*6.3. Scenario 3: The Number of Targets Is Time-Varying and Maneuvering*

Consider a nonlinear multi-source scenario with three sources. The number of sources is time-varying due to births and deaths, and the survival time of the three sources is 1–50 s, 10–50 s, 20–45 s, and the initial source state are *<sup>x</sup>*<sup>1</sup> <sup>=</sup> [−30;−0.5], *<sup>x</sup>*<sup>2</sup> <sup>=</sup> [5; 1.8], and *<sup>x</sup>*<sup>3</sup> <sup>=</sup> [60;−2.0]. The state transition matrix of the collaborative turning (CT) model is

$$F\_k = \begin{bmatrix} 1 & \sin(T\omega)/\omega \\ 0 & \cos(T\omega) \end{bmatrix} \tag{33}$$

where ω = 0.25 *rad* and other experimental conditions are the same as scenario 1.

Figure 8 shows the maneuvering target trajectory of three algorithms running one MC when α = 1.3, *L* = 100, and GSNR = 10 dB. It can be clearly seen from Figure 8 that the three methods lose the target when the target crosses at time 33, but after time 36, the MB-FLOM-MUSIC algorithm and the UT-MB-FLOM-MUSIC algorithm can still capture the target state. Compared with the MB-FLOM-MUSIC algorithm, the target state estimation value of the UT-MB-FLOM-MUSIC algorithm is closer to the true value.

**Figure 8.** Target trajectory, α = 1.3, L = 100, and GSNR = 10 dB.

In Figure 9, 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 9a that the RMSE of the UT-MB-FLOM-MUSIC algorithm is smaller than that of the other two algorithms. As can be seen from Figure 9b, when the target is maneuvering, the target is not captured by the three algorithms from time 33, but after time 36, the MB-FLOM-MUSIC algorithm and UT-MB-FLOM-MUSIC algorithm can still estimate the number of targets in time. Compared with the result of Figure 5b, the performance to capture targets of the UT-MB-FLOM-MUSIC algorithm is significantly weakened.

**Figure 9.** 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 2 shows the RMSE and computing performance of the MB-MUSIC algorithm, MB-FLOM-MUSIC algorithm and the UT-MB-FLOM-MUSIC algorithm. Compared with the results in Table 1, the RMSE and running time of the three algorithms are increased when the target is maneuvered. The RMSE of UT-MB-FLOM-MUSIC algorithm is smaller than other two algorithms when the running time is long.


