Laser self-mixing is in principle a simple and robust general purpose interferometric method, with the additional expressivity which results from nonlinearity. However, it is rather sensitive to unwanted changes in target reflectivity, which often hinders applications with non-cooperative targets. Here we analyze experimentally a multi-channel sensor based on three independent self-mixing signals processed by a small neural network. We show that it provides high-availability motion sensing, robust not only to measurement noise but also to complete loss of signal in some channels. As a form of hybrid sensing based on nonlinear photonics and neural networks, it also opens perspectives for fully multimodal complex photonics sensing.