  We study the methodology and potential theoretical systematics of measuring
Baryon Acoustic Oscillations (BAO) using the angular correlation functions in
tomographic bins. We calibrate and optimize the pipeline for the Dark Energy
Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results
obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile
Likelihood, and Markov Chain Monte Carlo. The fit results from the MLE are the
least biased and their derived 1-$\sigma$ error bar are closest to the Gaussian
distribution value after removing the extreme mocks with non-detected BAO
signal. We show that incorrect assumptions in constructing the template, such
as mismatches from the cosmology of the mocks or the underlying photo-$z$
errors, can lead to BAO angular shifts. We find that MLE is the method that
best traces this systematic biases, allowing to recover the true angular
distance values. In a real survey analysis, it may happen that the final data
sample properties are slightly different from those of the mock catalog. We
show that the effect on the mock covariance due to the sample differences can
be corrected with the help of the Gaussian covariance matrix or more
effectively using the eigenmode expansion of the mock covariance. In the
eigenmode expansion, the eigenmodes are provided by some proxy covariance
matrix. The eigenmode expansion is significantly less susceptible to
statistical fluctuations relative to the direct measurements of the covariance
matrix because of the number of free parameters is substantially reduced
