reference tag. tag.However,the method still suffer from the same problem For example,we set T=5.0 and '=2 and the number with basic method.At some positions in the localization area of antennas is 4.When a reference tag is selected,we have its the maximum power still needs to activating the target tag. activating power(25.7,18.7,30.7,29.7)by the 4 antennas.And For example,if the target tag is in center of localization area, we have activating power(28.7,29.7,24.7,22.7)for target tag. we need to use maximum power so that all reference tags are Compute with the two power vectors,we have the last three activated.So,the method still have a large maximum error.It corresponding elements |29.7-18.7>5.0,24.7-30.7]>5.0 makes the APS method can only reduce the minimum error and |22.7-29.7>5.0.The number of elements which have but it can not guarantee the maximum error to be less than a difference more than r is over threshold k'.Then we treat this smaller threshold. reference tag as false nearby reference tag. VII.ADAPTIVE GRID-BASED CALIBRATION METHOD Algorithm 1 Localization Algorithm-Finding Appropriate A.Motivation Power In the realistic application,user will get the located object 1:Set function R(p)as the RSSI value measured by RFID after the localization procedure.The user may give a feedback reader in power p; to set correct position when the estimated position is wrong. 2:First set minimum power as pi and maximum power as In recent years,several detection technologies such as RFID- P2: based activity sensing have a quick development.With those 3:Check if the tag can be identified by minimum power or technologies,the position where user takes the object from can it can not be identified by maximum power. be automatic detected easily.These auto-detection technologies 4:while p2 pi do can help us to have feedbacks for the localization result. Setp3=(p1+p2)/2: However.both the user's feedback and the auto-detection 6 if R(p3)=0 then technologies can not give accurate results.The feedback can 7: Set p3 to p1; just show a smaller area where the object is in.But the 8: else feedback fingerprints are very reliable,especially the scale of if R(p3+6)-R(p3-6)>0 then fingerprints is large. 10: Set p3 to pi; By dividing the localization area into grids,as shown 11: else in Fig.3,we can use the feedback to calibrate the next 12: Set pa to p2; localization result.In the realistic scenario,shelf can be easily 13: end if divided into grids.The feedback can distinguish the grid in 14安 end if which user takes the object. 15:end while 16:Power p3 is the appropriate transmitting power. When knowing which grid the target tag is in,we can measure the fingerprint of this tag and record it as automatic detected fingerprint database.We set this fingerprint database as RG.Each fingerprint in Rc is mapped to a grid in the Algorithm 2 Localization Algorithm-Adaptive Power Step localization area ping(APS) 1:Call Alg.1 to get Pipili [1,k]},each power pi is for B.Adaptive Grid-based Calibration(AGC) antenna A;: Considering the fingerprints of reference tags are used to 2:Set P as reader's transmitting power for each antenna. compute similarity between target and reference tags,the de- 3:Collect fingerprints of reference tags which can be identi- tailed information from each element in fingerprints is ignored. fied by at least'antenna. In regard to fingerprint data set Rc and relative position of 4:while The number of reference tag <A do each grid,each grid can has some rules Li.As shown in Fig.3, Set P+AP to P,set P as reader's power; the fingerprint r must match the rules Li.For Li,we can 6: Collect fingerprints in the same way again; generate a table containing the comparison li between each 2 Compute the similarity,find the nearest reference tags; element of fingerprint vector measured by different antennas. Filter the reference tags by records of activating power; It is generated by the fingerprint data set R 9:end while For example, we have two fingerprints 10:Estimating position of target tag by the selected reference 3000,1500.1000.500)and(3100.1400.980.450)in tags. Rc and they are related to grid 1.The difference between s1 and s2 is 1500 in the first fingerprint and 1700 in the second fingerprint,si is the ith element of fingerprint.To check C.Analysis if the target is in,we use the smaller difference to make a By detecting and avoiding the unstable region,adaptive decision.The smaller one above,value of 1500 is more than power stepping method can use appropriate transmitting power the threshold 200,which is set for determining the validity The power can only activate the target tag and the reference of rules.Then we can build a rule for target tag estimated in tags in the nearby area of target tag.By using the appropriate grid 1 that s1-s2>1500 of its fingerprint.If the target tag power,the APS method can improve the localization accuracy is not matching,its estimated position needs calibration.An in some conditions.The minimum error of the localization sys- exact example using the realistic experiment data is given in tem can be reduced by this method.Because the method avoid Section IX. the interference from the reference tags far away from target With these rules and grid-based fingerprint information,wereference tag. For example, we set τ = 5.0 and k = 2 and the number of antennas is 4. When a reference tag is selected, we have its activating power (25.7, 18.7, 30.7, 29.7) by the 4 antennas. And we have activating power (28.7, 29.7, 24.7, 22.7) for target tag. Compute with the two power vectors, we have the last three corresponding elements |29.7−18.7| > 5.0, |24.7−30.7| > 5.0 and |22.7 − 29.7| > 5.0. The number of elements which have difference more than τ is over threshold k . Then we treat this reference tag as false nearby reference tag. Algorithm 1 Localization Algorithm - Finding Appropriate Power 1: Set function R(p) as the RSSI value measured by RFID reader in power p; 2: First set minimum power as p1 and maximum power as p2; 3: Check if the tag can be identified by minimum power or it can not be identified by maximum power. 4: while p2 > p1 do 5: Set p3 = (p1 + p2)/2; 6: if R(p3)=0 then 7: Set p3 to p1; 8: else 9: if R(p3 + δ) − R(p3 − δ) > θ then 10: Set p3 to p1; 11: else 12: Set p3 to p2; 13: end if 14: end if 15: end while 16: Power p3 is the appropriate transmitting power. Algorithm 2 Localization Algorithm - Adaptive Power Step￾ping (APS) 1: Call Alg.1 to get P{pi|i ∈ [1, k]}, each power pi is for antenna Ai; 2: Set P as reader’s transmitting power for each antenna. 3: Collect fingerprints of reference tags which can be identi- fied by at least k antenna. 4: while The number of reference tag < λ do 5: Set P + ΔP to P, set P as reader’s power; 6: Collect fingerprints in the same way again; 7: Compute the similarity, find the nearest reference tags; 8: Filter the reference tags by records of activating power; 9: end while 10: Estimating position of target tag by the selected reference tags. C. Analysis By detecting and avoiding the unstable region, adaptive power stepping method can use appropriate transmitting power. The power can only activate the target tag and the reference tags in the nearby area of target tag. By using the appropriate power, the APS method can improve the localization accuracy in some conditions. The minimum error of the localization sys￾tem can be reduced by this method. Because the method avoid the interference from the reference tags far away from target tag. However, the method still suffer from the same problem with basic method. At some positions in the localization area, the maximum power still needs to activating the target tag. For example, if the target tag is in center of localization area, we need to use maximum power so that all reference tags are activated. So, the method still have a large maximum error. It makes the APS method can only reduce the minimum error but it can not guarantee the maximum error to be less than a smaller threshold. VII. ADAPTIVE GRID-BASED CALIBRATION METHOD A. Motivation In the realistic application, user will get the located object after the localization procedure. The user may give a feedback to set correct position when the estimated position is wrong. In recent years, several detection technologies such as RFID￾based activity sensing have a quick development. With those technologies, the position where user takes the object from can be automatic detected easily. These auto-detection technologies can help us to have feedbacks for the localization result. However, both the user’s feedback and the auto-detection technologies can not give accurate results. The feedback can just show a smaller area where the object is in. But the feedback fingerprints are very reliable, especially the scale of fingerprints is large. By dividing the localization area into grids, as shown in Fig. 3, we can use the feedback to calibrate the next localization result. In the realistic scenario, shelf can be easily divided into grids. The feedback can distinguish the grid in which user takes the object. When knowing which grid the target tag is in, we can measure the fingerprint of this tag and record it as automatic detected fingerprint database. We set this fingerprint database as RG. Each fingerprint in RG is mapped to a grid in the localization area. B. Adaptive Grid-based Calibration (AGC) Considering the fingerprints of reference tags are used to compute similarity between target and reference tags, the de￾tailed information from each element in fingerprints is ignored. In regard to fingerprint data set RG and relative position of each grid, each grid can has some rules Li. As shown in Fig.3, the fingerprint rT must match the rules Li. For Li, we can generate a table containing the comparison li between each element of fingerprint vector measured by different antennas. It is generated by the fingerprint data set RG. For example, we have two fingerprints (3000,1500,1000,500) and (3100, 1400, 980, 450) in RG and they are related to grid 1. The difference between s1 and s2 is 1500 in the first fingerprint and 1700 in the second fingerprint, si is the ith element of fingerprint. To check if the target is in, we use the smaller difference to make a decision. The smaller one above, value of 1500 is more than the threshold 200, which is set for determining the validity of rules. Then we can build a rule for target tag estimated in grid 1 that s1 − s2 ≥ 1500 of its fingerprint. If the target tag is not matching, its estimated position needs calibration. An exact example using the realistic experiment data is given in Section IX. With these rules and grid-based fingerprint information, we