# Through-Floor Vital Sign Searching for Trapped Person Using Wireless-Netted UWB Radars
## 3 Through-Floor Vital Sign Search
### Vital Sign Searching Procedure  
The schematic of the vital sign searching procedure is described in Figure 5 and is summarized as follows.  
(1) Record the four wireless-netted radars' spatial locations \((x_{1},y_{1},z_{1})\), \((x_{2},y_{2},z_{2})\), \((x_{3},y_{3},z_{3})\), and \((x_{4},y_{4},z_{4})\). The corresponding detection distances for the trapped person are represented by \(R_{1}\),\(R_{2}\), \(R_{3}\), and \(R_{4}\). Construct the detection distance vector \((R_{1},R_{2},R_{3},R_{4})\).  
(2) Invalid value elimination and classification. If \(R_{i}\
eq 0,i\in\{1,2,3,4\}\), the value of \(R_{i}\) is valid. Judge the number of effective values in the detection distance vector; the number of effective values might be 4, 3, 2, 1, 0.  
(3) Valid value number = 4. Choose three valid values each time and check whether the three observation points corresponding to the three valid values satisfy the \"triangle composition condition\". If the three observation points fail, we reselect three valid values from these four valid values. Otherwise, the three detection points can be used to calculate the spatial location of the target by using \"noncoherent positioning\" method. Then, repeat this procedure four times. For through-floor case, the \"noncoherent positioning\" equation set is  
\[\left\{\begin{array}{l}\left(x-x_{i}\right)^{2}+\left(y-y_{i}\right)^{2}+z^ {2}=R_{i}^{2}\\ \left(x-x_{i}\right)^{2}+\left(y-y_{i}\right)^{2}+z^{2}=R_{j}^{2}\\ \left(x-x_{k}\right)^{2}+\left(y-y_{k}\right)^{2}+z^{2}=R_{k}^{2}\end{array}\right. \tag{6}\]  
where \(i,j,k\in\{1,2,3,4\}\).  
Figure 4: Different MIMO array topologies and effective aperture with different scores. (**a**) Topology-I; (**b**) effective aperture with 36 score; (**c**) Topology-II; (**d**) effective aperture with 28 score.  
(4) Valid value number = 3. Use the \"noncoherent positioning\" method to obtain the spatial location of the target and judge the existence of the solution. If the solution with \(z<0\) exists, then it is the spatial location of the target. Otherwise, the \"triangle composition condition\" should be used to judge which observation point is improper and eliminate it by setting its detection distance to zero. The improper observation point always has the largest detection distance. Then, rejudge the number of the valid values.  
(5) Valid value number = 2. According to the \"triangle composition condition\", when the distances \(D_{i,j}\), \((i,j\in\{1,2,3,4\})\) between the two observation points and the two detection distances \(R_{i},R_{j}\), \((i,j\in\{1,2,3,4\})\) should satisfy the condition of \(R_{i}+R_{j}>D_{i,j}\). The detection distance \(R_{i}\), \((i\in\{1,2,3,4\})\), by processing the echoes obtained from the \(i\)-th UWB radar, is taken as the 1D solution. Otherwise, the observation point corresponding to the smaller value of \(R_{i},R_{j}\) is reserved as the 1D solution. Further, we can select two or three new observation points to reconstruct four observation points and repeat the above procedure.  
(6) Valid value number = 1. There is only the 1D solution. Further, we can keep the corresponding observation point, select three new observation points and repeat the above procedure.