Algorithm 1: Parameter estimation using Gauss-Newton method with backtracking line search.

Data: Observed data $\overline{\mathit{y}}$ and initial guess ${\mathit{c}}_0$, $MAXITER=30$, $TOL={10}^{-10}$, $\delta ={10}^{-5}$  Result: Parameters that fit the model $\mathit{y}$ to observed data $\overline{\mathit{y}}$ by minimizing the functional     $\mathcal{F}\left(\mathit{c}\right)=\frac{1}{2}\mathit{r}·\mathit{r}$ (11) with the chosen residual (9) or (10)  initialization $\mathit{c}\leftarrow {\mathit{c}}_0$;  $ITER\leftarrow 0$;