*2.5. GLMB RFS*

A generalized label multi-Bernoulli RFS under the state space X and the label space L has the following distribution [34]:

$$\pi\left(\boldsymbol{\lambda}\right) = \boldsymbol{\Lambda}\left(\boldsymbol{\lambda}\right) \sum\_{\boldsymbol{\xi}^{\boldsymbol{\xi}} \in \boldsymbol{\Sigma}} \boldsymbol{\omega}^{\left(\boldsymbol{\xi}\right)}\left(\boldsymbol{\mathcal{L}}\left(\boldsymbol{\lambda}\right)\right) \left[\boldsymbol{p}^{\left(\boldsymbol{\xi}\right)}\right]^{\boldsymbol{\lambda}}\tag{11}$$

where *<sup>ξ</sup>*<sup>=</sup> (*θ*1:*k*) <sup>∈</sup> <sup>Θ</sup> is a historical association maps. The non-negative *<sup>ω</sup>*(*ξ*) (*L*) and a probability density *p*(*ξ*) satisfy:

$$\sum\_{L \in \mathbb{L}} \sum\_{\xi \in \Xi} \omega^{(\xi)}\left(L\right) = 1\tag{12}$$

$$\int p^{(\xi)}\left(\mathbf{x},l\right)d\mathbf{x} = 1.\tag{13}$$
