  Recent CMB observations have resulted in very precise observational data. A
robust and reliable CMB reconstruction technique can lead to efficient
estimation of the cosmological parameters. We demonstrate the performance of
our methodology using simulated temperature and polarization observations using
cosmic variance limited future generation PRISM satellite mission. We generate
samples from the joint distribution by implementing the CMB inverse covariance
weighted internal-linear-combination (ILC) with the Gibbs sampling technique.
We use the Python Sky Model (PySM), d4f1s1 to generate the realistic foreground
templates. The synchrotron emission is parametrized by a spatially varying
spectral index, whereas the thermal dust emission is described as a
two-component dust model. We estimate the marginalized densities of CMB signal
and theoretical angular power spectrum utilizing the samples from the entire
posterior distribution. The best-fit cleaned CMB map and the corresponding
angular power spectrum are consistent with the CMB realization and the sky
angular power spectrum, implying an efficient foreground minimized
reconstruction. The likelihood function estimated by making use of the
Blackwell-Rao estimator is used for the estimation of the cosmological
parameters. Our methodology can estimate the tensor to scalar ratio $r\ge
0.0075$ for the chosen foreground models and the instrumental noise levels. Our
current work demonstrates an analysis pipeline starting from the reliable
estimation of CMB signal and its angular power spectrum to the case of
cosmological parameter estimation using the foreground model independent
Gibbs-ILC method.
