  In this study, we apply the Analytical method of Blind Separation (ABS) of
the cosmic microwave background (CMB) from foregrounds to estimate the CMB
temperature power spectrum from multi-frequency microwave maps. We test the
robustness of the ABS estimator and assess the accuracy of the power spectrum
recovery by using realistic simulations based on the seven-frequency Planck
data, including various frequency-dependent and spatially-varying foreground
components (synchrotron, free-free, thermal dust and anomalous microwave
emission), as well as an uncorrelated Gaussian-distributed instrumental noise.
Considering no prior information about the foregrounds, the ABS estimator can
analytically recover the CMB power spectrum over almost all scales with less
than $0.5\%$ error for maps where the Galactic plane region ($|b|<10^{\circ}$)
is masked out. To further test the flexibility and effectiveness of the ABS
approach in a variety of situations, we apply the ABS to the simulated Planck
maps in three cases: (1) without any mask, (2) imposing a two-times-stronger
synchrotron emission and (3) including only the Galactic plane region
($|b|<10^{\circ}$) in the analysis. In such extreme cases, the ABS approach can
still provide an unbiased estimate of band powers at the level of 1
$\mu\rm{K}^2$ on average over all $\ell$ range, and the recovered powers are
consistent with the input values within 1-$\sigma$ for most $\ell$ bins.
