# A Sector-Matching Probability Hypothesis Density Filter for Radar Multiple Target Tracking
## 4 Simulations
### Example 1: CV Motion Model
However, for the LGM-PHD filter, as there is an extra step in which the matrix \(U\) is used to determine trajectories, the computation speed of this process depends on the distance between the Gaussian components and the weight of the components. If a large number of measurements are generated in a given scan cycle, this also makes the computation time higher. Therefore, the computation times of the LGM-PHD and the SM-LGM-PHD filters vary randomly. The results show that the real-time performance of the proposed method for both the LGM-PHD filter and the basic GM-PHD filter is similar to that of the basic PHD filter and the LGM-PHD filter, and much better than that of the joint GLMB filter. In addition, extending the accumulation time can significantly reduce the calculation time. Figure 6: The estimations of the multi-target trajectories and the actual measurements in example 1 (CV motion model) for a sample run. (**a**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-GM-PHD filter for \(T_{s}=1\) s (\(T_{i}=2\) ms, \(\lambda=104\), \(p_{D,k}=0.8\)). (**b**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-LGM-PHD filter for \(T_{s}=1\) s, and the different trajectories are denoted by different color dots. (**c**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-GM-PHD filter in x and y coordinates for \(T_{s}=1\) s. (**d**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-LGM-PHD filter in x and y coordinates for \(T_{s}=1\) s.  
Figure 7: The estimations of the multi-target trajectories and the actual measurements in example 1 (CV motion model) for a sample run. (**a**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-GM-PHD filter for \(T_{s}=2\) s (\(T_{i}=4\) ms, \(\lambda=52\), \(p_{D,k}=0.96\)). (**b**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-LGM-PHD filter for \(T_{s}=2\) s, and the different trajectories are denoted by different color dots. (**c**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-GM-PHD filter in x and y coordinates for \(T_{s}=2\) s. (**d**) The actual measurements, actual trajectories and estimated trajectories obtained after filtering by the SM-LGM-PHD filter in x and y coordinates for \(T_{s}=2\) s.  
In Figures 9 and 10, the OSPA distances of the MATLAB simulation for 100 sample runs is given and the average OSPA distances are given in Table 2. Compared with the basic GM-PHD filter, the average tracking performance of the SM-LGM-PHD filter, the LGM-PHD filter, the SM-GM-PHD filter and the joint-GLMB filter in this scenario is improved by 22.66%, 13.47%, 7.78% and 62.29%, respectively, at \(T_{s}=1\) s (\(T_{i}=2\) ms, \(\lambda=104\), \(p_{D,k}=0.8\)), and 41%, 13.47%, 35.39% and 47.46%, respectively, at \(T_{s}=2\) s (\(T_{i}=4\) ms, \(\lambda=52\), \(p_{D,k}=0.96\)). Compared with the \(T_{s}=1\) s scenario, the performance of the SM-LGM-PHD filter and the SM-GM-PHD filter has been significantly improved. The LGM-PHD filter, the basic GM-PHD filter and the joint-GLMB filter are not time-matched, which is why the performance of these three filters is not that significantly improved, and the performance of the joint-GLMB filter even decreases. In addition, it can be seen in Figures 9b and 10b that the values of the OSPA location of the LGM-PHD filter, the basic GM-PHD filter and the joint-GLMB filter all increase with the accumulation of time. After 80 s, with the appearance of two targets, No.11 and No.12, at a higher speed, the targets' position estimation errors of the LGM-PHD filter, the basic GM-PHD filter and the joint-GLMB filter increase at a faster rate, while the SM-LGM-PHD filter and the SM-GM-PHD filter are not significantly affected.