Adaptive Low-Pass Filtering using Sliding Window Gaussian Processes

TL;DR

This paper introduces an adaptive low-pass filtering method based on Gaussian process regression that automatically tunes itself in real-time, effectively reducing noise without prior signal knowledge, suitable for dynamic applications.

Contribution

The paper presents a novel online adaptive low-pass filter using Gaussian processes with hyperparameter optimization, eliminating the need for prior tuning and ensuring bounded estimation error.

Findings

Estimation error of the method is uniformly bounded.

The approach is flexible and efficient in various simulation scenarios.

No prior signal knowledge is required for effective filtering.

Abstract

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.