## 4 Numerical Example  
The simulation was formulated in Matlab R2012a and the initial conditions were set as follows: Five hundred micro-sensors are assumed to be randomly planted on the ground in the square region of 40,000 square meters. These sensors integrate CMs receiving and sending modules, and the SMs can detect the target and transfer the target information via the CMs when the target passes by. The time interval was 1 s, and the detailed variables are listed in Table 4.  
The initial values are \(\Delta V_{k}(0)=0\) and \(V_{k}(0)=V_{\min}\). \(Clp_{k}(t)\) and \(RDp_{k}(t)\) in Equations (2) and (3) are considered as  
\[Clp_{k}(t)=RDp_{k}(t)= \begin{cases}V_{k}(t)/V_{\max}&if\ \ \Delta V_{k}(t-1)\
eq 0 \\ V_{\min}/V_{\max}&if\ \ \Delta V_{k}(t-1)=0\end{cases} . \tag{20}\]  
The target moves in constant-velocity (CV) driven by a zero-mean Gaussian noise process with a variance of 400 m\({}^{2}\) in 10 consecutive rounds. Figures 5-7 show in detail the state of the SMs at different times during the target movement via the BDIIM and DIDM methods. The target is plotted by a \"+\" (blue), which is supposed to have the same track in both methods and move from the left-lower location of the figure to an upper-right location. \"\(\bigstar\)\" (blue) represents the estimated target position. The dashed circle (blue) denotes the sensing and communicating area with the radii \(R_{s}\) and \(R_{s}+R_{c}\), respectively. \"\(\square\)\" (black) in the smallest size represents the \"sleep\" SMs. \"\(\blacktriangledown\)\" (red) represents the valid wake-up SMs, which are set to \"wake\" and successfully find the true target. \"\(\bigstar\)\" (green) represents the invalid wake-up SMs, which are set to \"wake\" but fail to find the target. The SM states in the 10 th, 20 th, and 30 th time intervals are compared. The results in the other time intervals are similar and are therefore saved. In counting the total number of green \"\(\bigstar\)\" outside the circle at these three time intervals, we find that the number of green \"\(\bigstar\)\" via the proposed BDIIM method is slightly less than the number obtained via the previous DIDM method. Meanwhile, in the area outside the circles where the target passes by, the number of green \"\(\bigstar\)\" via BDIIM is much less than that achieved via DIDM. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Var** & **Value** & **Var** & **Value** & **Var** & **Value** & **Var** & **Value** & **Var** & **Value** & **Var** & **Value** & **Var** & **Value** \\ \hline \(R_{S}\) & 30\(m\) & \(P_{d}\) & 0.9 & \(V_{\max}\) & 20 & \(c_{1}\) & 8 & \(c_{3}\) & 0 & \(m_{2}\) & 1.2 & \(m_{4}\) & 1 \\ \(R_{c}\) & 15\(m\) & \(P_{f}\) & 0.05 & \(V_{\min}\) & 1 &For the state of the CMs, as shown in Figures 8-10, the target is plotted by a \"+\" (blue). \"\(\blacktriangle\)\" (red) represents the valid wake-up CMs. \"\(\blacktriangledown\)\" (pink) represents the invalid wake-up CMs in which \"\(\blacktriangledown\)\" (green) represents the invalid wake-up CMs in the \"send/receive\" state. These figures show the detailed states of the CMs at the 10 th, 20 th, and 30 th time intervals during target movement, via the BDIIM and DIDM methods. Especially in the area outside the circles, where the target passes by, the number of green \"\(\blacktriangledown\)\" via the BDIIM is clearly much less than that obtained via the DIDM at each time interval. In other words, the proposed BDIIM method has a higher wake-up efficiency than the DIDM method, and the energy cost of the system is greatly reduced, while the estimation error of the target position also decreases. Further, the detailed data regarding the DIDM method and the proposed BDIIM method are curved, as shown in Figures 11 and 12. The dashed (blue) and solid (pink) lines represent the DIDM method and the proposed BDIIM method, respectively.