  We investigate the robustness of baryon acoustic oscillations (BAO)
measurements with a photometric galaxy sample using mock galaxy catalogues with
various sizes of photometric redshift (photo-$z$) uncertainties. We first
conduct the robustness of BAO measurements, assuming we have a perfect
knowledge of photo-$z$ uncertainties. We find that the BAO shift parameter
$\alpha$ can be constrained in an unbiased manner even for 3% photometric
redshift uncertainties up to $z\sim 1$. For instance, $\alpha=1.006 \pm 0.078$
with 95% confidence level is obtained from 3% photo-$z$ uncertainty data at
$z=1.03$ using the sample of $M_* \ge 10^{10.25} M_{\odot}/h^2$. We also find
that a sparse galaxy sample, e.g. $<2\times10^{-4}$ [$h$ Mpc$^{-1}]^3$ causes
additional noise in the covariance matrix calculation and can bias the
constraint on $\alpha$. Following this, we look into the scenario where
incorrect photometric redshift uncertainties are assumed in the fitting model.
We find that underestimating the photo-$z$ uncertainty leads to a degradation
in the constraining power on $\alpha$. However, the constrained value of
$\alpha$ is not biased. We also quantify the constraining power on $\Omega_{\rm
m0}$ assuming the LSST-like covariance and find that the 95% confidence level
is $\sigma(\Omega_{\rm m0})\sim0.03$-$0.05$ corresponding to the photo-$z$
uncertainties of 1% to 3% respectively. Finally, we examine whether the
skewness in the photometric redshift can bias the constraint on $\alpha$ and
confirm that the constraint on $\alpha$ is unbiased, even assuming a Gaussian
photo-$z$ uncertainty in our model.
