## 4 Simulation Results
The modified distance \(d_{\text{md}}(\xi^{i},\xi^{j})\) between \(\xi^{i}\) and \(\xi^{j}\) can be decomposed as follows [41]:  
\[d_{\text{md}}\Big{(}\xi^{i},\xi^{j}\Big{)}=\frac{w_{\gamma}}{c_{ \gamma}}d_{j,i}^{(c_{\gamma})}+\frac{w_{\mathbf{x}}}{c_{\mathbf{x}}}d_{j,i}^{ (c_{\gamma})}+\frac{w_{\Sigma}}{c_{\Sigma}}d_{j,i}^{(c_{\Sigma})}, \tag{56}\]  
where \(w_{\gamma}>0\), \(w_{\mathbf{x}}>0\), \(w_{\Sigma}>0\), \(w_{\gamma}+w_{\mathbf{x}}+w_{\Sigma}=1\), and  
\[d_{j,i}^{(c_{\gamma})} =\min\Big{(}c_{\gamma\gamma}\left|\gamma^{j}-\hat{\gamma}^{i} \right|\Big{)}, \tag{57}\] \[d_{j,i}^{(c_{\gamma})} =\min\Big{(}c_{\kappa}\left\|\mathbf{x}^{i}-\mathbf{\hat{x}}^{i} \right\|_{2}\Big{)},\] (58) \[d_{j,i}^{(c_{\Sigma})} =\min\Big{(}c_{\Sigma}\left\|\mathbf{\Sigma}^{j}-\mathbf{\hat{x }}^{i}\right\|_{F}\Big{)}, \tag{59}\]  
where \(|\cdot|\), \(||\cdot||_{2}\), and \(||\cdot||_{F}\) denote the absolute value, Euclidean norm, and Frobenius norm, respectively. \(c_{\gamma},c_{\kappa}\), and \(c_{\Sigma}\) are constants that correspond to the maximum expected  
Figure 3: Schematic diagram of the tracking scenario. (Black \(\bigcirc\) and \(\triangle\) symbols indicate each trajectory’s start and end, respectively; \(\square\) shows the target’s position at each moment, and a red ellipse characterizes the displayed extended shape of the target every five moments). error for the measurement rate, kinematic state, and extension. Here, we set \(w_{\gamma}=0.1\), \(w_{\mathbf{x}}=0.8\), \(w_{\mathbf{z}}=0.1\), \(c_{\gamma}=10\), \(c_{\mathbf{x}}=50\), \(c_{\mathbf{z}}=50\). We verified the performance of the proposed fusion algorithm in simulation experiments with different clutter rates \(\lambda_{c}\), different noise intensities \(\sigma_{v}\), and various single detection probabilities \(P_{d}\). We performed one hundred Monte Carlo simulations for each set of simulation parameters and obtained the time average and Monte Carlo average to obtain the final performance metrics: MGOSPA, location error (LE), missed error (ME), and false error (FE). To present the results, we combined the MGOSPA metric to highlight two key aspects, the MGOSPA error and cardinality error (CE), where the CE equals the sum of the ME and TE in the MGOSPA calculations. We take the time-averaged MGOSPA metric as an example, and it can be defined as follows:  
\[\frac{\sum_{t_{k}=1}^{T_{k}}\sum_{m_{c}=1}^{N_{m}}\text{MGOSPA}_{t_{k},m_{c}}} {T_{k}\cdot N_{m}}, \tag{60}\]  
where \(T_{k}\) and \(N_{m}\) are the total number of frames in a single Monte Carlo simulation and the number of Monte Carlo simulations, respectively. MGOSPA\({}_{t_{k},m_{c}}\) denotes the MGOSPA error at the \(t_{k}\)-th timestep of the \(m_{c}\)-th Monte Carlo simulation. The other error indicators are similarly defined. For further illustration, the traditional WGA/WAA approach adopts the idea of assignment fusion when performing MB fusion, i.e., it first uses an assignment algorithm to complete the assignment process for optimal fusion between different Bernoulli terms and then subsequently achieves the fusion of the two incoming Bernoulli terms according to the assignment result. The assignment process has requirements for the assignment threshold. It considers that the two Bernoulli terms that are larger than the assignment threshold will not be assigned, and on the contrary, they can participate in the assignment process. For the two GGIWs, the KLD was chosen to be their assignment distance, and the calculation of the KLD can be found in the supplementary materials of [42]. For a comprehensive comparison, we selected different assignment thresholds \(T_{h}\) in WGA and WAA; the thresholds chosen were 10, 50, 100, 200, and inf, where inf means that any two Bernoulli terms can be merged. The Hungarian algorithm [43] was chosen for WGA and WAA to complete the mapping during the assignment process. Simulation 1 was used to verify the tracking performance of different fusion approaches with varying clutter numbers.