that, for the $2$-endmember mixtures, GBM does not provide smaller RE than LMM, as expected. Indeed, as highlighted in paragraph \[subsec:bilinear\], GBM reduces to LMM if $\gamma_{i,j,p}=0,\ \forall i,j$, which is supposed to confer to GBM more flexibility than LMM. This might indicate that the unmixing algorithm associated with GBM has not properly converged for this dataset. This point is discussed in more details in Section \[sec:discussion\]. Regarding the abundance MSE, NM and LMM provide similar errors for two-endmember mixtures and all nonlinear models perform better than LMM for three-endmember mixtures.

        $2$ endm.                          $3$ endm.                         
  ---- ----------- --------------------------------------------------------- --------------------------------------------------------
   \*      LMM                            $7.70     $                                               $5.81    $
          o-LMM                           $15.0     $                                              $10.40    $
           FM       ${\textcolor[rgb]{0.00,0.00,1.00}{\mathbf{1.24}}}     $                   ${\mathbf{0.91}}    $
          o-FM                           $10.20     $                                               $7.66    $
           NM                             $7.70     $                                               $5.81    $
           GBM                           $10.13     $                                               $0.94   $
          PPNM                      ${\mathbf{1.28}}     $                    ${\textcolor[rgb]{0.00,0.00,1.00}{\mathbf{0.91}}}    $
   \*      LMM                      ${\mathbf{0.96}}     $                                          $3.17    $
           FM                            ${1.13}     $                        ${\textcolor[rgb]{0.00,0.00,1.00}{\mathbf{2.27}}}    $
           NM       ${\textcolor[rgb]{0.00,0.00,1.00}{\mathbf{0.92}}}     $                   ${\mathbf{2.44}}    $
           GBM                            $1.47     $                                              ${2.45}    $
          PPNM                           ${1.22}     $                                             ${2.62}    $

  : Two- and three-endmember orchard synthetic dataset. Abundance MSE ($\times 10^{-2}$) and RE ($\times 10^{-4}$) for various linear/nonlinear mixing models.\[tab:synth\_orchard\_RMSE\]

In Fig. \[fig:synth\_orchard\_wavelength\], the RDs are depicted as functions of wavelength, for the different linear and nonlinear mixing models. 