*4.4. Evaluation of Di*ff*erent Continuous Miss detection Durations*

Next, we consider the scenario that targets are undetected for continuous steps. Figure 7 shows the multi-target tracking results of different methods under continuous miss detection during 45 ≤ *k* ≤ 51, detection probability in other steps is set as *pD* = 0.9 and average number of false alarms is set as λ = 10 in simulations. Mean OSPA in Figure 7a is obtained by averaging 200 trials of Monte-Carlo simulation using Equation (26), and mean cardinality in Figure 7b is obtained using Equation (27). Figure 7 demonstrates that the PHD filter and CBMeMBer filter lose all targets when continuous miss detection during 45 ≤ *k* ≤ 51 occurs, which results that mean OSPA is up to the cut-off factor and mean cardinality is close to 0 from *k* = 45 to *k* = 100. The CPHD filter loses four targets when continuous miss detection occurs, while it can maintain one target after *k* = 51. Evidently, the proposed R-PHD filter can maintain all targets and its performance is almost immune to continuous miss detection.

**Figure 7.** OSPA and cardinality performances of different methods versus time under continuous miss detection during 45 ≤ *k* ≤ 51 (*pD* = 0.9, λ = 10): (**a**) mean OSPA; (**b**) mean cardinality.

Figure 8 illustrates multi-target tracking performances of different methods with respect to different continuous miss detection durations from *s* = 3 to *s* = 11, where the detection probability is set as *pD* = 0.9, average number of false alarms is set as λ = 10. Continuous miss detection duration is represented as *s*, and it always begins at time *k* = 45. That is to say, *s* = 3 indicates that targets are missed during 45 ≤ *k* ≤ 47. The mean OSPA with respect to different continuous miss detection durations is depicted in Figure 8a, and each data point is calculated using Equation (28). Mean RMSE of cardinality with respect to different continuous miss detection durations is depicted in Figure 8b, and each data point is calculated using Equation (29). The performances of the PHD filter, CPHD filter and CBMeMBer filter deteriorate as continuous miss detection duration increases, while that

of the proposed R-PHD filter is relatively stable and always superior than the other three methods. In conclusion, the proposed R-PHD filter can effectively track multiple targets when continuous miss detection occurs.

**Figure 8.** OSPA and cardinality performances of different methods with respect to different continuous miss detection durations from *s* = 3 to *s* = 11 (*pD* = 0.9, λ = 10): (**a**) mean OSPA; (**b**) mean RMSE of cardinality.
