# Adaptive Low-Pass Filtering using Sliding Window Gaussian Processes

arXiv: https://arxiv.org/abs/2111.03617 · HTML: https://mlsanity.com/paper/2111.03617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 5 Nov 2021.

## Builds on (most cited first, 3 of 3)

- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems](https://mlsanity.com/paper/1902.06278/) (2019)
- [The Impact of Data on the Stability of Learning-Based Control- Extended Version](https://mlsanity.com/paper/2011.10596/) (2020)

## Built on by (most cited first, 1 of 1)

- [Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacy](https://mlsanity.com/paper/2505.04468/) (2025)

## Abstract (arXiv)

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.