Table 1 Pseudo-code for the particle filter-based ATR algorithm

• For t = 1,..., T (number of frames)

   1. For j = 1,..., N _p (number of particles)

1.1 Draw samples ${\mathbf{X}}_t^j~p\left({\mathbf{X}}_t^j\mid {\mathbf{X}}_{t-1}^j\right)$ and ${\alpha }_t^j~p\left({\alpha }_t^j\mid {\alpha }_{t-1}^j\right)$ as in (10) and (11).

1.2 Compute weights $w_t^j=p\left({\mathbf{z}}_t\mid {\alpha }_t^j,{\mathbf{X}}_t^j\right)$ using (12).

End

   2. Normalize the weights such that ${\sum }_{j=1}^{N_p}{w}_t^j=1$.

   3. Compute the mean estimates of the kinematics and identity ${\widehat{\mathbf{X}}}_t={\sum }_{j=1}^{N_p}{w}_t^j{\mathbf{X}}_t^j$ and ${\widehat{\alpha }}_t={\sum }_{j=1}^{N_p}{w}_t^j{\alpha }_t^j$.

   4. Set $\left[{\alpha }_t^j,{\mathbf{X}}_t^j\right]=\text{resample}\left({\alpha }_t^j,{\mathbf{X}}_k^j,w_k^j\right)$ to increase the effective number of particles [39].

• End