  Compressed sensing, allows to acquire compressible signals with a small
number of measurements. In applications, a hardware implementation often
requires a calibration as the sensing process is not perfectly known. Blind
calibration, that is performing at the same time calibration and compressed
sensing is thus particularly appealing. A potential approach was suggested by
Sch\"ulke and collaborators in Sch\"ulke et al. 2013 and 2015, using
approximate message passing (AMP) for blind calibration (cal-AMP). Here, the
algorithm is extended from the already proposed offline case to the online
case, where the calibration is refined step by step as new measured samples are
received. Furthermore, we show that the performance of both the offline and the
online algorithms can be theoretically studied via the State Evolution (SE)
formalism. Through numerical simulations, the efficiency of cal-AMP and the
consistency of the theoretical predictions are confirmed.
