(a)rulel (b)rule2 (c)possible solution (a)possible casel (b)possible case2 (c)possible case3 Fig.8.Deploying reference tags Fig.9.Possible cases for the special package orientation for a single package.Note that,the antenna should be above or possible cases of the package orientation,as shown in Fig.8(c) below all the tags,and the package is at the same side against and Fig.9.Any of these possible cases can transform into the antenna plane during the scanning process. another case by rotating along the Y axis,but the relationships For simplicity,suppose the antenna is above all the tags of their perpendicular distances differ,so we can use these and ahead of all the tags along the X axis positive direction, relationships to vote for which case is the most possible case it moves along the Y axis,then the tag pair along the Z axis As we assume that the antenna is above all the tags and ahead is perpendicular to the antenna scanning direction.so their of all the tags along the X axis positive direction,let the perpendicular points should be the same.That is,the spacing perpendicular distances for T,T3,Ts be h,h3,hs,then for of their perpendicular points equals 0 in theory.Hence,if the case as Fig.8(c):h1<h3,h3>h5,for the possible the spacing of the perpendicular points for a tag pair along casel (Fig.9(a)):h<h3,h3<hs,for the possible case2 a certain axis is 0,it is probable that the tag pair is along (Fig.9(b)):h1 h3,h3<h5 and for the possible case3 the Z axis now,except for some special cases where there (Fig.9(c)):h1>h3,h3 >h5.There are multiple tag pairs is a tag pair along the X axis,then there are two tag pairs for the comparison,here we list part of them for explanation. that their perpendicular points spacings are equal to 0,we will Then,by comparing the relationships of different tag pairs, discuss it later.After identifying which tag pair is along the we vote for the possible cases,and select the case with the Z axis,we can determine the tags'order by comparing their highest score as our estimation result. perpendicular distances extracted from their angle profiles.As C.Discussion the antenna is above all the tags,the tag with the smaller There must be a side of the package parallel to the ground: perpendicular distance of the vertical tag pair should be above As we assume that there must be a side of the packages the other along the Z axis.However,such comparison ignores parallel to the ground (which means the package is on the the relationships of the perpendicular distances for other tags, ground or on other packages,not leans).thus the state of the it is easy to make a wrong decision with only one comparison package is limited,the angle estimation is restricted to along results.Note that,the spacings of the perpendicular points of the Z axis.If not,the searching space of finding the optimal the tags should stay the same when the package is upside angle expands,the simple solution is to add one more mobile down,as the package rotates around the Y axis by 180.So scanning along the direction different from the previous one. we can estimate the relative angle of the package first,then the 3D reconstruction can be realized as well. use the relationships of the perpendicular distances among There may exist serious tag missing when many packages different tag pairs to vote for the tags'order of the vertical are stacked closely:As packages are stacked in storage,the tag pair,then determine the bottom face of the package.When large amounts of tags and small separations between the tags selecting the tag pairs among all the tags on the package,it is from different packages may cause the coupling effect or the significant to avoid the tags in the blind direction by filtering interrogation failure [16-20].But it exceeds the research fields the tags with relative weak RSS compared with other tags on of this paper,so we ignore it now. the package.The angle estimation is based on the spacings of The difference of the perpendicular distances for the tag the perpendicular points for different tag pairs,as: pair parallel to the antenna plane may be much smaller than that for the tag pair perpendicular to the antenna plane with arg min ∑d-6,(o)训 (5) the same tag spacing:As shown in Fig.10,the tag pair i=1 (T1,T2}is perpendicular to the antenna plane,while the where N is the number of tag pairs,is the spacing between tag pair (T2,T3}is parallel to the antenna plane.Their tag the perpendicular points of a tag pair by measurement,i() spacings are the same,as Adh=Ad,but their perpendicular represents the spacing at relative angle o theoretically distance differences are not similar.Suppose the distance from Now,considering the case shown in Fig.8(c)for example, Ti to the antenna is Im,the tag spacing is 0.2m,so the we illustrate how to deal with the special cases where there perpendicular distance difference between T2 and T3 is only are two tag pairs whose perpendicular point spacings are 1.65cm,which is much smaller than that between Ti and both equal to 0.As the antenna moves along the y axis, T2(20cm).Since the distance difference is so small,the the perpendicular points of the tag pair on the same surface relationship of such tag pair is probably to be wrong.So, [T3,Ta}or [T5,T6}are at the same point.With the relative it is better to set weights for the tag pairs based on their order of the tag pair [T1,T2}.as the tag Ti is on the left perpendicular distance differences when voting for multiple of T2 along the antenna moving direction,there are four possible package orientations.   (a) rule1    (b) rule2    ܶଵ ܶଶ ܶହ ܶ଺ ܶଷ ܶସ (c) possible solution Fig. 8. Deploying reference tags for a single package. Note that, the antenna should be above or below all the tags, and the package is at the same side against the antenna plane during the scanning process. For simplicity, suppose the antenna is above all the tags and ahead of all the tags along the X axis positive direction, it moves along the Y axis, then the tag pair along the Z axis is perpendicular to the antenna scanning direction, so their perpendicular points should be the same. That is, the spacing of their perpendicular points equals 0 in theory. Hence, if the spacing of the perpendicular points for a tag pair along a certain axis is 0, it is probable that the tag pair is along the Z axis now, except for some special cases where there is a tag pair along the X axis, then there are two tag pairs that their perpendicular points spacings are equal to 0, we will discuss it later. After identifying which tag pair is along the Z axis, we can determine the tags’ order by comparing their perpendicular distances extracted from their angle profiles. As the antenna is above all the tags, the tag with the smaller perpendicular distance of the vertical tag pair should be above the other along the Z axis. However, such comparison ignores the relationships of the perpendicular distances for other tags, it is easy to make a wrong decision with only one comparison results. Note that, the spacings of the perpendicular points of the tags should stay the same when the package is upside down, as the package rotates around the Y axis by 180◦. So we can estimate the relative angle of the package first, then use the relationships of the perpendicular distances among different tag pairs to vote for the tags’ order of the vertical tag pair, then determine the bottom face of the package. When selecting the tag pairs among all the tags on the package, it is significant to avoid the tags in the blind direction by filtering the tags with relative weak RSS compared with other tags on the package. The angle estimation is based on the spacings of the perpendicular points for different tag pairs, as: arg min φ  N i=1 δ i − δi(φ) (5) where N is the number of tag pairs, δ i is the spacing between the perpendicular points of a tag pair by measurement, δi(φ) represents the spacing at relative angle φ theoretically. Now, considering the case shown in Fig. 8(c) for example, we illustrate how to deal with the special cases where there are two tag pairs whose perpendicular point spacings are both equal to 0. As the antenna moves along the Y axis, the perpendicular points of the tag pair on the same surface {T3, T4} or {T5, T6} are at the same point. With the relative order of the tag pair {T1, T2}, as the tag T1 is on the left of T2 along the antenna moving direction, there are four ܶହ ܶ଺    ܶଵ ܶଶ ܶଷ ܶସ (a) possible case1 ܶଵ ܶଶ ܶ଺ ܶହ ܶଵ ܶ଺ ܶହ ܶଶ    ܶସ ܶଷ (b) possible case2 ܶଵ ܶଶ    ܶସ ܶଷ ܶ଺ ܶହ (c) possible case3 Fig. 9. Possible cases for the special package orientation possible cases of the package orientation, as shown in Fig. 8(c) and Fig. 9. Any of these possible cases can transform into another case by rotating along the Y axis, but the relationships of their perpendicular distances differ, so we can use these relationships to vote for which case is the most possible case. As we assume that the antenna is above all the tags and ahead of all the tags along the X axis positive direction, let the perpendicular distances for T1, T3, T5 be h1, h3, h5, then for the case as Fig. 8(c): h1 < h3, h3 > h5, for the possible case1 (Fig. 9(a)): h1 < h3, h3 < h5, for the possible case2 (Fig. 9(b)): h1 > h3, h3 < h5 and for the possible case3 (Fig. 9(c)): h1 > h3, h3 > h5. There are multiple tag pairs for the comparison, here we list part of them for explanation. Then, by comparing the relationships of different tag pairs, we vote for the possible cases, and select the case with the highest score as our estimation result. C. Discussion There must be a side of the package parallel to the ground: As we assume that there must be a side of the packages parallel to the ground (which means the package is on the ground or on other packages, not leans), thus the state of the package is limited, the angle estimation is restricted to along the Z axis. If not, the searching space of finding the optimal angle expands, the simple solution is to add one more mobile scanning along the direction different from the previous one, the 3D reconstruction can be realized as well. There may exist serious tag missing when many packages are stacked closely: As packages are stacked in storage, the large amounts of tags and small separations between the tags from different packages may cause the coupling effect or the interrogation failure [16–20]. But it exceeds the research fields of this paper, so we ignore it now. The difference of the perpendicular distances for the tag pair parallel to the antenna plane may be much smaller than that for the tag pair perpendicular to the antenna plane with the same tag spacing: As shown in Fig. 10, the tag pair {T1, T2} is perpendicular to the antenna plane, while the tag pair {T2, T3} is parallel to the antenna plane. Their tag spacings are the same, as Δdh = Δdv, but their perpendicular distance differences are not similar. Suppose the distance from T1 to the antenna is 1m, the tag spacing is 0.2m, so the perpendicular distance difference between T2 and T3 is only 1.65cm, which is much smaller than that between T1 and T2 (20cm). Since the distance difference is so small, the relationship of such tag pair is probably to be wrong. So, it is better to set weights for the tag pairs based on their perpendicular distance differences when voting for multiple possible package orientations.