Algorithm 1 Proposed UKV–IRSA method.

INPUT $S_{\mathrm{pc},n}^k(f_r,{\tau }_m)$, satellite geometry, ${\mathrm{\Omega }}_R$, ${\mathrm{\Omega }}_{\varphi }$, ${\mathrm{\Omega }}_{\theta }$, ${\mathcal{F}}_{\mathrm{dr}}$, and $\mathcal{F}$    $\mathbf{for} f_{\mathrm{dr}}\in {\mathcal{F}}_{\mathrm{dr}}$        Apply DFRC using (18) and obtain $S_{\mathrm{DFRC},n}^k(R^{\prime },{\tau }_m;f_{\mathrm{dr}})$        $\mathbf{for} \mathit{\chi }=({\varphi }_{tg},{\theta }_{tg},R_r^{\prime })\in {\mathrm{\Omega }}_{\varphi }\times {\mathrm{\Omega }}_{\theta }\times {\mathrm{\Omega }}_R$ in a vectorized manner            $\mathbf{for} k=1:K,n=0:N-1$            Compute $R_{0,k}^{\prime }={\xi }_k({\varphi }_{tg},{\theta }_{tg})R_r^{\prime }$ via (28)            $\mathbf{for} f^{\prime }\in \mathcal{F}$                Compute $H_{n,k}(\mathit{\chi },f_{\mathrm{dr}},f^{\prime })$ along (29) using (30)            $\mathbf{end}$            ${\tilde{f}}_{\mathrm{dc},n,k}(\mathit{\chi },f_{\mathrm{dr}})\leftarrow {\arg \max }_{f^{\prime }\in \mathcal{F}}{\left|H_{n,k}(\mathit{\chi },f_{\mathrm{dr}},f^{\prime })\right|}^2$, and $p_{n,k}(\mathit{\chi },f_{\mathrm{dr}})\leftarrow {\max }_{f^{\prime }\in \mathcal{F}}{\left|H_{n,k}(\mathit{\chi },f_{\mathrm{dr}},f^{\prime })\right|}^2$            DC-compensate and integrate, then align to $G_{n,k}^{\mathrm{MRD}}(f;\mathit{\chi },f_{\mathrm{dr}})$ by IRSA (34)        $\mathbf{end}$        Compute ${\overline{f}}_{\mathrm{dc},k}(\mathit{\chi },f_{\mathrm{dr}})$ via (35)        Construct $\mathit{D}$ and $\mathit{b}$ under $\mathit{\chi }$; estimate ${\widehat{\mathit{v}}}_{tg}(\mathit{\chi },f_{\mathrm{dr}})$ via (46)        Compute ${\rho }_{\mathrm{dc}}(\mathit{\chi },f_{\mathrm{dr}})$ via (36)        Register frames via (37) and compute $\mathcal{J}(\mathit{\chi },f_{\mathrm{dr}})$ via (38)     $\mathbf{end}$   $\mathbf{end}$   $(\widehat{\mathit{\chi }},{\widehat{f}}_{\mathrm{dr}})\leftarrow {\arg \max }_{\mathit{\chi },f_{\mathrm{dr}}}\mathcal{J}(\mathit{\chi },f_{\mathrm{dr}})$ return $\widehat{\mathit{\chi }}$, ${\widehat{f}}_{\mathrm{dr}}$, $G_r(R_r^{\prime },f;{\widehat{\varphi }}_{tg},{\widehat{\theta }}_{tg},{\widehat{f}}_{\mathrm{dr}})$, and ${\widehat{\mathit{v}}}_{tg}$