Algorithm 2 Cross-Sensor Estimation and Gaussian Copula Residual Synthesis: Pipeline B

Require: Selected features ${\mathbf{X}}^{\det }$; residual targets $\mathbf{r}$; cross-sensor inputs ${\mathbf{X}}^{\mathrm{cross}}$; synthetic-sample fraction $\varphi =0.25$; noise ${\sigma }_{\mathrm{aug}}=0.01$ Ensure: Fused, augmented dataset $({\tilde{\mathbf{X}}}^{\mathrm{aug}},{\tilde{r}}^{\mathrm{aug}})$  Cross-Sensor Estimation: Fit $h_{\mathrm{BRR}}$, $h_{\mathrm{GPR}}$ on ${\mathbf{X}}^{\mathrm{cross}}\to y$ (training partition only, Section 3.5); append predictions as $\mathrm{syn}\text{\_}\mathrm{brr}$, $\mathrm{syn}\text{\_}\mathrm{gpr}$ to ${\mathbf{X}}^{\det }$, giving ${\mathbf{X}}^{\mathrm{b}}$  Rank Transformation: $u_i^{\left(j\right)}=\mathrm{rank}(x_i^{\left(j\right)})/(N+1)$ jointly over $({\mathbf{X}}^{\mathrm{b}},\mathbf{r})$, training partition only, using Equation (13)  Gaussian Mapping: $z_i^{\left(j\right)}={\Phi }^{-1}(u_i^{\left(j\right)})$ using Equation (14)  Covariance Estimation: $\Sigma =\mathrm{Cov}\left(\mathbf{Z}\right)$  Synthetic Sampling: ${\tilde{\mathbf{z}}}_i\sim \mathcal{N}(\mathbf{0},\Sigma )$, $i=1,\dots ,\lfloor \varphi N\rfloor$  Back-Transformation: ${\tilde{x}}_i^{\left(j\right)}=F_j^{-1}\left(\Phi ({\tilde{z}}_i^{\left(j\right)})\right)$ using Equation (16); each synthetic row carries its own synthetic residual value  Validation: Compute KS statistics, Wasserstein distances, correlation-matrix differences, and tail-dependence coefficients between real and synthetic samples  Fusion and Augmentation: Concatenate real and synthetic rows using Equation (17); apply noise augmentation using Equation (18)  return $({\tilde{\mathbf{X}}}^{\mathrm{aug}},{\tilde{r}}^{\mathrm{aug}})$