*6.2. Scenario 2: The Number of Targets Is Time-Varying*

Consider a linear multi-source scenario with three sources. The number of sources is time-varying due to births and deaths, the survival time of the four sources is 1–50 s, 10–50 s, 20–45 s, and the initial source states are *<sup>x</sup>*<sup>1</sup> <sup>=</sup> [−30;−0.5], *<sup>x</sup>*<sup>2</sup> <sup>=</sup> [5; 1.0], and *<sup>x</sup>*<sup>3</sup> <sup>=</sup> [60;−2.0].

Figure 3a shows the RMSE of angles for three algorithms for running 100 MC at α = 2, *L* = 100 and GSNR = 10 dB, and Figure 3b shows three sources trajectory for a single MC. It can be seen from Figure 3 that the likelihood function of the MUSIC spatial spectrum instead of the Multi-Bernoulli particle filter update stage can effectively estimate the target number and motion state, and also verify the feasibility of the literature [14] in the Gaussian noise environment. Although the error is large at time 35, the overall error is below 2 degrees. It can also be seen from Figure 3a that the RMSE of the UT-MB-FLOM-MUSIC algorithm is also smaller than other algorithms even in the Gaussian noise environment.

**Figure 2.** RMSE of angle under α = 1.3, *L* = 100 and GSNR = 10 dB: (**a**) The RMSE of 100 MC; (**b**) source trajectory of Single MC.

**Figure 3.** RMSE of angle under α = 2, *L* = 100 and GSNR = 10 dB: (**a**) The RMSE of 100 MC; (**b**) source trajectory of Single MC.

Since Gaussian noise does not reflect true signal interference, the α stable distribution can reflect the impact of impulse noise. Figure 4 shows the RMSE and cardinality estimation error plots for three algorithms running 100 MC when the characteristic index α is different and the GSNR = 10 dB, *L* = 100. It can be seen from Figure 4a that, in α = 1.1 ∼ 1.9, the RMSE error of the three estimation algorithms first decreases, and finally tends to be flat. It also can be seen that the RMSE of the UT-MB-FLOM-MUSIC algorithm is significantly smaller than the MB-FLOM-MUSIC and MB-MUSIC algorithms when α = 1.1 or α = 1.2, so that the UT-MB-FLOM-MUSIC algorithm has a better effect when handling the impulse noise environment. Since the characteristic index is close to 2 when α = 1.8 or α = 1.9, Figure 4b shows that the cardinality estimation error of the three algorithms approaches 0. It also shows that it is feasible to use the MUSIC spatial spectrum as a substitute for the likelihood function when the noise environment is close to Gaussian noise while the MUSIC algorithm cannot effectively estimate the number of targets in an impulse noise environment.

In Figure 5, we show the RMSE and cardinality estimation for tracking the multi-source motion when α = 1.3 and GSNR = 10 dB, MC = 100. It can be seen from Figure 5 that the RMSE of the UT-MB-FLOM-MUSIC algorithm is smaller than that of the other two algorithms. Although the RMSE will increase when the new target appears or disappears, it will decrease rapidly at the next time step. This phenomenon shows that the Multi-Bernoulli filter has a large recognition performance for the target and can quickly track the state of the target. Table 1 shows the RMSE and computing performance of the MB-MUSIC algorithm, MB-FLOM-MUSIC algorithm and the UT-MB-FLOM-MUSIC algorithm at one MC.

**Figure 4.** RMSE and cardinality error of angle under different α, *L* = 100, MC = 100 and GSNR = 10 dB: (**a**) The RMSE under different α; (**b**) cardinality error under different α.

**Figure 5.** RMSE and Cardinality estimation of angle under α = 1.3 and GSNR = 10 dB, MC = 100: (**a**) RMSE of angle; (**b**) Cardinality estimation of angle.


**Table 1.** Running Time (CV model).

The operating environment includes an Intel (R) Core (TM) i5-8500 CPU @ 3.00 GHz processor and a 64-bit operating system MATLAB 2014. It can be seen from Table 1 that the UT-MB-FLOM-MUSIC algorithm RMSE is smaller than other algorithms when the running time is too long.

Figure 6 analyzes the RMSE and probability of convergence (PROC) for three algorithms running 100 MC when α = 1.3 and GSNR = 0–16 dB. where PROC = <sup>1</sup> *K* \$*K i*=1 \$*MC <sup>j</sup>*=<sup>1</sup> 1*ij*/*MC* × 100%, and 1*ij* is defined as 1*ij* = 1, - - *<sup>x</sup>ij* <sup>−</sup> *<sup>x</sup>ij* - - - < ε 0, *otherwise* . let <sup>ε</sup> <sup>=</sup> 1. It can be seen from Figure 6a that the MB-FLOM-MUSIC and UT-MB-FLOM-MUSIC algorithms have higher accuracy than the MB-MUSIC in an impulse noise environment, and the UT-MB-FLOM-MUSIC algorithm has higher accuracy under the high GSNR. It can be seen form Figure 6b that as the SNR increases, the PROC increases. And at the same GSNR, the performance of the MB-FLOM-MUSIC algorithm is more significant.

**Figure 6.** RMSE and probability of convergence (PROC) of the angle under different GSNR, α = 1.3 MC = 100 and *L* = 100: (**a**) RMSE of angle; (**b**) PROC at different GSNR.

Figure 7 shows the RMSE of three algorithms running 100 MC when α = 1.3 and the snapshot number *L* = 50, 100, 150. It can be seen that the UT-MB-FLOM-MUSIC algorithm has the smallest RMSE and it works best when the snapshot number is *L* = 150.

**Figure 7.** RMSE for source tracking under different snapshots, α = 1.3 MC = 100 and GSNR = 10 dB.
