## 5 Conclusions  
This study proposes an information fusion method that combines WAA and WGA to solve the multi-group/extended target fusion tracking problem for distributed sensors with limited FOVs. The proposed method fuses a PMBM filter's posterior densities for different sensors, employing a sequential fusion process. Simulation experiments demonstrated that the proposed method performed better than the representative WAA and WGA methods for group/extended targets under limited FOV conditions, and further work will be carried out by applying the proposed method to a real-world system.  
Conceptualization, methodology, C.X. and H.L.; software and resources, C.X., M.H. and F.Z.; writing--original draft preparation, C.X.; writing--review and editing, M.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China under Grant 61921001.  
The datasets presented in this article are not readily available because the data are part of an ongoing study.  
The authors declare no conflicts of interest.  
The Simplification of the Optimization Objective Function in (40)  
Before simplifying the optimization objective, we give the following results for the calculation of the GGIW:  
\[\int\mathcal{GAMM}(\gamma;\alpha_{1},\beta_{1})\mathcal{GAMM}( \gamma;\alpha_{2},\beta_{2})d\gamma =\frac{\beta_{1}^{\alpha_{1}}\beta_{2}^{\alpha_{2}}\Gamma(\alpha_ {1}+\alpha_{2})}{(\beta_{1}+\beta_{2})^{(\alpha_{1}+\alpha_{2})}\Gamma(\alpha_ {1})\Gamma(\alpha_{2})}, \tag{11}\] \[\int\mathcal{N}(\mathbf{x};\mathbf{m}_{1},\mathbf{P}_{1}) \mathcal{N}(\mathbf{x};\mathbf{m}_{2},\mathbf{P}_{2})d\mathbf{x} =\mathcal{N}(\mathbf{m}_{1}-\mathbf{m}_{2};\mathbf{0},\mathbf{P}_ {1}+\mathbf{P}_{2}),\] (12) \[\int\mathcal{DW}(\mathbf{\Sigma};v_{1},\mathbf{V}_{1})\mathcal{DW }(\mathbf{\Sigma};v_{2},\mathbf{V}_{2})d\mathbf{\Sigma} =\frac{|\mathbf{V}_{1}|^{\frac{v_{1}}{2}}|\mathbf{V}_{2}|^{\frac{v_{2}}{2}} \Gamma_{d}(\frac{v_{1}+v_{2}+d+1}{2})}{|\mathbf{V}_{1}+\mathbf{V}_{2}|^{\frac{ v_{1}+v_{2}+D+1}{2}}\Gamma_{d}(\frac{v_{1}}{2})\Gamma_{d}(\frac{v_{2}}{2})}. \tag{13}\]  
Then, let us simplify the optimization objective function.  
\[\int(\sum_{i=1}^{l}a_{i}\mathcal{GGInv}(\xi;\xi^{i})-\sum_{j=1}^{l }\mathcal{GGInv}(\xi;\xi^{j}))^{2}d\xi \tag{14}\] \[= \int\biggl{\{}(\sum_{i=1}^{l}a_{i}\mathcal{GGInv}(\xi;\xi^{i}))^{2 }+(\sum_{j=1}^{l}\mathcal{GGInv}(\xi;\xi^{j}))^{2}-2\sum_{i=1}^{l}\sum_{j=1}^{l }a_{i}\mathcal{GGInv}(\xi;\xi^{i})\mathcal{GGInv}(\xi;\xi^{j})\biggr{\}}d\xi.\]  
The separation between the various goals considered in this study is wide, so the multiplication weight between different targets is too small to be ignored, and many scholars have also adopted this idea [13; 36]. Starting from this premise, (14) can be approximated as follows:  
\[\int\biggl{\{}(\sum_{i=1}^{l}a_{i}\mathcal{GGInv}(\xi;\xi^{i}))^{ 2}+(\sum_{j=1}^{l}\mathcal{GGInv}(\xi;\xi^{j}))^{2}-2\sum_{i=1}^{l}\sum_{j=1}^{ l}a_{i}\mathcal{GGInv}(\xi;\xi^{i})\mathcal{GGInv}(\xi;\xi^{j})\biggr{\}}d\xi\] \[\approx \int\biggl{\{}\sum_{i=1}^{l}a_{i}^{2}\mathcal{GGInv}(\xi;\xi^{i})^ {2}+(\sum_{j=1}^{l}\mathcal{GGInv}(\xi;\xi^{j}))^{2}-2\sum_{i=1}^{l}\sum_{j=1}^ {l}a_{i}\mathcal{GGInv}(\xi;\xi^{i})\mathcal{GGInv}(\xi;\xi^{j})\biggr{\}}d\xi. \tag{15}\]  
Since \(\sum_{j=1}^{l}\mathcal{GGInv}(\xi;\xi^{j})\) does not contain an optimization variable, it can be omitted. The final optimization objective function after omission becomes  
\[\int\Biggl{\{}\sum_{i=1}^{l}a_{i}^{2}\mathcal{GGInv}(\xi;\xi^{i})^{2}-2\sum_{ i=1}^{l}\sum_{j=1}^{l}a_{i}\mathcal{GGInv}(\xi;\xi^{i})\mathcal{GGInv}(\xi;\xi^{j}) \Biggr{\}}d\xi. \tag{16}\]