85:14·C.Wang et al.. 0.8 Signal with respiration Signal after eliminating respiration (ue!ped) 0.6 0.4 0.2 10 15 20 Time (s) Fig.11.Eliminating the moving effect from the mixed RF-signals. Hence,suppose there are n tags on the tag array,if we can obtain the scale factor i for different tags,the largest displacement of chest contour Al can be estimated as follows: 4nn cos a (16) Once we have the displacement Al,we can derive the phase change of each tag Ti during the respiration process as follows: Aa,=4 cos-4rA1cos&-在月A (17) n Si Then,we can subtract the estimated phase sequence A;from the filtered phase sequence,so as to remove the interference from the respiration signal. Based on the above analysis,it is critical to estimate the parameter i for different tags,we thus depict the solution as follows:Suppose for each tag Ti,the interpolated phase sequence from a specified time window W is i={0(t)).For any time t e W,we can add the phase of different tags together as (t)=10(t),and obtain the phase sequence s=(0 (t)).In this way,we are able to obtain the principal phase variation trend of all tags According to the time points of each adjacent peak and valley in say ti and ti+,which is corresponding to the largest displacement of the chest contour Al(t),we can calculate the corresponding phase change in for any tag Ti,and obtain the averaged phase change from m samples as follows: 房=216-6 (18) m j=1 As the displacement Al(t)is uniform for all tags,hence the value of Bi is proportional to the value of i,i.e., i=BiC,C is a constant.According to Eq.(17),we can replace i with Bi and compute the value of A. Figure 11 shows an example of eliminating the moving effect of respiration from the mixed RF-signals.In the signal with respiration,we use the red circle to mark the signal change due to the moving effect,which periodically arises based on the respiration pattern.Note that after the elimination,the periodic peaks and valleys caused by the respiration are almost removed.We can observe some periodicity for the remaining signals,which is corresponding to the heartbeat. Proc.ACM Interact.Mob.Wearable Ubiquitous Technol,Vol.2,No.2,Article 85.Publication date:June 2018.85:14 • C. Wang et al. Time (s) 5 10 15 20 Phase (Radian) -0.2 0 0.2 0.4 0.6 0.8 Signal with respiration Signal after eliminating respiration Fig. 11. Eliminating the moving effect from the mixed RF-signals. Hence, suppose there are n tags on the tag array, if we can obtain the scale factor ζi for different tags, the largest displacement of chest contour ∆l can be estimated as follows: ∆bl = 1 n Õn i ∆li ζi = λ 4nπ cos α Õn i ∆θi ζi . (16) Once we have the displacement ∆bl, we can derive the phase change of each tag Ti during the respiration process as follows: ∆cθi = 4π∆cli cos α λ = 4π∆blζi cos α λ = ζi n Õn i ∆θi ζi . (17) Then, we can subtract the estimated phase sequence ∆cθi from the filtered phase sequence, so as to remove the interference from the respiration signal. Based on the above analysis, it is critical to estimate the parameter ζi for different tags, we thus depict the solution as follows: Suppose for each tag Ti , the interpolated phase sequence from a specified time window W is Θi = {θi(t)}. For any time t ∈ W , we can add the phase of different tags together as θs(t) = Ín i=1 θi(t), and obtain the phase sequence Θs = {θs(t)}. In this way, we are able to obtain the principal phase variation trend of all tags. According to the time points of each adjacent peak and valley in Θs , say tj and tj+1, which is corresponding to the largest displacement of the chest contour ∆l(t), we can calculate the corresponding phase change in Θi for any tag Ti , and obtain the averaged phase change from m samples as follows: βi = 1 m Õm j=1 |θi(tj+1) − θi(tj)|. (18) As the displacement ∆l(t) is uniform for all tags, hence the value of βi is proportional to the value of ζi , i.e., ζi = βi · C, C is a constant. According to Eq.(17), we can replace ζi with βi and compute the value of ∆cθi . Figure 11 shows an example of eliminating the moving effect of respiration from the mixed RF-signals. In the signal with respiration, we use the red circle to mark the signal change due to the moving effect, which periodically arises based on the respiration pattern. Note that after the elimination, the periodic peaks and valleys caused by the respiration are almost removed. We can observe some periodicity for the remaining signals, which is corresponding to the heartbeat. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 2, No. 2, Article 85. Publication date: June 2018