## 3 Distributed Target Tracking Systems
### Estimation Refinement with ANN  
In order to improve positioning accuracy with particle filtering, one option is to determine an appropriate sample space for generating particles. As shown in Figure 5(top), the initial sample area  
Figure 5: The initial sample area (**top**); the refined bounding box based on the reference angle information (**bottom**). is the rectangle defined by blue lines and four corners: (1), (2), (3), and (4) ordered clockwise, which serves as a basis for estimation refinement. Observe that the target is located within the defined rectangle and the pink \"TOA\" circles represent the minimum and maximum range estimates. After importing the information of the defined rectangle and the tasking sub-cluster to the trained neural networking model, a reference angle information (RAI), (_i.e._, the angle information label with a red line), is proposed to refine the initial sample area for the prior density in Step 1 of Table 1. Without loss of generality, a tasking leader is applied as an example to describe the refinement procedures. With the RAI produced by the neural networking model, a threshold \(\theta_{th}\) (_i.e._, the angle between the red line and the blue line in Figure 5) is used to adjust the initial sample area. Given the information of transmission range and the position knowledge of sub-cluster members, the leader node can choose a sub-cluster member, which is an active sensor and has a minimum overlapping area between the communication coverage and the initial sample area, as a reference node to narrow down the sample area. This is attributed to the fact that the position information and the communication coverage of a reference node can be applied to help reshape the initial sample area for localizing the target. On the basis of the RAI (the red line), denote \(r_{1i}\) (\(r_{2j}\)) as the intersection between the initial sample area and the right-hand-side angle boundary (the left-hand-side angle boundary), where \(i\) and \(j\) are related to the four corners. Let \(R_{1}\) and \(R_{2}\) be the intersections between the initial sample area and the RAI. For this typical scenario, the intersections among the initial sample area, the right-hand-side angle boundary, the left-hand-side angle boundary, and the RAI (_i.e._, \(r_{11}\), \(r_{12}\), \(r_{23}\), \(r_{24}\), \(R_{1}\), and \(R_{2}\)) are mostly located within the transmission range of a reference node (Figure 5(bottom)). Referring to Figure 5(top), the intersections between the initial sample area and the communication coverage of the reference node can be regarded as new corners of the refined sample area (_i.e._, \((2)^{{}^{\prime}}\leftarrow(2)\), \((3)^{{}^{\prime}}\leftarrow(3)\), and \((4)^{{}^{\prime}}\leftarrow(4)\)) in Figure 5(bottom). Let \(A_{ref}\) be the communication coverage of the reference node. Thus, the final sample area is the intersection among \(A_{ref}\), the refined sample area defined by blue lines and four corners: (1), \((2)^{{}^{\prime}}\), \((3)^{{}^{\prime}}\), and \((4)^{{}^{\prime}}\) ordered clockwise, and the RAI with a threshold value of \(\theta_{th}\). However, Figure 6(left) shows that the deviation of RAI from the target direction and improperly selected threshold values of \(\theta_{th}\) (e.g., too small values of \(\theta_{th}\)) may lead to the exclusion of possible target locations during the refinement process, which results in an even worse estimate compared with the one without applying the neural networking model. Therefore, in order to avoid the estimation error caused by this scenario, the adjustment principle is to jointly consider the communication coverage of a reference node and the locations of the intersections (_i.e._, \(P_{r_{1i}}\), \(P_{r_{2j}}\), and \(P_{R_{k}}\)). Accordingly, if none of the intersection locations is within the communication coverage of the  
Figure 6: The deviation of RAI from the target (**left**); the updated RAI (**right**).