Algorithm 1: Solving RELAD regression (Equation (24)) by IRLS algorithm.

1:${\mathbf{W}}^{\left(0\right)}={\tilde{\mathbf{W}}}^{\left(0\right)}=\mathbf{I}$       ▷ Initialization of weights; $\mathbf{I}$ is the $N\times N$ identity matrix 2:${\underset{\_}{\delta }}^{\left(0\right)}=inf$             ▷ Absolute losses of all data are initialized to infinity 3:$t=0$ 4:repeat 5:    $t=t+1$ 6:    ${\underset{\_}{\mathit{m}}}_i^{\left(t\right)}={\left[{\mathbf{H}}_i^{\mathsf{T}}{\mathbf{W}}^{(t-1)}{\mathbf{H}}_i+{\gamma }_i{\tilde{\mathbf{W}}}^{(t-1)}\right]}^{-1}{\mathbf{H}}_i^{\mathsf{T}}{\mathbf{W}}^{(t-1)}\underset{\_}{\mathbf{1}}$   ▷ Closed-form WLS solution 7:    ${\underset{\_}{\delta }}^{\left(t\right)}=|{\mathbf{H}}_i{\underset{\_}{\mathit{m}}}_i^{\left(t\right)}-\underset{\_}{\mathbf{1}}|$                      ▷ Absolute losses 8:    ${\displaystyle \widehat{\sigma }=\frac{\mathrm{median}\left({\underset{\_}{\delta }}^{\left(t\right)}\right)}{0.6745}}$        ▷ Preliminary estimate of the standard deviation of ${\underset{\_}{\delta }}^{\left(t\right)}$ 9:    ${\displaystyle {\mathbf{W}}^{\left(t\right)}=\widehat{\sigma }\times diag\left(\min \left(\frac{1}{{\underset{\_}{\delta }}^{\left(t\right)}},{10}^6\right)\right)}$      ▷ The × operator is the scalar product 10:    ${\displaystyle {\tilde{\mathbf{W}}}^{\left(t\right)}=diag\left(\min \left(\frac{1}{\left|{\underset{\_}{\mathit{m}}}_i^{\left(t\right)}\right|},{10}^6\right)\right)}$ 11:until$|\mathrm{mean}\left({\underset{\_}{\delta }}^{\left(t\right)}\right)-\mathrm{mean}\left({\underset{\_}{\delta }}^{(t-1)}\right)|<ϵ$or$t\ge T$ 12:${\underset{\_}{\mathit{m}}}_i={\underset{\_}{\mathit{m}}}_i^{\left(t\right)}$                         ▷ Return the converged ${\underset{\_}{\mathit{m}}}_i$