*a. GLMB update*

Given the standard multitarget observation likelihood function (9), the posterior multitarget density is calculated as follows [11]

$$\pi^{(\varepsilon)}(X|Z^{(\varepsilon)}) = \Delta(X) \sum\_{(\boldsymbol{I},\boldsymbol{\varrho}) \in \mathcal{F}(\mathbb{L}) \times \boldsymbol{\Sigma}} \sum\_{\boldsymbol{\theta}^{(\varepsilon)} \in \boldsymbol{\Theta}} \omega^{(\varepsilon,\boldsymbol{I},\boldsymbol{\varrho},\boldsymbol{\theta}^{(\varepsilon)})}\_{(Z^{(\varepsilon)})} (\mathcal{L}(X)) \left[ p^{(\varepsilon,\boldsymbol{\varrho},\boldsymbol{\theta}^{(\varepsilon)})} (\cdot|Z^{(\varepsilon)}) \right]^{X},\tag{27}$$

where

$$\omega\_{Z^{(s)}}^{(s,l,\rho,\theta^{(s)})}(L) = \frac{\Gamma\_{Z^{(s)}}^{(s,l,\rho,\theta^{(s)})}}{\sum\_{(l,\theta)\in\mathcal{F}(\mathbb{L})\times\Xi} \sum\_{\theta^{(s)}\in\Theta} \Gamma\_{Z^{(s)}}^{(s,l,\rho,\theta^{(s)})}}\tag{28}$$

$$\Gamma\_{Z^{(s)}}^{(s,l,\rho,\theta^{(s)})} = \omega\_{Z^{(s)}}^{(s,l,\rho)}(L) \left[ \mathfrak{p}\_{Z^{(s)}}^{(s,\rho,\theta^{(s)})} \right]^{f} \tag{29}$$

$$p^{(s,\varrho,\theta^{(s)})}(\mathbf{x},\ell|Z^{(s)}) = \frac{p^{(s,\varrho)}(\mathbf{x},\ell)\mathbf{Y}\_{Z^{(s)}}^{(s)}(\mathbf{x},\ell;\theta^{(s)})}{p\_{Z^{(s)}}^{(s,\varrho,\theta^{(s)})}(\ell)}\tag{30}$$

$$\boldsymbol{\psi}\_{Z^{(s)}}^{(s,\varrho,\theta^{(s)})}(\ell) = \langle p^{(s,\varrho)}(\cdot,\ell), \boldsymbol{Y}\_{Z^{(s)}}^{(s)}(\cdot,\ell; \theta^{(s)}) \rangle \tag{31}$$

and Υ(*s*) *<sup>Z</sup>*(*s*)(*x*, -; *θ*(*s*)) is given in (10).
