*b. Prediction*

Given the posterior multitarget density at current time is a GLMB filtering density with the form of (21), the predicted multitarget density at next time step is calculated under the standard multitarget dynamic model (4) as follows [11]:

$$
\pi\_+^{(s)}(\mathbf{X}\_+) = \Delta(\mathbf{X}\_+) \sum\_{(l\_+,\varrho) \in \mathcal{F}(\mathbb{L}\_+) \times \Sigma} \omega\_+^{(s,l\_+,\varrho)}(\mathcal{L}(\mathbf{X}\_+)) \left[ p\_+^{(s,\varrho)} \right]^{\mathbf{X}\_+} \tag{32}
$$

where

$$
\omega\_{+}^{(s,l+,\varrho)}(L) = \omega\_{B}^{(s)}(f\_{+} \cap \mathbb{B}) \omega\_{S}^{(s,\varrho)}(f\_{+} \cap \mathbb{L}),\tag{33}
$$

$$p\_{+}^{(s,\rho)}(\mathbf{x},\ell) = \mathbf{1}\_{\mathbb{L}}(\ell)p\_{\mathbb{S}}^{(s,\rho)}(\mathbf{x},\ell) + \left(1 - \mathbf{1}\_{\mathbb{L}}(\ell)\right)p\_{\mathbb{B}}^{(s)}(\mathbf{x},\ell) \tag{34}$$

$$p\_S^{(s,\emptyset)}(\mathbf{x},\ell) = \frac{\langle P\_S^{(s)}(\cdot,\ell)f(\mathbf{x}|\cdot,\ell), p^{(s,\emptyset)}(\cdot,\ell)\rangle}{p\_S^{(s,\emptyset)}(\ell)},\tag{35}$$

$$p\_S^{(s,\rho)}(\ell) = \int \langle P\_S^{(s)}(\cdot,\ell)f(\mathbf{x}|\cdot,\ell), p^{(s,\rho)}(\cdot,\ell) \rangle d\mathbf{x} \tag{36}$$

$$
\omega\_S^{(s,\emptyset)}(L) = [\mathcal{P}\_S^{(s,\emptyset)}]^L \sum\_{I \subseteq \mathbb{L}} \mathbf{1}\_I(L) \left[ Q\_S^{(s,\emptyset)}(\ell) \right]^{I-L} \omega^{(s,\emptyset,\emptyset)} \tag{37}
$$

$$Q\_S^{(s,\varrho)}(\ell) = \langle 1 - P\_S^{(s)}(\cdot,\ell), p^{(s,\varrho)}(\cdot,\ell) \rangle. \tag{38}$$
