This paper proposes circular data processing tools dedicated to the tracking of the phase of GNSS signals in a Phase Open Loop, particularly in case of multi-channel signal structure. The objective of processing the phase in an open loop is to avoid time-correlation between two successive measurements. This allows the use of loop filters in order to smooth the measurements without producing unwanted oscillations in the phase estimations. In order to process the angular values produced by the Phase Open Loop, the choice had been made to develop a filter and a fusion operator in a Bayesian framework with circular statistics distributions. The proposed tools are assessed on synthetic and real data