Massive MIMO communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice. In this letter, we propose to perform online learning for channel estimation in a massive MIMO context, adding flexibility to physical channel models by unfolding a channel estimation algorithm (matching pursuit) as a neural network. This leads to a computationally efficient neural network structure that can be trained online when initialized with an imperfect model. The method allows a base station to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase. It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system.