Algorithm 3. CCRPF algorithm for maneuvering target tracking problem.

Initialization, $(\mathrm{for} i=1,\dots ,N_s),$

1.    $\mathrm{generate} x_0^{\left(i\right)}\sim p_0\left(x_0\right)$ $, \mathrm{assign} \mathrm{the} \cos \mathrm{t} C_0^{\left(i\right)}=0$ $, \mathrm{and} \mathrm{initialize} {\mathbf{\sigma }}_0^{2,\left(i\right)}.$

PMF Update

2.    Start with the initial waveform parameter $\mathbf{\theta }$. For each $\mathbf{\theta }$ compute:

3.      $\left\{{\widehat{x}}_{k-1}^{\left(i\right)},{\mathsf{\omega }}_{k-1}^{(i)}\right\}=\left\{x_{k-1}^{\left(i\right)},{\mathsf{\omega }}_{k-1}^{(i)}\right\}$ $, i=1,\dots ,N_s$ $, {\mathbf{z}}_k=f_y\left(x_k^{},w_k;\mathbf{\theta }\right)$

4.      ${\mathcal{R}}_k^{\left(i\right)}\left(\mathbf{\theta }\right)=\lambda C_{k-1}^{\left(i\right)}+{\Vert {\mathbf{z}}_k-f_y\left(f_x\left(x_{k-1}^{\left(i\right)}\right)\right)\Vert }^q$ $, q=1,2$ $; i=1,\dots ,N_s$ $, {\mathbf{\pi }}_k^{\left(i\right)}\propto \mu \left({\mathcal{R}}_k^{\left(i\right)}\right)=\frac{1}{{\left({\mathcal{R}}_k^{\left(i\right)}-\min {\left\{{\mathcal{R}}_k^{\left(i\right)}\right\}}_{i=1}^{N_s}+\delta \right)}^{\beta }}$

5.      $\mathrm{Resampling} {\widehat{x}}_{k-1}^{}={\left\{{\widehat{x}}_{k-1}^{\left(i\right)},{\widehat{C}}_{k-1}^{\left(i\right)}\right\}}_{i=1}^{N_s}$ $\mathrm{according} \mathrm{to} {\mathbf{\pi }}_k^{\left(i\right)}$

Particle Propagation and Waveform Selection

6.       $x_k^{\left(i\right)}\sim p_k\left(x_k^{}|{\widehat{x}}_{k-1}^{\left(i\right)}\right)$ $, \mathrm{compute} \mathrm{the} \mathrm{cost} C_k^{\left(i\right)}\left(\mathbf{\theta }\right)=\lambda C_{k-1}^{\left(i\right)}+{\Vert {\mathbf{z}}_k-f_y\left(x_k^{\left(i\right)}\right)\Vert }^q$

7.      $\mathrm{Compute} \mathrm{the} \cos \mathrm{t} \mathrm{function} {\mathbf{\theta }}_k^{*}=\underset{\mathbf{\theta }}{\arg \min }{C}_{\mathbf{\Theta }}^{\left(i\right)}\left({\mathbf{\theta }}_k|{\mathbf{z}}_{1:k-1}^{};{\mathsf{\Theta }}_{k-1}\right)+C_{\mathbf{\Theta }}\left({\mathbf{\theta }}_k\right)$

8.    $\mathrm{Select} \mathrm{the} \mathrm{optimal} \mathrm{waveform} \mathrm{parameter} {\mathbf{\theta }}_{\mathrm{k}}={\mathbf{\theta }}_k^{*}$

Particle and Measurement Recursive Update

9.      ${\widehat{x}}_k^{\left(i\right)}={\widehat{x}}_k^{\left(i\right)}$ $, {\mathbf{z}}_k=f_y\left(x_k^{},w_k;{\mathbf{\theta }}_{\mathrm{k}}\right)$ $, C_k^{\left(i\right)}=C_k^{\left(i\right)}\left({\mathbf{\theta }}_{\mathrm{k}}\right)$

10.      ${\mathbf{\sigma }}_k^{2,\left(i\right)}\left({\mathbf{\theta }}_{\mathrm{k}}\right)=\{\begin{array}{ll}{\sigma }_{k-1}^{2,\left(i\right)}& \mathrm{t}\le 10\\ \frac{k-1}{k}{\sigma }_{k-1}^{2,\left(i\right)}+\frac{{\Vert x_k^{\left(i\right)}-f_x\left({\widehat{x}}_{k-1}^{\left(i\right)}\right)\Vert }^2}{k\times \dim \left[x\right]}& \mathrm{t}>10\end{array}$, i = 1, …, Ns

Information Update and State Estimation

11.    ${\widehat{\mathbf{\pi }}}_k^{\left(i\right)}\propto {\mu }_2\left(C_k^{\left(i\right)};{\mathbf{\theta }}_{\mathrm{k}}\right)=\frac{1}{{\left(C_k^{\left(i\right)}-\min {\left\{C_k^{\left(i\right)}\right\}}_{i=1}^{N_s}+\delta \right)}^{\beta }},$$\mathrm{where} \alpha ,\beta >0. \mathrm{Normalize} \mathrm{the} \mathrm{PMF}.$

12.       ${\widehat{x}}_k={\widehat{x}}_k^{mean}={\displaystyle {\sum }_{i=1}^{N_s}{\widehat{\mathbf{\pi }}}_k^{\left(i\right)}{\widehat{x}}_k^{\left(i\right)}}$ $. \mathrm{Save} \mathrm{the} {\widehat{\mathbf{x}}}_k$ $\mathrm{and} {\widehat{\mathbf{P}}}_k^{}\left({\mathbf{\theta }}_{\mathrm{k}}\right).$