*4.3. Evaluation of Di*ff*erent Average Numbers of False Alarms*

Figure 5 depicts the mean OSPA and cardinality versus time over *P* = 200 Monte-Carlo runs, where the detection probability is set as *pD* = 0.95, independent of target state, and the average number of Poisson-distributed false alarms is set as λ = 20. Mean OSPA is depicted in Figure 5a, and each data point is calculated using Equation (26). Mean cardinality is depicted in Figure 5b, and each data point is calculated using Equation (27). Showed in Figure 5a, the mean OSPA of the R-PHD filter is usually smaller than that of the PHD filter and CBMeMBer filter, while it is bigger than that of the CPHD filter at most steps. Figure 5b illustrates that the number of targets estimation of the CPHD filter always lags behind the ground truth when target birth or target death occurs.

**Figure 5.** OSPA and cardinality performances of different methods versus time (*pD* = 0.95, λ = 20): (**a**) mean OSPA; (**b**) mean cardinality.

Figure 6 illustrates multi-target tracking performances of different methods with respect to different average numbers of false alarms from λ = 10 to λ = 30, where the detection probability is set as *pD* = 0.95. Mean OSPA with respect to different average numbers of false alarms is depicted in Figure 6a, and each data point is calculated using Equation (28). Mean RMSE of cardinality with respect to different average numbers of false alarms is depicted in Figure 6b, and each data point is calculated using Equation (29). Figure 6 shows that multi-target tracking performances of different methods deteriorate slightly as average number of false alarms increases. Furthermore, the R-PHD filter outperforms the other three methods at λ = 10, while it has inferior OSPA performance compared to the PHD filter and CPHD filter and inferior cardinality performance compared to the CPHD filter at <sup>λ</sup> = 30. That is because the hypothesis *pD* >> <sup>1</sup> <sup>−</sup> *<sup>e</sup>*−*p*0<sup>λ</sup> is no longer valid when the number of clutters is considerable. Generally, the proposed method can provide a satisfactory result under high average numbers of false alarms.

**Figure 6.** OSPA and cardinality performances of different methods with respect to different average numbers of false alarms from λ = 10 to λ = 30 (*pD* = 0.95): (**a**) mean OSPA; (**b**) mean RMSE of cardinality.
