  When signals are measured through physical sensors, they are perturbed by
noise. To reduce noise, low-pass filters are commonly employed in order to
attenuate high frequency components in the incoming signal, regardless if they
come from noise or the actual signal. Therefore, low-pass filters must be
carefully tuned in order to avoid significant deterioration of the signal. This
tuning requires prior knowledge about the signal, which is often not available
in applications such as reinforcement learning or learning-based control. In
order to overcome this limitation, we propose an adaptive low-pass filter based
on Gaussian process regression. By considering a constant window of previous
observations, updates and predictions fast enough for real-world filtering
applications can be realized. Moreover, the online optimization of
hyperparameters leads to an adaptation of the low-pass behavior, such that no
prior tuning is necessary. We show that the estimation error of the proposed
method is uniformly bounded, and demonstrate the flexibility and efficiency of
the approach in several simulations.
