*4.2. Evaluation of Di*ff*erent Detection Probabilities*

Figure 3 depicts the mean OSPA and cardinality versus time over *P* = 200 Monte-Carlo runs, where the detection probability is set as *pD* = 0.85, independent of target state, and the average number of Poisson-distributed false alarms is set as λ = 10. Mean OSPA is depicted in Figure 3a, and each data point is calculated as

$$\frac{1}{P} \sum\_{p=1}^{P} OSPA\_{p,k\prime} \tag{26}$$

where *OSPAp*,*<sup>k</sup>* is OSPA distance at time *k* in *p*th Monte-Carlo trial. Mean cardinality is depicted in Figure 3b, and each data point is calculated as

$$\frac{1}{P} \sum\_{p=1}^{P} \hat{N}\_{p,k|k\prime} \tag{27}$$

where *<sup>N</sup>*<sup>ˆ</sup> *<sup>p</sup>*,*k*|*<sup>k</sup>* is the estimated number of targets at time *<sup>k</sup>* in *<sup>p</sup>*th Monte-Carlo trial. Due to low detection probability, the measurements from targets are intermittent, and the PHD filter, CPHD filter and CBMeMBer filter can't obtain excellent results. The mean OSPA of the R-PHD filter is usually smaller than that of the competing methods, and the mean cardinality of the R-PHD filter is closer to the ground truth. It is worth noting that OSPA distances at time 11 and 91 are apparently large in all filters, due to simultaneous birth or death of two targets. Figure 3 illustrates that the proposed method can effectively track multiple targets under low detection probability.

**Figure 3.** OSPA and cardinality performances of different methods versus time (*pD* = 0.85, λ = 10): (**a**) mean OSPA; (**b**) mean cardinality.

Then, we compare multi-target tracking performances of different methods with respect to different detection probabilities from *pD* = 0.7 to *pD* = 1. Figure 4 illustrates the multi-target tracking results, where the average number of false alarms is set as λ = 10 for all simulations. Mean OSPA with respect to different detection probabilities is depicted in Figure 4a, and each data point is calculated as

$$\frac{1}{PT\_{\text{total}}} \sum\_{p=1}^{P} \sum\_{k=1}^{T\_{\text{total}}} OSPA\_{p,k\prime} \tag{28}$$

where *OSPAp*,*<sup>k</sup>* is OSPA distance at time *k* in *p*th Monte-Carlo trial. Mean Root Mean Square Error (RMSE) of cardinality with respect to different detection probabilities is depicted in Figure 4b, and each data point is calculated as

$$\frac{1}{T\_{\text{total}}} \sum\_{k=1}^{T\_{\text{total}}} \sqrt{\frac{1}{P} \sum\_{p=1}^{P} \left(N\_k - \hat{N}\_{p, \text{k}\vert k}\right)^2} \tag{29}$$

where *<sup>N</sup>*<sup>ˆ</sup> *<sup>p</sup>*,*k*|*<sup>k</sup>* is the estimated number of targets at time *<sup>k</sup>* in *<sup>p</sup>*th Monte-Carlo trial, and *Nk* is real number of targets at time *k*. Figure 4 shows that mean OSPA and mean RMSE of cardinality both decrease monotonically as detection probability increases in the PHD filter, CPHD filter and CBMeMBer filter. In addition, the performance of the R-PHD filter is relatively stable, and the proposed method presents better performance than baselines when detection probability is no more than 0.95. It should be mentioned that when detection probability is 1, that is to say, there is no miss detection, the R-PHD filter has inferior performance than the other three methods, which can be explained by the Type I error rate in SPRT.

**Figure 4.** OSPA and cardinality performances of different methods with respect to different detection probabilities from *pD* = 0.7 to *pD* = 1 (λ = 10): (**a**) mean OSPA; (**b**) mean RMSE of cardinality.
