Adaptive Low-Pass Filtering using Sliding Window Gaussian Processes
This addresses the need for adaptive filtering in applications like reinforcement learning and control where prior signal knowledge is unavailable, though it is an incremental improvement over existing methods.
The paper tackles the problem of adaptive low-pass filtering for noisy signals without requiring prior tuning, by proposing a method based on Gaussian process regression with sliding windows and online hyperparameter optimization, and demonstrates its effectiveness through simulations with a uniformly bounded estimation error.
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.