Algorithm 1 Match multiple objects to multiple tags of multiple feasible solutions according to different pairs of 1:Extract the vector:After continuous scanning,we respectively identify phase values.It is found that the multiple hyperbolas of differ- the peak value from the quadratic fitting curve of depth and RSSI.For ent feasible solutions all intersect at a small area which is very each object Oi,we label it with a vector (di),and add the vector to close to the target tag's real position.We thus set the central a set O;for each tag Ti,we label it with a vector (ri),and add the vector to a set T. point of the intersection region as the estimate value of the 2:while O+2 and T≠odd tag's position. 3: Match the objects and tags:For each object OiE O with vector (.di),respectively add those objects O;EO and those tags T;E T Canddse solution of l with6;∈[e-δ，6+into the set O and Te.In regard to the depth value di,compute the rank of Oi in the set O as k.Select the tag T;ETe with the rank of k in regard to the RSSI ri,and pair the object anddste Solution of (A. O;with the tag T Real Position(-60,180) 4 Calibrate the matching results:For any tag Ti ET paired with mul- tiple objects,select the object O;from these objects with the closest rank similarly,and pair the object O;with the tag Ti.Respectively 0 remove the object O;and the tag T;from set O and T 5:end while A2 90 6:Output the matched pairs of objects and tags. Figure 8.Multiple solutions of the tag's position After deriving the target tag's position,we can further derive Pair the Tags with Objects according to Depth and Phase the angle when the tag is at the perpendicular point of the Since a new brand of COTS RFID systems,like the ImpinJ, RFID antennas,that is the moment when the perpendicular are able to extract the phase value from the RF-signals of tags, bisector of the midpoint of the antenna pairs crosses the tag. it provides us a new opportunity to differentiate the positions We use the pair(0,8)to denote this situation,here e denotes of the tagged objects with a more accurate approach.In this the offset angle of the antenna,and o denotes the vertical dis- section,we present our approach to pair the tags with objects tance.The pair (0,is computed as follows:0=arctan according to the correlations between the depth and phase in and 8=Vx2+y2.Therefore,we can further leverage an continuous scanning. algorithm like Algorithm 1 to match multiple tags to multiple objects.The only difference is that we can directly pair the According to the analysis shown in Figure 6,given the two phase values of RF-signals extracted from two antennas sep- objects OiO with the tags Ti ET according to the distance arated with a distance d(d=25cm in our implementation), between the vector (0i,di)and the vector (0j,6j),since they can accurately estimate the positions of the objects/tags. there could be multiple solutions for the tag's position,which could be represented with multiple hyperbolas in the two- Discussion dimensional space.In fact,we can leverage continuous scan- Robustness ning to figure out a unique solution by filtering out those un- Due to the environmental issues like the multi-path fading and qualified solutions.The idea is as follows:for each snapshot object occlusion,the system may fail to identify some of the ti(i=1 ~m)of the continuous scanning,for a specified tag objects and the tags.Moreover,in some situations,it is essen- T,we can respectively extract the phase values(01,02)from tial to isolate the recognizable object with non-recognizable the two antennas,then compute the feasible distances (di,d2) ones.Hence,it is possible that the cardinality of objects identi- between the tag and two antennas.We further compute the fied by the depth camera is not equal to the cardinality of tags set of feasible positions in a global coordinate system as Si. identified by the RFID antenna.This leads to imperfect match- Then,by computing the intersection of different sets Si for all ing between the objects and tags.Our solution is able to tackle snapshots,we are able to figure out a unique solution for the this problem by using the two-dimensional matching method tag's position as follows:S=Si. with regression analysis.By means of continuous scanning via rotation,in regard to the tags and objects,we can derive their As a matter of fact,as long as two pairs of phase values are vertical distances in the horizontal dimension and horizontal obtained,we are able to further derive the unique solution of distances in the horizontal dimension,respectively from the the tag's position by computing the intersection of multiple depth camera and the RFID antenna.Then we perform the feasible solutions.Figure 8 shows an example of deriving the regression analysis on the vertical distances and horizontal unique solution.Suppose a target tag is deployed at the coordi- distances between the tags and objects,and filter out those nate (-60.180).We first obtain the phase values (2.58.5.81) outliers according to the regression model.After that.we from the two antennas when they are respectively at the posi- pair the tags with objects according to their two dimensional tion of A and A2.After the antenna pairs are rotated with a de- positions.This approach effectively mitigates the interference gree of 40,we then obtain the phase values(5.56,2.49)from from those tags and objects which fail to be identified and the two antennas when they are respectively at the position isolates the recognizable object with non-recognizable ones. of A and A2.In this way,we can obtain three pairs of phase values(2.58,5.81),(2.58,5.56)and(5.81,2.49),which are Scalability respectively collected from antenna pairs (A1,A2),(A1,A). Our technical solution is primarily based on the distinction and(A2,A2).We can respectively use them to compute the of depth(vertical distance)from the tagged objects.How- feasible solutions in a unified coordinate system.As shown ever,even if multiple objects are of the same depth,our so- in Figure 8,we use different colors to label the hyperbolas lution is still able to distinguish these objects via continuousAlgorithm 1 Match multiple objects to multiple tags 1: Extract the vector: After continuous scanning, we respectively identify the peak value from the quadratic fitting curve of depth and RSSI. For each object Oi , we label it with a vector hθi ,dii, and add the vector to a set O; for each tag Tj , we label it with a vector hθj ,rji, and add the vector to a set T. 2: while O , ∅ and T , ∅ do 3: Match the objects and tags: For each object Oi ∈ O with vector hθi ,dii, respectively add those objects Oj ∈ O and those tags Tj ∈ T with θj ∈ [θi −δ,θi +δ] into the set Oc and Tc. In regard to the depth value di , compute the rank of Oi in the set Oc as k. Select the tag T ∗ j ∈ Tc with the rank of k in regard to the RSSI rj , and pair the object Oj with the tag T ∗ j . 4: Calibrate the matching results: For any tag Tj ∈ T paired with mul￾tiple objects, select the object Oi from these objects with the closest rank similarly, and pair the object Oi with the tag Tj∗. Respectively remove the object Oi and the tag Tj from set O and T. 5: end while 6: Output the matched pairs of objects and tags. Pair the Tags with Objects according to Depth and Phase Since a new brand of COTS RFID systems, like the ImpinJ, are able to extract the phase value from the RF-signals of tags, it provides us a new opportunity to differentiate the positions of the tagged objects with a more accurate approach. In this section, we present our approach to pair the tags with objects according to the correlations between the depth and phase in continuous scanning. According to the analysis shown in Figure 6, given the two phase values of RF-signals extracted from two antennas sep￾arated with a distance d (d=25cm in our implementation), there could be multiple solutions for the tag’s position, which could be represented with multiple hyperbolas in the two￾dimensional space. In fact, we can leverage continuous scan￾ning to figure out a unique solution by filtering out those un￾qualified solutions. The idea is as follows: for each snapshot ti(i = 1 ∼ m) of the continuous scanning, for a specified tag T, we can respectively extract the phase values (θ1,θ2) from the two antennas, then compute the feasible distances (d1,d2) between the tag and two antennas. We further compute the set of feasible positions in a global coordinate system as Si . Then, by computing the intersection of different sets Si for all snapshots, we are able to figure out a unique solution for the tag’s position as follows: S = ∩ m i=1 Si . As a matter of fact, as long as two pairs of phase values are obtained, we are able to further derive the unique solution of the tag’s position by computing the intersection of multiple feasible solutions. Figure 8 shows an example of deriving the unique solution. Suppose a target tag is deployed at the coordi￾nate (−60,180). We first obtain the phase values (2.58,5.81) from the two antennas when they are respectively at the posi￾tion of A1 and A2. After the antenna pairs are rotated with a de￾gree of 40◦ , we then obtain the phase values (5.56,2.49) from the two antennas when they are respectively at the position of A 0 1 and A 0 2 . In this way, we can obtain three pairs of phase values (2.58,5.81), (2.58,5.56) and (5.81,2.49), which are respectively collected from antenna pairs hA1,A2i, hA1,A 0 1 i, and hA2,A 0 2 i. We can respectively use them to compute the feasible solutions in a unified coordinate system. As shown in Figure 8, we use different colors to label the hyperbolas of multiple feasible solutions according to different pairs of phase values. It is found that the multiple hyperbolas of differ￾ent feasible solutions all intersect at a small area which is very close to the target tag’s real position. We thus set the central point of the intersection region as the estimate value of the tag’s position. The horizontal coordinate:x(cm) -100 -50 0 50 100 The vertical coordinate:y(cm) 0 50 100 150 200 250 300 Candidate Solution of (A1 , A2 ) Candidate Solution of (A1 , A2 ) Candidate Solution of (A1 , A2 ) Candidate Solution of (A1 , A2 ) Candidate Solution of (A1 , A'1 ) Candidate Solution of (A2 , A'2 ) Real Position(-60,180) Candidate Region A1 A2 A1’ A2’ Figure 8. Multiple solutions of the tag’s position After deriving the target tag’s position, we can further derive the angle when the tag is at the perpendicular point of the RFID antennas, that is the moment when the perpendicular bisector of the midpoint of the antenna pairs crosses the tag. We use the pair hθ,δi to denote this situation, here θ denotes the offset angle of the antenna, and δ denotes the vertical dis￾tance. The pair hθ,δi is computed as follows: θ = arctan| x y |, and δ = p x 2 +y 2 . Therefore, we can further leverage an algorithm like Algorithm 1 to match multiple tags to multiple objects. The only difference is that we can directly pair the objects Oi ∈ O with the tags Tj ∈ T according to the distance between the vector hθi ,dii and the vector hθj ,δji, since they can accurately estimate the positions of the objects/tags. Discussion Robustness Due to the environmental issues like the multi-path fading and object occlusion, the system may fail to identify some of the objects and the tags. Moreover, in some situations, it is essen￾tial to isolate the recognizable object with non-recognizable ones. Hence, it is possible that the cardinality of objects identi- fied by the depth camera is not equal to the cardinality of tags identified by the RFID antenna. This leads to imperfect match￾ing between the objects and tags. Our solution is able to tackle this problem by using the two-dimensional matching method with regression analysis. By means of continuous scanning via rotation, in regard to the tags and objects, we can derive their vertical distances in the horizontal dimension and horizontal distances in the horizontal dimension, respectively from the depth camera and the RFID antenna. Then we perform the regression analysis on the vertical distances and horizontal distances between the tags and objects, and filter out those outliers according to the regression model. After that, we pair the tags with objects according to their two dimensional positions. This approach effectively mitigates the interference from those tags and objects which fail to be identified and isolates the recognizable object with non-recognizable ones. Scalability Our technical solution is primarily based on the distinction of depth (vertical distance) from the tagged objects. How￾ever, even if multiple objects are of the same depth, our so￾lution is still able to distinguish these objects via continuous