Algorithm 1 Position Estimation with the Proposed Algorithm

1. Initialization Generate grids ${G_{x,y}^t|}_{t=0}$ for $x=1, \dots , X$ and $y=1, \dots , Y$, considering the coverage and performance of the radar system. For example, in our radar system, one grid is a square of 0.2${ \mathrm{m}}^2$. 2. For $x=1, \dots , X$ and $y=1, \dots , Y$, calculate the cumulative likelihood as follows: $$G_{x,y}^t=G_{x,y}^{t-1}{\displaystyle \sum }_{i=1}^N{\displaystyle \sum }_{k=1}^Mℒ(p_{x,y}|z_{i,k}) ,$$ (8) $ℒ(p_{x,y}|z_{i,k})$ is the likelihood function of a particular point $p_{x,y}$ in grids, when the $k$th target is detected by the $i$th radar. $G_{x,y}^t$, which is the grid value at time $t$, is generated by recursively exploiting $G_{x,y}^{t-1}$. A probability of target existence of a particular point can be shown through these generated grids $G_{x,y}^t$. 3. For $x=1, \dots , X$ and $y=1, \dots , Y$, normalize the cumulative likelihood for recursive operation as follows: $$G_{x,y}^t=\frac{G_{x,y}^t}{{{\displaystyle \sum }}_{x=1}^X{{\displaystyle \sum }}_{y=1}^Y{G}_{x,y}^t},$$ (9) The normalizing process is required to make the sum of grids is to be one, and determine the effectivity of grids regarding re-initialization. 4. Find the coordinates over the threshold to estimate the location of multiple targets such that $$G_{x,y}^t>G_{thresh} ,$$ $G_{thresh}$ is set adaptively according to the average number of targets detected by the radars. This is because if there is a large number of targets detected by the radars, the value of normalized probability of target existence represented by the cumulative likelihood will be reduced. 5. Calculate the effectivity of grids as follows: $$N_{eff}=\frac{1}{{{\displaystyle \sum }}_{x=1}^X{{\displaystyle \sum }}_{y=1}^Y{\left(G_{x,y}^t\right)}^2} ,$$ (10)