# SMC-CPHD Filter with Adaptive Survival Probability for Multiple Frequency Tracking
## 2 Processing Steps of the SMC-CPHD Filter
Therefore, we have proposed the adaptive survival probability as earlier described, and the results are shown in Figure 2:1

The results in Figure 7 show that the estimated results of both frequency and cardinality represent close to the true value. The cardinality value differs from the true value when the time index is from 101 to 109, as seen in Figure 7b, because the distance between the two frequencies at that time is too close, meaning that the estimate accuracy is reduced. To evaluate the tracking performance, an optimal sub-pattern assignment (OSPA) [42], which is a general performance index used in the multiple target tracking field, was used as a performance index. Table 1 shows the results from Figures 4-7 by the OSPA index, and the proposed method with adaptive survival probability (A_CPHD) has a small OSPA index compared to the existing methods. This means that the estimate performance of frequency and cardinality was improved. The improvement of the computational efficiency was also found through a smaller calculation time than the CC_CPHD without adaptive survival probability. These results can be considered as the effect of adaptive gating due to applying the probability by the conditions. the number of targets (frequencies) to estimate increased, and the number of candidates for iterative clustering consequently increased, which results from increasing the calculation time. From the simulation results for both cases, the combination of FCM and cardinality compensation methods (CC_CPHD) shows a significant improvement in performance over existing methods. However, depending on the scenarios and the degree of the clutter, the estimated cardinality may be more than the actual cardinality, as in Figures 6b and 10b. From the perspective of ultimately eliminating frequencies, as mentioned briefly previously, the mitigation performance can be degraded because the number of frequencies to be removed is increased; thus it is hard to respond to this situation. However, the addition of the proposed adaptive survival probability shows more robust performance in the clutter or scenarios. Consequently, through the above simulation results, we confirmed that the proposed adaptive survival probability is effective in improving performance compared to constant survival probability under any clutter conditions. This was because survival probability affected the weight of the particles, resulting in an adaptive gating effect. However, a review of the resampling methods may be necessary because sample impoverishment may occur if the adaptive boundary is incorrectly set. ## 6 Conclusions

We proposed an SMC-CPHD filter with adaptive survival probability for multiple frequency tracking to enhance the tracking performance in the conventional SMC-CPHD filter. The survival probability of the particles in the filter was adjusted using the pre-designed exponential function. In order to confirm whether the proposed survival probability affects the stability of the filter, the error bounds in the prediction process were analyzed. Moreover, the ICI based compensation technique was added to improve cardinality tracking performance. To evaluate the proposed method's performance, MATLAB-based simulations were performed. As a result, we confirmed that the tracking performance of the multiple frequencies and the accuracy of cardinality estimates were improved compared to the existing filters. Conceptualization, S.Y.K. ; methodology, S.Y.K. ; validation, S.Y.K. and C.H.K. ; formal analysis, S.Y.K. and C.H.K. ; investigation, S.Y.K. ; writing--original draft preparation, S.Y.K. ; writing--review and editing, S.Y.K. and C.H.K. ; visualization, S.Y.K. ; supervision, C.H.K. and C.G.P. ; funding acquisition, C.G.P. All authors have read and agreed to the published version of the manuscript. This work was supported by AI-based Flight Control Research Laboratory funded by the Defense Acquisition Program Administration under Grant UD200045 CD. Not applicable. The authors declare no conflict of interest.