*2.2. CBMeMBer Filter*

The CBMeMBer filter is outlined as follows and the details can be found in [18,21]. It approximates the posterior multi-target density by a multi-Bernoulli RFS. The multi-Bernoulli RFS consists of *M* independent Bernoulli RFSs *X*(*i*) , that is, *<sup>X</sup>* <sup>=</sup> <sup>∪</sup>*<sup>M</sup> i*=1*X*(*i*) . The probability density of Bernoulli RFS *X*(*i*) is

$$\pi(\mathbf{X}^{(i)}) = \begin{cases} 1 - r^{(i)}, \mathbf{X}^{(i)} = \mathcal{Q} \\ r^{(i)} p^{(i)}(\mathbf{x}), \mathbf{X}^{(i)} = \langle \mathbf{x} \rangle \end{cases} \tag{11}$$

where *<sup>r</sup>*(*i*) <sup>∈</sup> [0, 1] is the target existence probability and *<sup>p</sup>*(*i*)(·) is a spatial distribution. Therefore, the probability density of multi-Bernoulli RFS *X* is given by

$$\pi(\mathbf{X}) = \prod\_{i=1}^{M} \left( 1 - r^{(i)} \right) \sum\_{1 \le i\_1 \ne \dots \ne i\_n \le M} \prod\_{j=1}^{n} \frac{r^{(i\_j)} p^{(i\_j)}(\mathbf{x}\_j)}{1 - r^{(i\_j)}} \tag{12}$$

where *n* is the number of targets.

The multi-Bernoulli RFS *X* is completely described by the multi-Bernoulli parameter set (*r*(*i*), *<sup>p</sup>*(*i*)(*x*))*<sup>M</sup> i*=1 , and the probability density of the multi-Bernoulli RFSs *X* can be abbreviated by (*r*(*i*), *<sup>p</sup>*(*i*)(*x*))*<sup>M</sup> i*=1 . The CBMeMBer filter consists of a prediction step and an update step.
