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

â€¢ Initialization: Draw ${\mathbf{X}}_{0}^{j}~N\left({X}_{0},1\right)$, and ${\mathrm{Î±}}_{0}^{j}={\mathrm{Î±}}_{0}$ âˆ€j âˆˆ {1,..., N p }. Here X0 and Î±0 are the initial kinematic state and identity values, respectively.

â€¢ For t = 1,..., T (number of frames)

â€ƒâ€ƒâ€ƒ1. For j = 1,..., N p (number of particles)

1.1 Draw samples ${\mathbf{X}}_{t}^{j}~p\left({\mathbf{X}}_{t}^{j}âˆ£{\mathbf{X}}_{t-1}^{j}\right)$ and ${\mathrm{Î±}}_{t}^{j}~p\left({\mathrm{Î±}}_{t}^{j}âˆ£{\mathrm{Î±}}_{t-1}^{j}\right)$ as in (10) and (11).

1.2 Compute weights ${w}_{t}^{j}=p\left({\mathbf{z}}_{t}âˆ£{\mathrm{Î±}}_{t}^{j},\phantom{\rule{2.77695pt}{0ex}}{\mathbf{X}}_{t}^{j}\right)$ using (12).

End

â€ƒâ€ƒâ€ƒ2. Normalize the weights such that ${âˆ‘}_{j=1}^{{N}_{p}}{w}_{t}^{j}=1$.

â€ƒâ€ƒâ€ƒ3. Compute the mean estimates of the kinematics and identity ${\stackrel{^}{\mathbf{X}}}_{t}={âˆ‘}_{j=1}^{{N}_{p}}{w}_{t}^{j}{\mathbf{X}}_{t}^{j}$ and ${\stackrel{^}{\mathrm{Î±}}}_{t}={âˆ‘}_{j=1}^{{N}_{p}}{w}_{t}^{j}{\mathrm{Î±}}_{t}^{j}$.

â€ƒâ€ƒâ€ƒ4. Set $\left[{\mathrm{Î±}}_{t}^{j},\phantom{\rule{2.77695pt}{0ex}}{\mathbf{X}}_{t}^{j}\right]=\text{resample}\left({\mathrm{Î±}}_{t}^{j},\phantom{\rule{2.77695pt}{0ex}}{\mathbf{X}}_{k}^{j},\phantom{\rule{2.77695pt}{0ex}}{w}_{k}^{j}\right)$ to increase the effective number of particles [39].

â€¢ End