*6.1. Simulation Experiments*

The performance test was done to compare the results with respect to FTD performance and the accuracy of estimated clutter measurement density for the cases, which utilized:


The sets of simulation experiments are presented for multi-target tracking in a heterogeneous environment with varying the number of targets.

The sampling time of sensor *T* was 1 s, and the measurement noise covariance was **R***<sup>k</sup>* = 25**I**2*m*2. The target detection probability *PD* and the gate probability *PG* were 0.8 and 0.99, respectively. One simulation run consisted of 50 scans, and the total number of Monte Carlo simulation runs was 500. To initialize the track, the two point differencing method [14] was employed if the calculated velocity obtained from two consecutive scans was smaller than the predetermined maximum velocity constraint *Vmax* = 25 m/s.

In these simulations, the following four evaluation indices were calculated:


The confirmed track was defined as one whose posterior target existence probability calculated by (29) was bigger than a predetermined confirmed threshold. Among confirmed tracks, the tracks satisfying the following equation were classified as the confirmed true tracks for tracking performance evaluation purposes:

$$(\mathbf{x}\_k - \hat{\mathbf{x}}\_{k|k}^\tau)^\top (\mathbf{P}\_{0|0}^\tau)^{-1} (\mathbf{x}\_k - \hat{\mathbf{x}}\_{k|k}^\tau) \precsim \gamma\_{true} \tag{46}$$

where **x***<sup>k</sup>* and **P***<sup>τ</sup>* <sup>0</sup>|<sup>0</sup> are the state vector of the true target and the initial error covariance matrix of the confirmed track *τ*, respectively. Conversely, each confirmed track met the following test, and it became a confirmed false track.

$$(\mathbf{x}\_k - \hat{\mathbf{x}}\_{k|k}^\tau)^\top (\mathbf{P}\_{0|0}^\tau)^{-1} (\mathbf{x}\_k - \hat{\mathbf{x}}\_{k|k}^\tau) \gg \gamma\_{false\prime} \tag{47}$$

The confirmed true track rate (CTTR) is an evaluation index showing the statistical ratio of confirmed true tracks over time. The position root mean squared error is the distance error between the confirmed true track and the true target, and it was obtained only for the confirmed true tracks over time. The track retention test statistic is an evaluation index of the multi-target tracking algorithms and accumulates statistics on how much the confirmed true tracks are retained or lost between retention test start time (RST) and retention test end time (RET). In these simulations, RST and RET were designated to be 15 and 35, respectively. The retention test was to check the following items, and they were used to indicate the statistical ratio representing the robustness of each algorithm for the period in which the targets were located in the immediate vicinity:


The clutter measurement density estimation performance is an evaluation index of how closely the estimated clutter measurement density follows the true clutter measurement density using the clutter measurement density estimation method. The performance of the proposed algorithm was tested in comparison with the existing SCMDE algorithm for multi-target tracking by varying the number of targets in a heterogeneous clutter environment. Simulations were performed for 3, 5, and 7 targets in three scenarios, and the performance of clutter measurement density estimation was analyzed as the number of targets increased. In addition, the effectiveness and the robustness of the tracking performance were verified through a test with real radar data.
