*5.2. SCM-JTC-CBMeMBer Filter*

In this simulation, all three classes of ship targets will appear in the surveillance area. Target A appears at time *k* = 5 and disappears at time *k* = 55 with initial state *x* (1) <sup>0</sup> = [1000m 1000m − 9.82m/s − 9.82m/s] T. Target B appears at time *k* = 15 and disappears at time *k* = 65 with initial state *x* (2) <sup>0</sup> = [1000m − 1000m − 9.82m/s 9.82m/s] T. Target C appears at time *k* = 25 and disappears at time *k* = 75 with initial state *x* (3) <sup>0</sup> = [−1000m − 1000m 9.82m/s 9.82m/s] T. The Poisson average clutter rate is λ*<sup>c</sup>* = 3. The surveillance area is [−2000m, 2000m] × [−2000m, 2000m]. Target surviving probability and detection probability are *pS*,*<sup>k</sup>* = *pD*,*<sup>k</sup>* = 0.99. The sampling interval *t* is 1 s and the total simulation time is 100 s. The target births are modeled as multi-Bernoulli RFS with π*<sup>B</sup>* = %*r* (*i*) *<sup>B</sup>* , *p* (*i*) *<sup>B</sup>* (*x*|Z) & <sup>4</sup> , where

*i*=1 *r* (1) *<sup>B</sup>* = *r* (2) *<sup>B</sup>* = *r* (3) *<sup>B</sup>* = *r* (4) *<sup>B</sup>* = 0.02 *p* (*i*) *<sup>B</sup>* (*c*1|Z) = *<sup>p</sup>* (*i*) *<sup>B</sup>* (*c*2|Z) = *<sup>p</sup>* (*i*) *<sup>B</sup>* (*c*3|Z) = 1/3 *p* (*i*) *<sup>B</sup>* (*x*|Z) = <sup>N</sup>(*x*; *<sup>m</sup>*(*i*), *<sup>P</sup>*(*i*)) *P*(1) = *P*(2) = *P*(3) = *P*(4) = *diag*([100 m<sup>2</sup> 100 m<sup>2</sup> 10 m2/s2 10 m2/s2]) *<sup>m</sup>*(1) = [1000 m 1000 m <sup>−</sup> 10 m/s <sup>−</sup> 10 m/s] T *<sup>m</sup>*(2) = [1000 m <sup>−</sup> 1000 m <sup>−</sup> 10 m/s 10 m/s] T *<sup>m</sup>*(3) = [−1000 m <sup>−</sup> 1000 m 10 m/s 10 m/s] T *<sup>m</sup>*(4) = [−1000 m 1000 m 10 m/s <sup>−</sup> 10 m/s] T (95)

The trajectory tracking results for a single run are shown in Figure 6. As can be clearly seen from Figure 6, under the clutter environments, the proposed SCM-JTC-CBMeMBer filter can estimate target number and state correctly, and it can also obtain correct target classification, which will be further validated by the repeated Monte Carlo trials.

**Figure 6.** Multi-target tracking results for a single run: (**a**) the true target trajectories and received measurements; (**b**) estimated target trajectories.

To further test the performance of the proposed SCM-JTC-CBMeBer filter, 50 Monte Carlo runs are carried out under the same scenario as above. Specifically, the metric of Optimal Subpattern Assignment (OSPA) distance [34] is used to evaluate the multi-target tracking results, and the CBMeMBer filter is also considered as a comparison.

The OSPA distance and cardinality estimation are shown in Figure 7, and the target classification results are plotted in Figure 8.

From Figure 7, we can see that the SCM-JTC-CBMeMBer filter can effectively estimate the target state and target number. At the instant when the target appears and disappears, a slight degradation in estimation performance is observed, which is the normal phenomenon confronted in multi-target tracking. Compared with the conventional CBMeMBer filter (which can only be used for multi-target tracking purposes rather than targets classification), the SCM-JTC-CBMeMBer filter has almost the same performance in target tracking.

As can be seen from Figure 8, the SCM-JTC-CBMeMBer filter can also correctly classify multiple targets, and the classification probability of each target is very high (almost reaches one).

**Figure 7.** Estimated target state: (**a**) Optimal Subpattern Assignment (OSPA) distance; (**b**) the estimated cardinality.

**Figure 8.** Results of targets classification: (**a**) Ship Target A; (**b**) Ship Target B; (**c**) Ship Target C.
