# SMC-CPHD Filter with Adaptive Survival Probability for Multiple Frequency Tracking
## 2 Processing Steps of the SMC-CPHD Filter
The intermediate frequency was 9.548 MHz, and the sampling frequency was 38.192 MHz. Figure 3: True trajectory (case 2): (**a**) Measurement and clutter; (**b**) Cardinality. Figure 2: True trajectory (case 1): (**a**) Measurement and clutter; (**b**) Cardinality; (**c**) The Poisson average rate of clutter according to time index. The A_CPHD was compared with the following methods: The first method is \"C_CPHD\", which is a conventional CPHD filter with k-means clustering. The second method is \"FCM_CPHD\", which is a conventional CPHD filter applying FCM clustering so that it is robust in the presence of heavy noise and clutter. The last method is \"CC_CPHD\", which is the FCM_CPHD applying cardinality compensation [22] with the ICI method and iterative clustering, which was recently proposed. In the first and second cases, the tracking and cardinality estimate results from each method are presented as shown in Figures 4-11. The top panel of each figure indicates the frequency tracking result, and the bottom panel of each figure shows the cardinality estimate result. In each top graph, the true trajectory is indicated by the solid red line, the measurements with the clutter are shown by the gray crosses, and the black dots present the estimation results. In each bottom graph, the estimation result of cardinality is shown in the solid black line, and the true value of cardinality is presented by the solid black line. As shown in Figure 2c, the distribution of clutter varies with time. The clutter had the Poisson distribution property. Here, the Poisson average rate value (\(\lambda\)) in the frequency measurement was changed over a total of 300 simulation runs. Figure 4: The result of the C_CPHD (case 1): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 5: The result of the FCM_CPHD (case 1): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 8: The result of the C_CPHD (case 2): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 6: The result of the CC_CPHD (case 1): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 7: The result of the A_CPHD (case 1): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 11: The result of the A_CPHD (case 2): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 10: The result of the CC_CPHD (case 2): (**a**) Frequency tracking; (**b**) Cardinality estimate. Figure 9: The result of the FCM_CPHD (case 2): (**a**) Frequency tracking; (**b**) Cardinality estimate. In Figure 4, the C_CPHD was used. As shown in this figure, tracking loss partially occurs, and the cardinality error was also severe. The results of FCM_CPHD are shown in Figure 2:0 Through these results, we confirmed that the tracking performance of the FCM_CPHD was a little better than that of the C_CPHD due to the robustness of the clustering method when there is a lot of noise in the measurement. However, there was still tracking loss, and estimated errors of cardinality still remained even though FCM clustering was used. Therefore, we proposed the cardinality compensation method to improve the tracking performance. According to Figure 6, the performance of the frequency tracking and the cardinality estimate were ameliorated when the CC_CPHD was used. However, as shown in Figure 6b, the true value of cardinality is 2 when the time index is 165, but the estimated value is 3. We eventually aim to eliminate the frequency of the interference signal by using the estimation result as the notch frequency. Therefore, the problem arises of increasing the dimension of the notch filter if the number of the frequency to be removed is estimated to be more than the true number. In addition, as shown in Figure 6a, a performance improvement of the algorithm is needed to prevent this situation because this is a result of estimating the wrong frequencies, resulting in the elimination of frequency components that should not be removed.