*3.1. Survival Probability Dependent on Target State*

Measurement of a specific target is not collected due to either miss detection or death of the target. Multi-target tracking algorithms should take some compensation measures for the former reason,

while do nothing for the latter. The way to distinguish between the two reasons is to consider the survival probability of the target. If this survival probability is larger than a threshold, algorithms can confirm the target is persisting and compensate miss detection. The earlier versions of the SMC-PHD filter consider the survival probability as a constant which is independent of target state and can't be used to judge whether the target survives. This paper defines a new survival probability dependent on target state, which is used as one of the conditions to revise posterior particle weights.

Intuitively, targets usually enter sensor FoV from the boundary and exit also from the boundary. The survival probability of a specific target can be very high when it is located in the middle of FoV. On the contrary, the survival probability of a specific target drops rapidly when it is located near the boundary of FoV and moves outwards. Without the loss of generality from an algorithmic viewpoint, this paper considers a rectangular FoV which possesses four boundaries, up and down, left and right, and then the survival probability of a target at time *k* is

$$p\_S^k = \min \{ p\_{S, \mu p'}^k p\_{S, \text{down} \prime}^k p\_{S, \text{left} \prime}^k p\_{S, \text{right} \prime}^k \} \tag{8}$$

where *p<sup>k</sup> <sup>S</sup>*,*up*, *pk <sup>S</sup>*,*down*, *pk <sup>S</sup>*,*le f t*, *pk <sup>S</sup>*,*right* are the survival probabilities of the target with respect to the four boundaries, respectively.

Suppose the particles representing the target at time *k* are *xi k*|*k* , *i* = 1, ··· , *vk*|*k*, where each particle is a four-dimensional vector *xi <sup>k</sup>*|*<sup>k</sup>* <sup>=</sup> *pi <sup>x</sup>*, *vi <sup>x</sup>*, *pi <sup>y</sup>*, *vi y T* , representing the target position and velocity along the x-axis and y-axis, respectively, and then the target state and corresponding variance can be estimated as *mean*, *xi k*|*k* and var, *xi k*|*k* - . If the particles follow Gaussian distribution and the four variables in particles are independent of each other, the state of this target follows Gaussian distribution *N* % *px*, *vx*, *py*, *vy T* , *diag* σ2 *px*, σ<sup>2</sup> *vx*, σ<sup>2</sup> *py*, σ<sup>2</sup> *vy*& , where *vx* <sup>=</sup> *mean*, *vi x* - , σ<sup>2</sup> *vx* <sup>=</sup> var, *vi x* and so on. Based on the above discussion, the survival probability of the target with respect to the right boundary is

$$p\_{S, right}^k = \Pr\left(u \le \frac{b\_{right} - p\_{\rm x} - \upsilon\_{\rm x}T}{\sqrt{\sigma\_{px}^2 + \sigma\_{vx}^2 T^2}}\right) \tag{9}$$

where *u* ∼ *N*(0, 1), *bright* is the position of the right boundary, and *T* is the sampling period. Meanwhile, the survival probabilities of the target with respect to the other three boundaries have similar results.

It should be mentioned that a specific target and corresponding particles share the identical survival probability, which is used for the predictor equation and revising posterior particle weights.
