## 3 Improved Multi Mobile Agent Data Fusion Scheme
### Data Fusion Algorithm
Based on this assumption, only a small area of the ROI target near the received signal energy will be significantly greater than 0, therefore, ignoring the boundary effect of ROI, \(\overline{P_{d}}(x_{t},y_{t})\) simplifies to as the value of \(x_{t}\) and \(y_{t}\). \[\overline{P_{d}}(x_{t},y_{t})\approx\overline{P_{d}}(0,0)=\frac{1}{b^{2}}\int _{-\frac{b}{2}}^{\frac{b}{2}}\int_{-\frac{b}{2}}^{\frac{b}{2}}P_{d}(x,y,0,0)dxdy \tag{26}\]  
Among them:  
\[P_{d}(x,y,0,0)=Q(\tau-\sqrt{\frac{P_{0}}{1+\alpha(x^{2}+y^{2})^{\frac{b}{2}}}}) \tag{27}\]  
We can divide Equation (26) into the following two parts, one part is the integration of \(\frac{b}{2}\) radius circle, the other part is the integration of the remaining part of the ROI. If we use polar coordinates, the first part will be much simpler:  
\[\eta\approx E\{\Lambda_{2}|H\}=\sum\limits_{i=1}^{N}E\{I_{i}|H_{1}\}=\sum \limits_{i=1}^{N}P_{di} \tag{19}\]0  
The second part of the integration is the integration around the circle, \(d\) is very large, and \(P_{d}\) is very close to \(P_{fa}\). Therefore, it is reasonable to draw the following approximation:  
\[\eta\approx E\{\Lambda_{2}|H\}=\sum\limits_{i=1}^{N}E\{I_{i}|H_{1}\}=\sum \limits_{i=1}^{N}P_{di} \tag{19}\]1The approximation is conservative, because \(d\) is replaced by a larger number of \(\left(\frac{\sqrt{2}b}{2}\right)\), similarly:  
\[\eta\approx E\{\Lambda_{2}|H\}=\sum\limits_{i=1}^{N}E\{I_{i}|H_{1}\}=\sum \limits_{i=1}^{N}P_{di} \tag{19}\]2  
Therefore, the detection probability \(P_{d}\) of system level is:  
\[\eta\approx E\{\Lambda_{2}|H\}=\sum\limits_{i=1}^{N}E\{I_{i}|H_{1}\}=\sum \limits_{i=1}^{N}P_{di} \tag{19}\]3  
The multi-mobile agent framework obtains the fusion results based on target detection probability and false alarm rate function of sensor nodes in the clusters. This paper takes the target classification as an example to introduce the calculation model. We turn the sensor's detection rate into a confidence range, where local sensor nodes assign a certain degree of determination to the data processing results of the fusion mobile agent. For example, in a target classification program, the confidence range may be 40\(\sim\)70% that the passing target is a diesel truck, 20\(\sim\)30% that the passing target is an SUV [39]. Multiple models use random distribution of confidence itself. The simplest is the uniform distribution, where the model places the same weight on the self-confidence values of the confidence level, and the Gauss distribution. If the degree of confidence is closer to the center, the weight is greater. The integrated algorithm must be simple and efficient, because it must meet energy efficiency and real-time response. A satisfactory solution algorithm is the overlap function. Originally proposed by [PERSON], and the function is like the histogram function. According to the degree of confidence generated by multi sensor nodes, the number of sensor nodes with the same confidence level combine in the overlap function. The mobile agent at each stop point of the route obtains a partial integration result from the earlier mobile sensor node. These results determine whether the mobile agent needs to continue its mobile route [40]. The following Figure 8 is an example. It illustrates the structure of overlapping functions of 6 sensor nodes which are uniformly distributed. The horizontal axis stands for the confidence range with a range of 0\(\sim\)1, the vertical axis stands for the number of sensor nodes with the same confidence values. For example, the figure shows that the sensor node confidence range 0.5\(\sim\)0.6 includes s1, s2, s3 and s6. The integrated information depends on the greatest overlap value [41] in the maximum coverage. For example, as shown in Figure 8, the region [A,B] stands for the integration of information, where the confidence degree of each sensor in this region overlaps most. First, a processing center uses a design overlapping function of generating and analyzing, sends each result to the processing center (RMS) for information integration.