## 4 Simulation and Analysis
### Simulation and Analysis of Different Three Algorithm  
In this part, we compare the performance of Pd-GM-PHD, Pd-GM-CPHD and Beta-GM-CPHD in different clutter environments. Simulation results are shown in Figures 12-14, which show the estimation of target number. Also, the average time OSPA distance is used to evaluate the performance of the algorithm, which is shown in Table 4. At the same time, statistical results are given in Table 5, in which the  
From Figures 12-14, we can see that the three algorithms can get a good performance in estimating the target number in different clutter environments. This is due to fact the CPHD algorithm jointly propagates the intensity function and the cardinality distribution while PHD algorithm just propagates the intensity function. Hence, the Pd-GM-PHD algorithm has a bigger fluctuation than Pd-GM-CPHD and Beta-GM-CPHD in the estimation of the target number. As the detection probability decreases with distance, after 180 s, the detection probability affects the tracking performance even more; after 250 s, the detection probability is near 0.2, which causes a more unreliable measurement to be used to update the process in Pd-GM-CPHD algorithm, and also the Beta-GM-CPHD performs not as well.  
Table 4 shows the average OSPA distance with three algorithms in different clutter environments. The smaller time average OSPA-distance is shown in the Pd-GM-CPHD algorithm in different clutter environments, which we can see in Table 4. Pd-GM-PHD is worse than Beta-GM-CPHD algorithm no matter the clutter intensity.  
At the same time, the running time of three algorithms in different scenario is analysis and compared, statistical results are shown in Table 5. The PC platform is Intel (R) Core (TM) i5-4460, CPU @ 3.20 GHz, RAM 8.0 G, MATLAB (R2014b, The MathWorks, Inc., Natick, MA, USA, 2014)).  
Table 5 shows that with the increase of the clutter intensity, the average running time of these algorithms will increase. Compared with Beta-GM-CPHD, the computational load of Pd-GM-PHD and Pd-GM-CPHD is very small, which makes sure it can be used in practice. Above all, the noveldetection probability proposed in this paper can get good performance in the GM-PHD and GM-CPHD algorithms with applications in underwater MTT systems.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time Average OSPA-Distance (m)** & **Pd-GM-PHD** & **Pd-GM-CPHD** & **Beta-GM-CPHD** \\ \hline \(\kappa_{k}=5\) & 35.26 & 25.22 & 30.94 \\ \(\kappa_{k}=10\) & 37.34 & 26.54 & 34.7 \\ \(\kappa_{k}=20\) & 41.51 & 30.05 & 35.18 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of time average OSPA-distance (m) in different clutter environments.  
Figure 14: Comparison of target number estimation in clutter intensity \(\kappa_{k}=20\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Clutter Intensity** & **Pd-GM-PHD** & **Pd-GM-CPHD** & **Beta-GM-CPHD** \\ \hline \(\kappa_{k}=5\) & 2.86 & 5.76 & 44.32 \\ \(\kappa_{k}=10\) & 3.17 & 6.57 & 51.15 \\ \(\kappa_{k}=20\) & 4.48 & 10.55 & 69.35 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The average running time when tracking four targets (s).