*2.1. Target Dynamic Model*

Suppose there are *Q* scattered targets in a two dimensional space. The *q*th(*q* = 1, 2, ... , *Q*) target is initially located at , *x q* <sup>0</sup>, *y q* 0 - , with initial velocity ,. *x q* 0, . *y q* 0 - . Assuming that all of the targets move in a uniform linear line, the dynamic model of the target can be described as:

$$\mathbf{X}\_k^q = \mathbf{F} \mathbf{X}\_{k-1}^q + \mathbf{W}^q \tag{1}$$

in (1), **X***<sup>q</sup> <sup>k</sup>* <sup>=</sup> *x q k* , *y q k* , . *x q k* , . *y q k* <sup>T</sup> is the state vector of target *<sup>q</sup>* at time index *<sup>k</sup>*, where , *x q k* , *y q k* and ,. *x q k* , . *y q k* are the position and velocity of target *q* at time index *k*, respectively. **F** is the target state transition matrix, which can be expressed as:

$$\mathbf{F} = \begin{bmatrix} 1 & 0 & T & 0 \\ 0 & 1 & 0 & T \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \tag{2}$$

where *T* denotes the revisit time. The term **W***<sup>q</sup>* is the process noise of target *q*, which can be assumed as zero-mean Gaussian noise with a known covariance **Q***<sup>q</sup>* ,

$$\mathbf{Q}^q = \sigma\_{q,w}^2 \begin{bmatrix} \frac{T^3}{3} & 0 & \frac{T^2}{2} & 0\\ 0 & \frac{T^3}{3} & 0 & \frac{T^2}{2} \\ \frac{T^2}{2} & 0 & T & 0 \\ 0 & \frac{T^2}{2} & 0 & T \end{bmatrix} \tag{3}$$

where σ<sup>2</sup> *<sup>q</sup>*,*<sup>w</sup>* denotes the process noise intensity of target *q*.
