IEEE TRANSACTIONS ON MOBILE COMPUTING,VOL.XX,NO.XX,2019 (a)Rulel (b)Rule2 (c)Possible solution Linear Scanning Fig.10.Rules of deploying tags Fig.11.Experiment setup of linear fitting accuracy with different tag orientations final processed data are (1.4m,1.42m)and (1.23m,1.47m), respectively.Compared to ground-truth (1.3m,1.46m),the 15 accuracy improves a lot with the outliers elimination. 4.3 Determine Package Orientation for Each Single Package To reconstruct a single package,it makes the same sense to determine the package orientation,so we just need to iden- T1-T2T3-T4T5-T6T1-T3T3-T5 TI T2 T3 T4 T5 T6 tify the bottom face of this package,and estimate the relative rotation angle of the vertical sides against the antenna Fig.12.Accuracy along scanning Fig.13.Accuracy along orthogo- direction nal direction of scanning plane in a specified coordinate system.Here,the "antenna plane"refers to the extended plane of the antenna's front Fig.10(c),the results are plotted in Fig.12 and Fig.13. surface,which should be perpendicular to the ground in our We observe that the accuracy of projected position lo along settings.When the antenna performs the mobile scanning the scanning direction keeps stable with different orientations, linearly,it is just in the antenna plane. while the perpendicular distance h does not have the same high accuracy as lo.Fig.12 plots the accuracy of lo along the 4.3.1 Tag Layout antenna scanning direction,i.e.,the absolute separation Aiming at determining the package orientation only by once error between two tags along the scanning direction.Most 1D mobile scanning,we need to deploy tags in an efficient of the absolute separation errors of different tag pairs are and robust way.The design principle of tag deployment is to below 1.8cm,even in the worst case,the separation achieves use as fewer tags as possible to depict the package uniquely, around 92.3%accuracy.Fig.13 plots the accuracy of the accurately and conveniently.Specifically,as the package perpendicular distance h along the orthogonal direction to can be with any orientation in the 3D space,we should the scanning.The error is much larger than the separation pay attention to ensuring there are always enough effective error along the scanning direction.For tags with the same tags reflecting the signals to the antenna.Meanwhile,as for orientation,the near-far relationships between tags and the identifying the bottom face of the package,it is the same to antenna are reliable,but for tags with different orientations, find which tags are along the vertical axis and what order the error may incur the wrong near-far relationship,i.e.,T3 these tags are with.Therefore,we make two rules as follows. has the smaller h than T2,but T3 has the larger estimated h. 1) The orientations of tags should be along different orthog- Therefore,when using position indicators,we can leverage onal axes(in Fig.10(a)).With this rule,tags along one the projected positions of tags with different orientations, direction at most are in the blind direction,so other and prefer the perpendicular distances of tags with the same tags can response to the antenna successfully. orientation for comparison or calculation. 2) Tags should be deployed along different orthogonal axes (in Fig.10(b)).With this rule,whatever the orienta- 4.3.3 Determine Package Orientation tion of the package is,there is always one tag pair To determine the package orientation,it demands to identify along the vertical axis. the bottom face of the package and the relative angle of the Combining the above two rules,Fig.10(c)illustrates vertical sides in a specified coordinate system.Considering a possible tag deployment satisfying these two rules.No our assumption that one side of the cube package must be matter what orientation the package is,there are four tags parallel to the ground,when we deploy tags like the solution at least to avoid the signal blind direction.Also,there is described in Fig.10(c),we can identify which tag pair is always one tag pair along the Z axis.By determining the along the Z axis and what order the tag pair is in fact.In tags'order of this tag pair,we can derive which side of the this case,let the antenna do the mobile scanning along the package is on the ground then. X or Y axis only once,we can determine the orientation for a single package.Note that,the antenna should be above 4.3.2 Linear Fitting of Tags with Different Orientations or below all the tags,and the package is at the same side Considering that tags in the layout as Fig.10(c)have against the antenna plane during the scanning process different orientations,we carry out experiments to check For simplicity,suppose the antenna is above all the tags whether different orientations among tags have effects on and ahead of all the tags along the X axis positive direction, the accuracy of the linear fitting.As shown in Fig.11,it moves along the y axis,then the tag pair along the Z we arrange six tags with three orientations as required in axis is perpendicular to the antenna scanning direction,soIEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. XX, NO. XX, 2019 7 X Z Y X (a) Rule1 Y X Z Y X (b) Rule2 Y X Z Y ! " # $ % & (c) Possible solution Fig. 10. Rules of deploying tags final processed data are (1.4m, 1.42m) and (1.23m, 1.47m), respectively. Compared to ground-truth (1.3m, 1.46m), the accuracy improves a lot with the outliers elimination. 4.3 Determine Package Orientation for Each Single Package To reconstruct a single package, it makes the same sense to determine the package orientation, so we just need to iden￾tify the bottom face of this package, and estimate the relative rotation angle of the vertical sides against the antenna plane in a specified coordinate system. Here, the “antenna plane” refers to the extended plane of the antenna’s front surface, which should be perpendicular to the ground in our settings. When the antenna performs the mobile scanning linearly, it is just in the antenna plane. 4.3.1 Tag Layout Aiming at determining the package orientation only by once 1D mobile scanning, we need to deploy tags in an efficient and robust way. The design principle of tag deployment is to use as fewer tags as possible to depict the package uniquely, accurately and conveniently. Specifically, as the package can be with any orientation in the 3D space, we should pay attention to ensuring there are always enough effective tags reflecting the signals to the antenna. Meanwhile, as for identifying the bottom face of the package, it is the same to find which tags are along the vertical axis and what order these tags are with. Therefore, we make two rules as follows. 1) The orientations of tags should be along different orthog￾onal axes (in Fig. 10(a)). With this rule, tags along one direction at most are in the blind direction, so other tags can response to the antenna successfully. 2) Tags should be deployed along different orthogonal axes (in Fig. 10(b)). With this rule, whatever the orienta￾tion of the package is, there is always one tag pair along the vertical axis. Combining the above two rules, Fig. 10(c) illustrates a possible tag deployment satisfying these two rules. No matter what orientation the package is, there are four tags at least to avoid the signal blind direction. Also, there is always one tag pair along the Z axis. By determining the tags’ order of this tag pair, we can derive which side of the package is on the ground then. 4.3.2 Linear Fitting of Tags with Different Orientations Considering that tags in the layout as Fig. 10(c) have different orientations, we carry out experiments to check whether different orientations among tags have effects on the accuracy of the linear fitting. As shown in Fig. 11, we arrange six tags with three orientations as required in 0.5 m 0.3 m 0.5 m 0.3 m 1 m Linear Scanning !" !# !$ !% !& !' Fig. 11. Experiment setup of linear fitting accuracy with different tag orientations T1-T2 T3-T4 T5-T6 T1-T3 T3-T5 0 1 2 3 4 Error (cm) Fig. 12. Accuracy along scanning direction T1 T2 T3 T4 T5 T6 0 5 10 15 Error (cm) Fig. 13. Accuracy along orthogo￾nal direction of scanning Fig. 10(c), the results are plotted in Fig. 12 and Fig. 13. We observe that the accuracy of projected position l0 along the scanning direction keeps stable with different orientations, while the perpendicular distance h does not have the same high accuracy as l0. Fig. 12 plots the accuracy of l0 along the antenna scanning direction, i.e., the absolute separation error between two tags along the scanning direction. Most of the absolute separation errors of different tag pairs are below 1.8cm, even in the worst case, the separation achieves around 92.3% accuracy. Fig. 13 plots the accuracy of the perpendicular distance h along the orthogonal direction to the scanning. The error is much larger than the separation error along the scanning direction. For tags with the same orientation, the near-far relationships between tags and the antenna are reliable, but for tags with different orientations, the error may incur the wrong near-far relationship, i.e., T3 has the smaller h than T2, but T3 has the larger estimated h. Therefore, when using position indicators, we can leverage the projected positions of tags with different orientations, and prefer the perpendicular distances of tags with the same orientation for comparison or calculation. 4.3.3 Determine Package Orientation To determine the package orientation, it demands to identify the bottom face of the package and the relative angle of the vertical sides in a specified coordinate system. Considering our assumption that one side of the cube package must be parallel to the ground, when we deploy tags like the solution described in Fig. 10(c), we can identify which tag pair is along the Z axis and what order the tag pair is in fact. In this case, let the antenna do the mobile scanning along the X or Y axis only once, we can determine the orientation 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