**2. Background**

Some fundamentals on multitarget state-space model, the CPHD filter, and GLMB filter will be summarized in this section. Following the convention in [11], single target states are denoted with lower-case letters (i.e., *x*) while upper-case letters denote multitarget states (i.e., *X*). The corresponding spaces are denoted by blackboard bold letters (X,L,Z,*etc*). The sequence of variable *Xi*, *Xi*+1, ..., *Xj* is abbreviated by *Xi*:*j*. In this work the inner product \$ *<sup>f</sup>*(*x*)*g*(*x*)*dx* is rewritten as *<sup>f</sup>* , *<sup>g</sup>*. Given a set *<sup>S</sup>*, the finite subsets of *S* is written as F(*S*), and 1*S*(·) denotes the indicator function of *S*. For a finite set *X*, |*X*| represents its the number of elements, and the product <sup>∏</sup>*x*∈*<sup>X</sup> <sup>f</sup>* (*x*) for some real-valued function *<sup>f</sup>* is denoted by the multitarget exponential *f <sup>X</sup>*, with *f* <sup>∅</sup> = 1. Further, the generalized Kronecker-delta function *δ<sup>Y</sup>* whose arguments can be arbitrary sets, vectors, integers, etc., is defined as follows

$$\delta\_Y[X] = \begin{cases} 1 & \text{if } \quad X = Y \\ 0 & \text{otherwise.} \end{cases} \tag{1}$$
