We present a pipeline that allows recovering reliable information for all four Stokes parameters with high accuracy. Its novelty relies on the treatment of the instrumental effects already prior to the computation of the Stokes parameters contrary to conventional methods, such as the Muller matrix one. The instrumental linear polarization is corrected across the whole telescope beam and significant Stokes $Q$ and $U$ can be recovered even when the recorded signals are severely corrupted. The accuracy we reach in terms of polarization degree is of the order of 0.1-0.2 %. The polarization angles are determined with an accuracy of almost 1$^{circ}$. The presented methodology was applied to recover the linear and circular polarization of around 150 Active Galactic Nuclei. The sources were monitored from July 2010 to April 2016 with the Effelsberg 100-m telescope at 4.85 GHz and 8.35 GHz with a cadence of around 1.2 months. The polarized emission of the Moon was used to calibrate the polarization angle. Our analysis showed a small system-induced rotation of about 1$^{circ}$ at both observing frequencies. Finally, we identify five sources with significant and stable linear polarization; three sources remain constantly linearly unpolarized over the period we examined; a total of 11 sources have stable circular polarization degree $m_mathrm{c}$ and four of them with non-zero $m_mathrm{c}$. We also identify eight sources that maintain a stable polarization angle over the examined period. All this is provided to the community for polarization observations reference. We finally show that our analysis method is conceptually different from the traditionally used ones and performs better than the Muller matrix method. Although it was developed for a system equipped with circularly polarized feeds it can easily be modified for systems with linearly polarized feeds as well.
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