4.1.1. Linear Dynamic Model

In this experiment, we use a constant velocity model for the dynamic of the system. The state vector consists of information regarding the planar position and the velocity of the objects, which is *xk* = *px*, *py*, *p*˙ *<sup>x</sup>*, *p*˙ *<sup>y</sup>* .*T* ; while the measurement vector contains the position of the object, which is *zk* = [*zx*, *zy*] *<sup>T</sup>*. The transition and observation models are given respectively as follows:

$$f\_{+}(\mathbf{x}\_{+}|\mathbf{x}) = \mathcal{N}(\mathbf{x}\_{+}; F\mathbf{x}, Q)$$

$$h(z|\mathbf{x}) = \mathcal{N}(z; H\mathbf{x}, \mathbb{R})$$

where *F* = *I*<sup>2</sup> Δ*I*<sup>2</sup> 02 *I*<sup>2</sup> , *Q* = *σ*<sup>2</sup> *v* Δ<sup>4</sup> <sup>4</sup> *<sup>I</sup>*<sup>2</sup> <sup>Δ</sup><sup>3</sup> <sup>2</sup> *I*<sup>2</sup> Δ3 <sup>2</sup> *<sup>I</sup>*<sup>2</sup> <sup>Δ</sup><sup>2</sup> *<sup>I</sup>*<sup>2</sup> , *H* = - *I*<sup>2</sup> 02 , *R* = *σ*<sup>2</sup> *I*2. Particularly, in this experiment, we set *σ<sup>v</sup>* = 5 m/s and *σ* = 15 m.

The surveillance region is the [−1000, 1000] m × [−1000, 1000] m area, the total time step is *K* = 100, and Δ = 1. The ground truth plot for this experiment is given in Figure 1. The surviving probability is set to *pS* = 0.99, and the detection probability is *pD* = 0.95. Clutter rate is set to 66 false alarms per scan. The birth probability is set to *rB* <sup>=</sup> 0.03. The states of expected births are *<sup>m</sup>*(1) *<sup>B</sup>* = [0.1, 0, 0.1, 0] *T*, *m*(2) *<sup>B</sup>* = [400, 0, −600, 0] *<sup>T</sup>*, *m*(3) *<sup>B</sup>* = [−800, 0, −200, 0] *<sup>T</sup>*, and *m*(4) *<sup>B</sup>* = [−200, 0, 800, 0] *<sup>T</sup>*. The covariance matrix at birth is *PB* = *diag*([10, 10, 10, 10]). The number of hypotheses for GLMB filter is capped at 20, 000 components. In this experiment, we smooth the entire tracking interval from *k* = 1 to *k* = *K*. The threshold for the smoother to prune the track is set to *τ<sup>t</sup>* = 3 time steps.

We conduct the experiment over 100 Monte Carlo runs. The means of the estimated Optimal Subpattern Assignment (OSPA) error [55] and OSPA<sup>2</sup> error [52,56] are given respectively in Figures 2 and 3. Figure 4 shows the GLMB filter and proposed tracker-estimated cardinality of objects set for each time step along with the true values.

**Figure 1.** Ground truth for linear dynamic scenario (circle: track start position, triangle: track end position).

**Figure 3.** OSPA2 error for linear dynamic scenario.

**Figure 4.** Estimated cardinality for linear dynamic scenario.
