*4.1. Simulation Scenery*

In this section, we use computer simulations to demonstrate the effectiveness and performance of the proposed method. Suppose FoV is a two-dimensional region [−50, 50] × [0, 100] in which multiple targets appear or disappear at any time. The state equation and the measurement equation of single target can be represented as follows:

$$\mathbf{x}\_{k} = \begin{bmatrix} 1 & T & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & T \\ 0 & 0 & 0 & 1 \end{bmatrix} \mathbf{x}\_{k-1} + \begin{bmatrix} T^{2}/2 & 0 \\ T & 0 \\ 0 & T^{2}/2 \\ 0 & T \end{bmatrix} \begin{bmatrix} n\_{1} \\ n\_{2} \end{bmatrix} \tag{24}$$

$$z\_k = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \mathbf{x}\_k + \begin{bmatrix} w\_1 \\ w\_2 \end{bmatrix} \tag{25}$$

where target state *xk* <sup>=</sup> *pxk*, *vxk*, *pyk*, *vyk<sup>T</sup>* consists of the target position and velocity along the x-axis and y-axis, only target position is measured represented as *zk*, sampling period *T* = 1, and the process noise and the measurement noise are both zero mean Gaussian noises: [*n*1, *n*2] *<sup>T</sup>* <sup>∼</sup> *<sup>N</sup>* , [0, 0] *<sup>T</sup>*, *diag*[0.01, 0.01] - , [*w*1, *w*2] *<sup>T</sup>* <sup>∼</sup> *<sup>N</sup>* , [0, 0] *<sup>T</sup>*, *diag*[0.09, 0.09] - . This paper considers five targets with motion parameters showed in Table 1, and the total time of simulation is *Ttotal* = 100. Figure 2 depicts the simulation scenery in x-y coordinate system.


**Table 1.** Motion parameters of targets

**Figure 2.** Simulation scenery in x-y coordinate system.

Cardinality and Optimal Sub-Pattern Assignment (OSPA) distance [43] between real set of target states and estimated set of target states are employed as performance evaluation criterions, and the cut-off factor and the order used in OSPA are *c* = 10, *p* = 2, respectively. The performance of the proposed Refined PHD (R-PHD) filter is evaluated in comparison with the standard PHD filter, CPHD filter, and CBMeMBer filter, and the filters here are all implemented with SMC implementations. Survival probability is set as 0.99 in PHD, CPHD and CBMeMBer. In R-PHD, the threshold *Lth* and *pth S* are set as 0.1 and 0.5 respectively, and Type I and II error rates are set as α = 0.1 and β = 0.1, respectively. In all four filters, 1000 particles are used for per target, and the probability density of newborn targets is modeled as Gaussian mixture of target initial states with the covariance of *diag*[1, 0.1, 1, 0.1].
