I did the chi-square fitting of the simulated spectra with the grid-interpolated AMBRE model templates. This fitting generates a probability distribution function of a reference model as functions of the stellar parameters. The PDF is combined with the PDF from broad-band SED fitting to determine the best fit model. This spectral fitting process takes ~110 min for a star with a single thread process.
 
Spectra: 

• Simulated spectra: ETC simulator outputs of AMBRE models. 7.5min and 15min exposures.
• Grid-interpolated AMBRE templates: ~60000 templates. RBF interpolations at grid steps of delta_Teff = 50 K, delta_logg = 0.25, delta_Z = 0.0, delta_[a/Fe] = 0.2, which roughly corresponds to a 1% flux accuracy.
   

This is an example of results.
In the confidence contours, we can find that all the parameters are well determined. So, the spectrum of the minimum reduced chi-square is very similar to the input spectrum. Note that the flux (y-axis) is roughly scaled to match with each other at this time.

This is another example.
In this case, the Teff (5800 K) at the minimum red chi sq is lower than the input (6000 K). Therefore, its spectrum is redder than the input. The line widths are narrower than those of the input spectrum. The broad-band SED fitting of this case determined Teff more accurately than the spectral fitting. The combined PDF will find a better model template.

The broad-band fitting PDF of this case.

The chi-square fitting of spectra works at <~ 17 mag. These are the PDFs of 13 mag and 17 mag, respectively. In the case of 17 mag, Z and [a/Fe] are determined, while Teff and Log(g) are weakly determined.
The saw-shaped distributions of Z and [a/Fe] come from the non-uniformity of the parameter grids of AMBRE. I will make up these gaps.
Combined PDFs and the best-fit spectra are reported in PIPE2D-374.
 
 
r = 13 mag:

 
r = 17 mag: