antenna-tag Mismatching direction calculation.Then given the tuple direction Va are unknown,meaning that it is difficult to deduce [N:,6},the orientation of tag Ti in the tag array can be the tag orientation V:based on the mismatching direction calculated as: om of only one tag.Besides,this equation also explains the Vi=RiVr. (7) difference of mismatching directions in Fig.3(b)and Fig.3(c). Here,R;is the rotation matrix of tag Ti,which rotates around which is caused by the change of the antenna-tag direction Va. the normal vector N,with the rotation offset 6.Particularly, B.Modeling RSSI Pattern of Tag Array with Spin-antenna 16i-6ol is the angle difference between tag Ti and To,whose value is the multiple of a.Finally,based on the calculated Tag array deployment.Since it is difficult to estimate the orientation of tag Ti,we can rewrite Eq.(4)as: tag orientation Vt based on one tag,the key idea is to deploy multiple tags as a tag array to estimate the orientation of the (MVom)·(R:Vr)=0. (8) tag array.However,the tag array is relatively small compared Therefore,we can calculate the mismatching direction om with the distance between the tag array and the antenna,thus, from Vo,accordingly. the antenna-tag directions Va of different tags are almost the The mismatching direction of each tag in the tag array is same.Hence,the traditional tag array deployment with the more sensitive to the rotation offset 6 compared with the tag same tag orientation cannot provide the more discrimination plane orientation N:or the antenna-tag direction Va.Since of tag orientation compared with one tag.Based on the the mismatching directions in Eq.(5)are not linearly related understanding,we vary the orientations of tags in the tag array. to the tag array orientation and the antenna-tag direction, Hence,even though one tag is misread due to mismatching, we use several experiments to examine the discrimination of we can still read other tags with different orientations.Without mismatching directions in the orientation estimation of the tag loss of generality,in our system we attach N tags on the plane array.By changing the tag plane orientation,i.e.,N:and the as shown in Fig.5.The orientation difference between adjacent antenna-tag direction,ie.,Vd,we vary the rotation offset 6 tags is set to a =2m/N,which maximizes the orientation from 0 to and calculate the corresponding om based on Eq. 5

Then, based on the vector projection Pφ and the tag orientation Vt, the PLF in the uplink is calculated as Gp,u = |Pφ · Vt| 2 . Actually, the PLF represents the magnitude of the projection of the polarization vector Pφ along the tag orientation Vt, which reflects the reflective area of the tag [2, 7]. For the downlink transmission, given the orientation of the tag Vt as shown in Fig. 4(b), which is the polarization direction of the dipole tag, the projected polarization vector Pt at the antenna position is calculated similar to Eq. (1) as: Pt = (xt,p, yt,p, zt,p) = MVt. (3) Since the linearly polarized antenna is a patch antenna, it can be regarded as a panel to receive the signal backscattered from the tag [7], while the tag only receives the matching signal of its orientation. Therefore, different from the uplink PLF, the downlink PLF is the projection of Pt on the antenna plane, i.e., the XZ-plane, which is Gp,d = xt,p 2 + zt,p 2 . Based on the PLF in the uplink and the downlink, we can calculate the theoretical RSSI change based on the PLF, and use it to calculate the mismatching directions in Section V-B. Mismatching direction. As investigated in the empirical study, we try to use the mismatching direction to estimate the tag orientation. The mismatching direction, denoted as φm, is defined as the spin angle of the antenna, when the projection of antenna polarization is orthogonal to the tag direction, i.e., Pφ ⊥ Vt, and the RSSI value reaches its minimum value. Based on the orthogonal relationship, Pφ · Vt = 0, which is expanded as: (MVφ) · Vt = 0. (4) Then, we can deduce the mismatching direction φm as: tan φm = (1 − x 2 d )xt − xdydyt − xdzdzt xdzdxt + ydzdyt − (1 − z 2 d )zt , (5) where Vt = [xt, yt, zt] T is the tag orientation vector. Accord￾ing to Eq. (5), both the tag orientation Vt and the antenna-tag direction Vd are unknown, meaning that it is difficult to deduce the tag orientation Vt based on the mismatching direction φm of only one tag. Besides, this equation also explains the difference of mismatching directions in Fig. 3(b) and Fig. 3(c), which is caused by the change of the antenna-tag direction Vd. B. Modeling RSSI Pattern of Tag Array with Spin-antenna Tag array deployment. Since it is difficult to estimate the tag orientation Vt based on one tag, the key idea is to deploy multiple tags as a tag array to estimate the orientation of the tag array. However, the tag array is relatively small compared with the distance between the tag array and the antenna, thus, the antenna-tag directions Vd of different tags are almost the same. Hence, the traditional tag array deployment with the same tag orientation cannot provide the more discrimination of tag orientation compared with one tag. Based on the understanding, we vary the orientations of tags in the tag array. Hence, even though one tag is misread due to mismatching, we can still read other tags with different orientations. Without loss of generality, in our system we attach N tags on the plane as shown in Fig. 5. The orientation difference between adjacent tags is set to α = 2π/N, which maximizes the orientation � � � Antenna Tag array plane � � Spin axis & � � �* �+ Fig. 5. Polarization modeling of a tag array. difference. Therefore, the differences of φm between adjacent tags are also maximized, which provides the maximum dis￾crimination. Since the antenna-tag directions Vd are similar for different tags in the tag array, we consider all tags are deployed at the same position with different orientations. Definition of the tag array orientation. Basically, the 3D orientation is usually expressed with three angles, e.g., the Euler angles. For simplicity, we decompose the three angles of the orientation of the tag array into two parts. 1) The incline orientation represents the orientation of the tag array plane, which is denoted as the unit normal vector of the plane Nt = [xn, yn, zn] T . It is determined by two angles. 2) The rotation offset represents the rotation angle of the tag array inside the plane. Without loss of generality, we randomly choose a labeled tag T0 in the tag array and use the angle difference δ from the reference orientation to represent it. The reference orientation is defined from the unit normal vector Nt as: Vr = " p yn x 2 n + y 2 n , p −xn x 2 n + y 2 n , 0 #T , (6) which is a unit vector along the intersecting line between the XY plane and the tag plane as shown in Fig. 5. Then, we can use the tuple {Nt, δ} to define the orientation of the tag array. Mismatching direction calculation. Then given the tuple {Nt, δ}, the orientation of tag Ti in the tag array can be calculated as: Vi = RiVr. (7) Here, Ri is the rotation matrix of tag Ti , which rotates around the normal vector Nt with the rotation offset δi . Particularly, |δi −δ0| is the angle difference between tag Ti and T0, whose value is the multiple of α. Finally, based on the calculated orientation of tag Ti , we can rewrite Eq. (4) as: (MVφm) · (RiVr) = 0. (8) Therefore, we can calculate the mismatching direction φm from Vφm, accordingly. The mismatching direction of each tag in the tag array is more sensitive to the rotation offset δ compared with the tag plane orientation Nt or the antenna-tag direction Vd. Since the mismatching directions in Eq. (5) are not linearly related to the tag array orientation and the antenna-tag direction, we use several experiments to examine the discrimination of mismatching directions in the orientation estimation of the tag array. By changing the tag plane orientation, i.e., Nt and the antenna-tag direction, i.e., Vd, we vary the rotation offset δ from 0 to π and calculate the corresponding φm based on Eq. 5

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 6

0 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

80 Matching RSSI 60 Unmatched angles (3]3ue 24 ed Rss 50 Estimaed RSSI. 100150200250300 Deflection angle() 00 200 Fig.10.Relative direction estimation. direc-(b)Calibrating phase based on antenna relative to the tag array.The relative topology is tions from theoretical RSSI matching RSSI shown in Fig.7,where the relative direction is based on the Fig.9.Signal preprocessing Local Coordinate System (LCS)of the tag array.According values based on the RSSI variation.We first segment the sig- to the phase model in Section IV-C.the basic idea is to nals based on the spinning cycle and resample the raw signals. derive the direction of the antenna with respect to the tag Since the linearly polarized antenna is symmetric based on array by comparing the collected phase difference with the the empirical study in Fig.3,the spin angle of one cycle is theoretical phase difference.Particularly,given the calibrated 180 instead of 360.Therefore,we segment the signals into phase difference A0i.0.j=0:.j-00.;between the tag Ti and windows,where the spin angles in each window range from 0 To in the j-th window,we search for the antenna direction in to 180.Then,we resample the signals in each window with the LCS,that maximizes the similarity between the computed the cubic spline interpolation to tackle the random sampling phase difference A.0.and the collected phase difference problem in the RFID system.Specifically,based on the stable RSSI variation pattern studied in Section III-C,we set the Ao.This antenna direction,denoted as based on RSSI value to -80dBm for the misreading tags.After the the phase model,is our estimate for V.The maximization resampling,we have the RSSI vector Si={s1,...,s} formulation calculates the similarity of the phase differences based on the imaginary number to remove the periodical and phase vector i.=01,...,}of tag Ti in the j-th ambiguity of2πas: window,where w is the resampling window size. Then,we estimate the mismatching directions from the RSSI variation by comparing the collected RSSI vector Sij 寸a=arg max J△.0d-eJ△84,0J (12) with the theoretical RSSI trace.Formally,the mismatching Vaesa direction m.i of tag Ti can be calculated as: whereJ is v-I and S3 represents the possible unit direction vectors in the 3D space.In regard to A0i.0.j,it can be om.=arg min (sk -sp)2. (11) calculated from Eq.(9)and Eq.(10),based on the preset tag pm,∈0，x）k=1 array deployment.Fig.10 uses an example to show the results Here,sp.is the k-th theoretical RSSI value calculated from of the maximization formulation,where N=5.We find our m.i based on the Section IV-A.Fig.9(a)uses an example method can uniquely determine the relation direction of the to show the estimation process.The initial m equals to 90, antenna based on the maximization formulation. while the theoretical RSSI trace (red line)is totally different D.Coordinate System Transformation from the collected RSSI.By sliding the trace towards the left, We then transform the estimated antenna directionV in we find the difference between the collected RSSI vector and the Local Coordinate System (LCS)to the global coordinate the theoretical RSSI (original line)is minimum when om= system (GCS),which is defined in Section III,and then 10.Then,we get the estimated mismatching direction 10. estimate the position of tag array in the GCS.The basic idea is After that,we calibrate the phase value in each window to estimate the possible position of tag array in the GCS based according to the observation in Section III-C,the phase values on the position of the tag array in the previous window and around the mismatching direction are noisy due to the multi- the phase change of each tag between consecutive windows. path effect.The basic idea is to calibrate the phase value based Specifically,given the phase change A0ij=0.j-0j-1 of on the reliable RSSI collections around the matching direction. the tag Ti,we search for the position of the tag array,that Fig.9(b)shows the calibration flow with an example.We first maximizes the similarity between the computed phase change select the phase collections where the collected RSSI value Aij and the collected phase change Aij.This position is close to the matching RSSI value.Then we use a weighted of the tag array,denoted as C.is our estimate for Cj The average algorithm to calibrate the phase in each window.where optimization formulation can be written as: the weights are the corresponding RSSI values.In Fig.9(b), we use the matching phase and the matching RSSI to calibrate the phase via weighted averaging.We use ii to represent the C=arg min J△0i-eJ△8， (13) CEA calibrated phase of tag T in the j-th window. Here,A is the candidate positions of the tag array based on C.Relative Direction Estimation based on RF Phase C-1 and the moving speed between the consecutive windows. After the signal preprocessing,we use the calibrated phase To calculate the phase change Aj,we first transform the values 6i;of the tag array to estimate the direction of the position of the tag array in the LCS to the GCS.Then >

0 100 200 300 Spinning direction (°) -50 -40 -30 -20 -10 0 Signal power (dB) Measured RSSI Theoretical RSSI, m = 90 Estimated RSSI, m=10 Examining mismatching directions (a) Estimating mismatching direc￾tions from theoretical RSSI 0 50 100 150 Spinning angle (°) -70 -60 -50 -40 RSSI (dBm) 0 1 2 3 4 5 6 Phase (radian) Matching RSSI Matching phase Unmatched angles Spinning direction (b) Calibrating phase based on matching RSSI Fig. 9. Signal preprocessing. values based on the RSSI variation. We first segment the sig￾nals based on the spinning cycle and resample the raw signals. Since the linearly polarized antenna is symmetric based on the empirical study in Fig. 3, the spin angle of one cycle is 180◦ instead of 360◦ . Therefore, we segment the signals into windows, where the spin angles in each window range from 0 ◦ to 180◦ . Then, we resample the signals in each window with the cubic spline interpolation to tackle the random sampling problem in the RFID system. Specifically, based on the stable RSSI variation pattern studied in Section III-C, we set the RSSI value to −80dBm for the misreading tags. After the resampling, we have the RSSI vector Si,j = {s1, · · · , sw} and phase vector Θi,j = {θ1, · · · , θw} of tag Ti in the j-th window, where w is the resampling window size. Then, we estimate the mismatching directions from the RSSI variation by comparing the collected RSSI vector Si,j with the theoretical RSSI trace. Formally, the mismatching direction φbm,i of tag Ti can be calculated as: φbm,i = arg min φbm,i∈[0,π) Xw k=1 (sk − sp,k) 2 . (11) Here, sp,k is the k-th theoretical RSSI value calculated from φbm,i based on the Section IV-A. Fig. 9(a) uses an example to show the estimation process. The initial φbm equals to 90◦ , while the theoretical RSSI trace (red line) is totally different from the collected RSSI. By sliding the trace towards the left, we find the difference between the collected RSSI vector and the theoretical RSSI (original line) is minimum when φbm = 10◦ . Then, we get the estimated mismatching direction 10◦ . After that, we calibrate the phase value in each window according to the observation in Section III-C, the phase values around the mismatching direction are noisy due to the multi￾path effect. The basic idea is to calibrate the phase value based on the reliable RSSI collections around the matching direction. Fig. 9(b) shows the calibration flow with an example. We first select the phase collections where the collected RSSI value is close to the matching RSSI value. Then we use a weighted average algorithm to calibrate the phase in each window, where the weights are the corresponding RSSI values. In Fig. 9(b), we use the matching phase and the matching RSSI to calibrate the phase via weighted averaging. We use θi,j to represent the calibrated phase of tag Ti in the j-th window. C. Relative Direction Estimation based on RF Phase After the signal preprocessing, we use the calibrated phase values θi,j of the tag array to estimate the direction of the 0 50 100 150 200 250 300 350 Deflection angle (°) 0 20 40 60 80 Elevation angle ( ° ) 1 2 3 4 Fig. 10. Relative direction estimation. antenna relative to the tag array. The relative topology is shown in Fig. 7, where the relative direction is based on the Local Coordinate System (LCS) of the tag array. According to the phase model in Section IV-C, the basic idea is to derive the direction of the antenna with respect to the tag array by comparing the collected phase difference with the theoretical phase difference. Particularly, given the calibrated phase difference ∆θi,0,j = θi,j − θ0,j between the tag Ti and T0 in the j-th window, we search for the antenna direction in the LCS, that maximizes the similarity between the computed phase difference ∆θbi,0,j and the collected phase difference ∆θi,0,j . This antenna direction, denoted as Vb 0 d based on the phase model, is our estimate for V 0 d . The maximization formulation calculates the similarity of the phase differences based on the imaginary number to remove the periodical ambiguity of 2π as: Vb 0 d = arg max Vb 0 d∈S3      X N i=1 e J∆θbi,0,j − e J∆θi,0,j      2 , (12) where J is √ −1 and S 3 represents the possible unit direction vectors in the 3D space. In regard to ∆θbi,0,j , it can be calculated from Eq. (9) and Eq. (10), based on the preset tag array deployment. Fig. 10 uses an example to show the results of the maximization formulation, where N = 5. We find our method can uniquely determine the relation direction of the antenna based on the maximization formulation. D. Coordinate System Transformation We then transform the estimated antenna direction Vb 0 d in the Local Coordinate System (LCS) to the global coordinate system (GCS), which is defined in Section III, and then estimate the position of tag array in the GCS. The basic idea is to estimate the possible position of tag array in the GCS based on the position of the tag array in the previous window and the phase change of each tag between consecutive windows. Specifically, given the phase change ∆θi,j = θi,j − θi,j−1 of the tag Ti , we search for the position of the tag array, that maximizes the similarity between the computed phase change ∆θbi,j and the collected phase change ∆θi,j . This position of the tag array, denoted as Cbj , is our estimate for Cj . The optimization formulation can be written as: Cbj = arg min Cbj∈A      X N i=1 e J∆θbi,j − e J∆θi,j      2 . (13) Here, A is the candidate positions of the tag array based on Cj−1 and the moving speed between the consecutive windows. To calculate the phase change ∆θbi,j , we first transform the position of the tag array in the LCS to the GCS. Then 7

X-asix -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 between tasnerent (f)Rotation error with different tag-(g)Translation error 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 8

0 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

variation,which is caused by the polarization direction change system can still accurately track the 3D motion of the relatively of the spin-antenna.Overall,our solution can accurately track complex environment with the heavy multi-path effect the translation and the rotation in the 3D space VII.CONCLUSION C.Impact of Number of Tags In this paper,we propose to track the 3D motion of a The tracking error of both the translation and the rota- tag array labeled objects via a spinning linearly polarized tion decreases when the number of tags increases.Then we antenna.By modeling the relationship between the tag array compare the tracking accuracy with the three tag arrays to and the spinning antenna,our system is able to sufficiently evaluate the impact of the number of tags.Fig.12(c)shows suppress the ambient signal interference and extract the most the translation error with the number of tags.We find that distinctive features.Based on the calibrated features.we design as the number of tags increases from 3 to 5,the translation corresponding solutions to track the translation based on the error along the X-axis decreases from 10.1cm to 6.6cm,and phase values,and estimate the rotation of the tag array from the translation error along the Z-axis decreases from 6.8cm to the RSSI variation.The extensive experiment results on the 5.7cm.The translation error along the Y-axis does not largely real testbed show that our solution can achieve an average reduce,because all the tags share the similar phase change due translation error of 13.6cm and an average rotation error of to the translation along the Y-axis.For the rotation error in 8.3°in the3 D space. Fig.12(d).we find that the error of the tag plane orientation ACKNOWLEDGMENTS decreases dramatically as we increase the number of tags.It This work is supported in part by National Natural Science is because the increment of the number of tags will increase Foundation of China under Grant Nos.61872174,61832008 phase pairs exponentially based on the phase model in Section 61872173,61802169;JiangSu Natural Science Foundation IV-C,providing more phase differences for the estimation. under Grant No.BK20180325.This work is partially sup- Besides,the error of the tag array rotation maintains small ported by Collaborative Innovation Center of Novel Software when we increase the number of tags,indicating the RSSI Technology and Industrialization.Lei Xie is the corresponding variation is stable to estimate the orientation of each tag author. D.Impact of Distance between Tag Array and Antenna REFERENCES The tracking error slightly increases as the distance between [1]H.Ding,L.Shangguan,Z.Yang.J.Han,Z.Zhou,P.Yang,W.Xi,and J.Zhao.Femo:A platform for free-weight exercise monitoring with the tag array and the antenna increases.We evaluate the rfids.In Proc.of ACM SenSys,2015. impact of the distance between the tag array and the antenna by [2]D.M.Dobkin.The rf in RFID:uhf RFID in practice.Newnes.2012. conducting the experiments at the distance of 150cm,250cm [3]M.Izz.Z.Li.H.Liu,Y.Chen,and F.Li.Uber-in-light:Unobtrusive and 350cm away from the antenna,respectively.Fig.12(e) visible light communication leveraging complementary color channel. 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variation, which is caused by the polarization direction change of the spin-antenna. Overall, our solution can accurately track the translation and the rotation in the 3D space. C. Impact of Number of Tags The tracking error of both the translation and the rota￾tion decreases when the number of tags increases. Then we compare the tracking accuracy with the three tag arrays to evaluate the impact of the number of tags. Fig. 12(c) shows the translation error with the number of tags. We find that as the number of tags increases from 3 to 5, the translation error along the X-axis decreases from 10.1cm to 6.6cm, and the translation error along the Z-axis decreases from 6.8cm to 5.7cm. The translation error along the Y -axis does not largely reduce, because all the tags share the similar phase change due to the translation along the Y -axis. For the rotation error in Fig. 12(d), we find that the error of the tag plane orientation decreases dramatically as we increase the number of tags. It is because the increment of the number of tags will increase phase pairs exponentially based on the phase model in Section IV-C, providing more phase differences for the estimation. Besides, the error of the tag array rotation maintains small when we increase the number of tags, indicating the RSSI variation is stable to estimate the orientation of each tag. D. Impact of Distance between Tag Array and Antenna The tracking error slightly increases as the distance between the tag array and the antenna increases. We evaluate the impact of the distance between the tag array and the antenna by conducting the experiments at the distance of 150cm, 250cm and 350cm away from the antenna, respectively. Fig. 12(e) shows the translation error along with the distance between the tag array and the antenna. It is found that the translation error along the Y -axis is as low as 2.2cm, when the distance is 150cm, and then increases to 4.1cm, when the distance increases to 350cm. Therefore, even if the distance between the tag array and the antenna indeed affects the translation error, our system can always keep the high tracking accuracy as the distance increases. For the rotation error in Fig. 12(f), the rotation errors are always below 15◦ , even if the actual error increases along with the increment of the distance between the tag array and the antenna. E. Impact of Multi-path Effect Our solution can accurately track the 3D motion in the heavy multi-path effect environment. Finally, to evaluate the robustness of the spin-antenna in the 3D motion tracking, we deploy multiple iron plates around the spin-antenna to generate the heavy multi-path effect. Fig. 12(g) and Fig. 12(h) show the corresponding translation error and the rotation error of the heavy and the light multi-path effect. It is found that even if the heavy multi-path effect leads to about 15cm translation error for both the X-axis and the Y -axis, we can still achieve the high accuracy for the Y -axis. Besides, we also find that the rotation error of the tag array rotation is also as small as 3.1 ◦ with the heavy multi-path effect. It indicates that the relative RSSI variation is stable enough to resist the interference of the multi-path effect. Therefore, the results proof that our system can still accurately track the 3D motion of the relatively complex environment with the heavy multi-path effect. VII. CONCLUSION In this paper, we propose to track the 3D motion of a tag array labeled objects via a spinning linearly polarized antenna. By modeling the relationship between the tag array and the spinning antenna, our system is able to sufficiently suppress the ambient signal interference and extract the most distinctive features. Based on the calibrated features, we design corresponding solutions to track the translation based on the phase values, and estimate the rotation of the tag array from the RSSI variation. The extensive experiment results on the real testbed show that our solution can achieve an average translation error of 13.6cm and an average rotation error of 8.3 ◦ in the 3D space. ACKNOWLEDGMENTS This work is supported in part by National Natural Science Foundation of China under Grant Nos. 61872174, 61832008, 61872173, 61802169; JiangSu Natural Science Foundation under Grant No. BK20180325. This work is partially sup￾ported by Collaborative Innovation Center of Novel Software Technology and Industrialization. Lei Xie is the corresponding author. REFERENCES [1] H. Ding, L. Shangguan, Z. Yang, J. Han, Z. Zhou, P. Yang, W. Xi, and J. Zhao. Femo: A platform for free-weight exercise monitoring with rfids. In Proc. of ACM SenSys, 2015. [2] D. M. Dobkin. The rf in RFID: uhf RFID in practice. 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