*3.1. Prediction of Track State and Existence Probability*

The existence event of a target in the surveillance region at scan *k* is denoted by *χ<sup>τ</sup> <sup>k</sup>* as a random event, and *χ*¯*<sup>τ</sup> <sup>k</sup>* is the complement of *<sup>χ</sup><sup>τ</sup> <sup>k</sup>* . The existence of a target propagates by the Markov chain one model [5,6]:

$$P\left\{\chi\_{k-1}^{\mathsf{T}}|\mathbf{Z}^{k}\right\} = p\_{11}P\left\{\chi\_{k-1}^{\mathsf{T}}|\mathbf{Z}^{k-1}\right\},\tag{11}$$

where *p*<sup>11</sup> is the transition probability of target existence.

The trajectory state of each track *τ* is propagated using the prediction step of the Kalman filter:

$$\boldsymbol{\hat{\mathfrak{x}}}\_{k|k-1}^{\boldsymbol{\tau}} = \boldsymbol{\Phi}\_{k} \boldsymbol{\mathfrak{x}}\_{k-1|k-1}^{\boldsymbol{\tau}} \tag{12}$$

$$\mathbf{P}\_{k|k-1}^{\tau} = \boldsymbol{\Phi}\_{k} \mathbf{P}\_{k-1|k-1}^{\tau} (\boldsymbol{\Phi}\_{k})^{\top} + \mathbf{Q}\_{k}.\tag{13}$$
