cot Algorithm 2:Calibration by tag arrays 1 Orientation Estimation: 2 The antenna moves along the Z axis to estimate the Z-coordinates of the all the tags; 3 Distinguish the three tag arrays on different surfaces; 4 Judge the flip state of the object by finding the tag array which is on the bottom/top surface; Fig.8.Segmentation for the points in P 5 Select the target tag array and calibrate the Z-coordinate of the target tag array according to Eq.7; Algorithm 1:Multipath Suppression 6 Target Tag Array Localization: 7 The antenna moves along the X axis to localize the tags Input:Point set P={(io,cot）,…,(im,cotm in the target tag array in the X-Y plane; Output:New point set P removed the outliers s Calculate the location of the target tag array and estimate 1 Split P into k subset using a slide window: the rotation angle of the object according to Eq.8; Sp={SP1·,SPw}: 9 Object Localization: 2 Changing rate set for the subsets:A =0; 10 Calculate the 3D coordinates of the object based on the 3 Calculation for average changing rate step: location of the target tag array and the rotation angle of 4 for each Sp in Sp do the object according to Eq.9; 5 Calculate a fitting line li for the points in Sp; 11 return 3D coordinates of the object 6 Add the scope ai of li to A: 7A={a1,…,ak: s Outliers finding and removing step: whole algorithm is described in Algorithm 2. 9 Find outliers in A and remove the points in 1)Orientation Estimation:The orientation of the tagged corresponding subsets in Sp; objects must be firstly determined before performing an ac- 10 for each subset which has been removed do curate 3D localization for the tagged objects.First,we need if Sp,and Sp+2 are removed then to distinguish the tag arrays on three mutually orthogonal L Remove SP if it has not been removed; surfaces.Recall that the 2-coordinates of the tags in the three tag arrays have different characteristics.In practice,we 13 return a new point set P first move the antenna along the Z axis to estimate the Z- coordinates of all the tags,then the three tag arrays can be distinguished by comparing the Z-coordinate of each tag in the tag arrays.As illustrated in Fig.9(a),the antenna moves above idea,we only need to find the outliers in A and remove the corresponding subsets in Sp.and the above finding process along the Z axis to calculate the Z-coordinate of the all the can be considered as a one class SVM problem.After the tags.Fig.9(b)shows the localization results.Notice that the Z-coordinates of the tags in Array 1 and Array 2 are equal above step,the subsets which contain continuous occurrences and in Array 3 are different,so we can easily correspond the of outliers are partly removed.We can further remove the other red points in Figure.9(b)to Array 3.Since the tag array on unexpected subsets in Sp using the continuity of the outliers again.That is to say,if the subsets Sp,and Sp+2 are removed, the top/bottom surface has the maximum or the minimum Z- then the subset pshould be removed too.As a result,we coordinate value,so,the green points with the minimum Z- removed the outliers in P for the estimation of do and o.The coordinates in Fig.9(b)correspond to Array 1 and we can also multipath suppression algorithm is shown in Algorithm 1. infer that Array 1 is at the bottom.Finally,the blue points corresponds to Array 2.After the above process,the flip state C.Calibration by tag arrays of the object is figured out.In addition,as mentioned before, After the AoA localization for each tag in the tag array,we the rotation angle of the object can be estimated from the can leverage the fixed layout of the tag array to calibrate the target tag array in which every tag is attached along the Z result of each tag in order to estimate the 3D coordinates and axis and on the vertical surface of the object,so here Array 2 orientation of the object.In general,this part includes three can be chosen as the target tag array. main components:first,we use the calculated Z-coordinates We next optimize the Z-coordinate of the target tag array. of all the tags to infer the rough orientation of the object,from Let ze be the Z-coordinate of the target tag array's center and which we distinguish the three tag arrays on different surfaces be the Z-coordinate for the ith tag calculated through AoA and select a target tag array for further localization in the X- localization.As the Z-coordinate of each tag in the target tag Y plane.Then,we localize the target tag array in the X-Y array is the same,then,ze can be considered as the average plane and estimate the rotation angle of the object.Finally,we Z-coordinate of all the tags in the target tag array: get the 3D coordinates of the object referring to the location n of the target tag array and the rotation angle of the object.The 2e =1名 (7)ܵ௣భ ܵ௣ೖషభ ܵ௣౟ ܵ௣ೖ ܵ௣మ X ߠ ‘… Fig. 8. Segmentation for the points in P Algorithm 1: Multipath Suppression Input: Point set P = {(x˜0, cot ˜θ0 ) , · · · , ( x˜m, cot ˜θm )} Output: New point set P ′ removed the outliers 1 Split P into k subset using a slide window: SP = {SP1 , · · · , SPk }; 2 Changing rate set for the subsets: A = ∅; 3 Calculation for average changing rate step: 4 for each SPi in SP do 5 Calculate a fitting line li for the points in SPi ; 6 Add the scope ai of li to A; 7 A = {a1, · · · , ak}; 8 Outliers finding and removing step: 9 Find outliers in A and remove the points in corresponding subsets in SP ; 10 for each subset which has been removed do 11 if SPj and SPj+2 are removed then 12 Remove SPj+1 if it has not been removed; 13 return a new point set P ′ above idea, we only need to find the outliers in A and remove the corresponding subsets in SP , and the above finding process can be considered as a one class SVM problem. After the above step, the subsets which contain continuous occurrences of outliers are partly removed. We can further remove the other unexpected subsets in SP using the continuity of the outliers again. That is to say, if the subsets SPj and SPj+2 are removed, then the subset SPj+1 should be removed too. As a result, we removed the outliers in P for the estimation of d0 and x0. The multipath suppression algorithm is shown in Algorithm 1. C. Calibration by tag arrays After the AoA localization for each tag in the tag array, we can leverage the fixed layout of the tag array to calibrate the result of each tag in order to estimate the 3D coordinates and orientation of the object. In general, this part includes three main components: first, we use the calculated Z-coordinates of all the tags to infer the rough orientation of the object, from which we distinguish the three tag arrays on different surfaces and select a target tag array for further localization in the X￾Y plane. Then, we localize the target tag array in the X-Y plane and estimate the rotation angle of the object. Finally, we get the 3D coordinates of the object referring to the location of the target tag array and the rotation angle of the object. The Algorithm 2: Calibration by tag arrays 1 Orientation Estimation: 2 The antenna moves along the Z axis to estimate the Z-coordinates of the all the tags; 3 Distinguish the three tag arrays on different surfaces; 4 Judge the flip state of the object by finding the tag array which is on the bottom/top surface; 5 Select the target tag array and calibrate the Z-coordinate of the target tag array according to Eq.7; 6 Target Tag Array Localization: 7 The antenna moves along the X axis to localize the tags in the target tag array in the X-Y plane; 8 Calculate the location of the target tag array and estimate the rotation angle of the object according to Eq.8; 9 Object Localization: 10 Calculate the 3D coordinates of the object based on the location of the target tag array and the rotation angle of the object according to Eq.9; 11 return 3D coordinates of the object whole algorithm is described in Algorithm 2. 1) Orientation Estimation: The orientation of the tagged objects must be firstly determined before performing an ac￾curate 3D localization for the tagged objects. First, we need to distinguish the tag arrays on three mutually orthogonal surfaces. Recall that the Z-coordinates of the tags in the three tag arrays have different characteristics. In practice, we first move the antenna along the Z axis to estimate the Z￾coordinates of all the tags, then the three tag arrays can be distinguished by comparing the Z-coordinate of each tag in the tag arrays. As illustrated in Fig.9(a), the antenna moves along the Z axis to calculate the Z-coordinate of the all the tags. Fig.9(b) shows the localization results. Notice that the Z-coordinates of the tags in Array 1 and Array 2 are equal and in Array 3 are different, so we can easily correspond the red points in Figure.9(b) to Array 3. Since the tag array on the top/bottom surface has the maximum or the minimum Z￾coordinate value, so, the green points with the minimum Z￾coordinates in Fig.9(b) correspond to Array 1 and we can also infer that Array 1 is at the bottom. Finally, the blue points corresponds to Array 2. After the above process, the flip state of the object is figured out. In addition, as mentioned before, the rotation angle of the object can be estimated from the target tag array in which every tag is attached along the Z axis and on the vertical surface of the object, so here Array 2 can be chosen as the target tag array. We next optimize the Z-coordinate of the target tag array. Let zc be the Z-coordinate of the target tag array’s center and zbi be the Z-coordinate for the i th tag calculated through AoA localization. As the Z-coordinate of each tag in the target tag array is the same, then, zc can be considered as the average Z-coordinate of all the tags in the target tag array: zc = ∑n i=1 zbi n (7)