[Paper Review] Data-Driven Denoising of Stationary Accelerometer Signals

Daniel Engelsman, Itzik Klein|arXiv (Cornell University)|Jun 13, 2022

Inertial Sensor and Navigation49 references4 citations

TL;DR

This paper proposes data-driven denoising methods for stationary accelerometer signals using machine learning, specifically k-Nearest Neighbors (kNN) and deep learning models, to outperform traditional signal processing techniques. The approach achieves a one-order-of-magnitude reduction in angular errors during stationary coarse alignment, demonstrating superior noise suppression and navigation performance on both simulated and real-world data.

ABSTRACT

Modern navigation solutions are largely dependent on the performances of the standalone inertial sensors, especially at times when no external sources are available. During these outages, the inertial navigation solution is likely to degrade over time due to instrumental noises sources, particularly when using consumer low-cost inertial sensors. Conventionally, model-based estimation algorithms are employed to reduce noise levels and enhance meaningful information, thus improving the navigation solution directly. However, guaranteeing their optimality often proves to be challenging as sensors performance differ in manufacturing quality, process noise modeling, and calibration precision. In the literature, most inertial denoising models are model-based when recently several data-driven approaches were suggested primarily for gyroscope measurements denoising. Data-driven approaches for accelerometer denoising task are more challenging due to the unknown gravity projection on the accelerometer axes. To fill this gap, we propose several learning-based approaches and compare their performances with prominent denoising algorithms, in terms of pure noise removal, followed by stationary coarse alignment procedure. Based on the benchmarking results, obtained in field experiments, we show that: (i) learning-based models perform better than traditional signal processing filtering; (ii) non-parametric kNN algorithm outperforms all state of the art deep learning models examined in this study; (iii) denoising can be fruitful for pure inertial signal reconstruction, but moreover for navigation-related tasks, as both errors are shown to be reduced up to one order of magnitude.

Motivation & Objective

• To address the challenge of denoising low-cost MEMS accelerometer signals in stationary conditions, where gravity introduces large, variable bias.
• To overcome limitations of model-based filtering, which depend heavily on accurate calibration and noise modeling that are often unattainable in practice.
• To evaluate whether data-driven approaches can outperform conventional signal processing techniques in inertial signal reconstruction and navigation accuracy.
• To benchmark learning-based models against classical filters using both simulated and real-world accelerometer data.
• To assess the impact of denoising on a navigation-relevant task: stationary coarse alignment (SCA).

Proposed method

• The authors employ k-Nearest Neighbors (kNN) and deep learning models to denoise stationary accelerometer signals based on learned patterns from training data.
• The kNN model uses semantic similarity between input signals and their k-nearest neighbors in the feature space to reconstruct cleaner signals.
• A comprehensive dataset is constructed using simulated IMU data with controlled noise and real-world data from a smartphone and a high-end inertial sensor as ground truth.
• Signal denoising performance is evaluated using reconstruction error metrics such as Relative Absolute Error (RAE).
• The effectiveness of denoising is further validated through the stationary coarse alignment (SCA) procedure, measuring angular error reduction in roll and pitch estimation.
• The study compares multiple learning-based models and classical signal processing filters (e.g., moving average, ARMA, EMD) under identical conditions.

Figure 1: Denoising mapping function $f:\boldsymbol{x}\rightarrow\hat{\boldsymbol{x}}$

Experimental results

Research questions

• RQ1 Can data-driven denoising models outperform traditional signal processing filters in reconstructing clean accelerometer signals from noisy, stationary measurements?
• RQ2 How do learning-based models perform in reducing angular errors during the stationary coarse alignment (SCA) procedure compared to conventional filtering methods?
• RQ3 What is the impact of real-world noise and unknown error sources on the generalization and performance of data-driven denoising models?
• RQ4 To what extent do the denoising capabilities of kNN and deep learning models translate into improved navigation solution accuracy?
• RQ5 Can non-parametric models like kNN generalize effectively to real-world accelerometer data with complex, unknown noise patterns?

Key findings

• The kNN-based denoising model reduced the reconstruction error (RAE) by approximately 9.38% compared to noisy inputs in experimental validation, indicating superior signal fidelity.
• In the stationary coarse alignment task, the kNN model reduced the RMSE of roll angle from 0.30042° to 0.03398°, and pitch from 0.50251° to 0.06676°, representing a one-order-of-magnitude improvement.
• The experimental results showed a significant performance gap between simulated and real-world scenarios, with real-world noise patterns degrading model performance less than expected, likely due to the model’s robustness to unknown error sources.
• The kNN model outperformed all other tested models, including deep learning and classical filters, in both simulated and real-world settings, particularly in angular error reduction.
• The study confirms that data-driven approaches can generalize well to real-world accelerometer data, even with unknown or unmodeled noise, and significantly improve navigation accuracy.
• Despite limitations in interpretability and generalization to unseen dynamics, the results demonstrate that learning-based denoising is a viable and effective alternative to conventional filtering in stationary inertial signal processing.

Figure 2: One-layer recurrent neural network (RNN)