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Denoising IMU Gyroscopes with Deep Learning for Open-Loop Attitude Estimation

Martin Brossard, Silvere Bonnabel, Axel Barrau

arXiv:2002.10718v2cs.ROstat.ML

TL;DR

The paper tackles denoising and bias correction for low-cost IMU gyroscopes so that robot attitude can be estimated by dead reckoning. It learns gyro corrections and orientation increments with a supervised dilated-convolution approach, achieving strong attitude results on EuRoC and TUM-VI, including competition with visual-inertial methods without vision.

  • Problem

    Low-cost IMU gyroscopes are noisy and biased, making accurate open-loop attitude estimation difficult and motivating learned denoising.

  • Method

    The method learns gyro corrections from ground truth using a dilated convolutional network, orientation-increment loss, and augmented training data.

  • Results

    The method outperforms OriNet, improves accurate calibrated IMU performance by a factor of 2 to 4, and reaches median errors of 1.34 deg /min on EuRoC and 0.68 deg /min on TUM-VI.

  • Takeaways & Limitations

    Open-loop integration of learned noise-free gyro measurements can compete with state-of-the-art visual-inertial methods for attitude estimation without vision.

  • Takeaways & Limitations

    The approach requires a proper dataset, and the current method is restricted to one IMU for training and testing.

Abstract

from arXiv · show

This paper proposes a learning method for denoising gyroscopes of Inertial Measurement Units (IMUs) using ground truth data, and estimating in real time the orientation (attitude) of a robot in dead reckoning. The obtained algorithm outperforms the state-of-the-art on the (unseen) test sequences. The obtained performances are achieved thanks to a well-chosen model, a proper loss function for orientation increments, and through the identification of key points when training with high-frequency inertial data. Our approach builds upon a neural network based on dilated convolutions, without requiring any recurrent neural network. We demonstrate how efficient our strategy is for 3D attitude estimation on the EuRoC and TUM-VI datasets. Interestingly, we observe our dead reckoning algorithm manages to beat top-ranked visual-inertial odometry systems in terms of attitude estimation although it does not use vision sensors. We believe this paper offers new perspectives for visual-inertial localization and constitutes a step toward more efficient learning methods involving IMUs. Our open-source implementation is available at https://github.com/mbrossar/denoise-imu-gyro.

I. INTRODUCTION

The paper addresses noisy and biased low-cost IMU gyroscopes by learning gyro corrections, enabling open-loop attitude estimation without vision. It combines a supervised convolutional approach, orientation-increment loss, and evaluation across drone and handheld datasets.

  • Low-cost IMUs suffer from noise and biases caused by effects including axis misalignment, scale factors, and time-varying offsets.
  • The proposed method uses deep learning to denoise gyroscopes and obtains attitude estimates by open-loop integration of the corrected measurements.
  • The method models orientation increments from low-cost IMUs and uses a convolutional network to regress gyro corrections.
  • Its training procedure uses a trackable loss function for estimating relative orientation increments.
  • On drone and handheld-device datasets, the method outperforms OriNet and competes with visual-inertial methods without using vision.
  • The implementation is open source, and training takes 5 minutes per dataset.

II. KINEMATIC & LOW-COST IMU MODELS

The paper formulates attitude propagation by integrating angular-velocity increments on SO(3), while modeling low-cost IMU measurements with bias, noise, calibration, and gravity-related effects. These models explain why raw measurements drift and motivate learning noise-free gyro increments.

  • Kinematic model: Orientation is propagated by integrating angular-velocity increments with the SO(3) exponential map.
  • Kinematic model: Errors in an estimated rotation propagate through successive open-loop integration steps.
  • Low-cost IMU sensor model: High-frequency IMU measurements contain angular-rate and acceleration signals corrupted by quasi-constant biases and commonly modeled white Gaussian noise.
  • Low-cost IMU sensor model: The intrinsic calibration matrix represents axis misalignment, scale factors, and gyro sensitivity to linear acceleration.
  • Low-cost IMU sensor model: Calibration parameters and biases vary with temperature and stress, while practical vibrations can make measurement noise colored rather than white.
  • Network context: The proposed network uses dilated convolutions over a 448-sample window, corresponding to 2.24 seconds of past information.

III. LEARNING METHOD FOR DENOISING THE IMU

The method learns gyro corrections from local IMU windows and integrates the corrected increments in open loop to estimate orientation. A dilated-convolution network supplies time-varying corrections while static calibration parameters are optimized during training.

  • The approach estimates noise-free gyro increments by correcting measured gyros before open-loop orientation integration.
  • The model combines learned time-varying corrections with static parameters for gyro axis misalignment, scale factors, and bias.
  • The network uses a past local window of N = 448 measurements, representing 2.24 s of information before each timestamp.
  • The local-window design excludes measurements outside the window and supports training with 8 or fewer minutes of data.
  • Dilated convolutions expand the receptive field while preserving temporal ordering and using relatively little computation and memory.

C. Loss Function based on Integrated Gyro Increments

The loss compares integrated orientation increments rather than instantaneous gyro errors, because high-frequency ground truth is unavailable. Its design uses robust, rotation-invariant errors at reduced frequencies while avoiding excessive trajectory-specific overfitting.

  • The loss uses integrated orientation increments because ground truth angular velocity at the 200 Hz IMU rate is infeasible to obtain.
  • The Huber loss provides robustness to ground truth outliers.
  • The integrated loss is invariant to global rotations, matching the rotational invariance of IMU measurements.
  • The chosen increments correspond to approximately 12 Hz and 6 Hz errors for j = 16 and j = 32.
  • Using an excessively large j or overall orientation error can cause overfitting to specific training trajectories.

D. Efficient Computation of (8)-(10)

The implementation accelerates integrated-loss computation through parallel matrix multiplication and subsampling. The experiments use held-out sequences from two datasets, with regularization and augmentation addressing limited training data and overfitting.

  • Viewing integration as a multiplication tree reduces computation to log2(j) batch GPU operations and increases training speed by 32/log2(32) ≈ 6.
  • Subsampling one increment every j timestamps prevents repeatedly counting the same orientation increment.
  • Gaussian-noise augmentation is applied during each training epoch, using a standard deviation of 0.01 deg/s.
  • The method is evaluated on held-out sequences from drone and handheld-device datasets with train, validation, and test partitions.

2) TUM-VI:

On TUM-VI, the study compares the proposed inertial method with raw and calibrated IMUs, OriNet, and several visual-inertial systems. The comparison includes both standalone IMU estimates and visual-inertial systems supplied with corrected gyro measurements.

  • 2) TUM-VI:: The TUM-VI split uses the first 50 s of room 1, room 3, and room 5 for training, with the remaining rooms reserved for testing.
  • 2) TUM-VI:: The proposed IMU is evaluated against visual-inertial methods while using only inertial signals in the standalone comparison.
  • 2) TUM-VI:: The comparison includes raw IMU, calibrated IMU, OriNet, the proposed IMU, VINS-Mono, loop-closure VINS-Mono, Open-VINS, and corrected-gyro Open-VINS.
  • 2) TUM-VI:: Each method is run ten times and results are averaged on a workstation without computational-limitations deterioration.

D. Evaluation Metrics

The evaluation uses orientation-error metrics computed with a standard toolbox, including absolute and relative trajectory errors. Relative orientation error is collected over fixed displacement intervals to provide distance-based odometry comparisons.

  • The methods are evaluated using AOE and ROE metrics computed with the toolbox of.
  • The AOE computes mean square error between ground-truth and estimated orientations after aligning the estimated trajectory at n = 0.The metric uses the SO(3) logarithm map over a sequence of length M.
  • ROE compares relative orientation over timestamp pairs corresponding to IMU displacements of 7, 21, or 35 meters.Median and percentile statistics are computed over the resulting sub-trajectory errors.
  • Distance-based ROE is recommended for odometry comparisons because AOE is highly sensitive to when estimation error occurs.The paper also reports yaw-only variants and notes that inertial-only errors scale with time, whereas visual-method errors generally scale with distance.

E. Results

On unseen test sequences, the proposed method improves orientation estimates over raw and calibrated inertial baselines, outperforms OriNet, and competes with visual-inertial methods. Small gyro corrections produce substantial estimation improvements, although cross-method comparisons depend on dataset and algorithm settings.

  • Raw IMU orientation estimates deviate from ground truth in less than 10 s.
  • Calibrating the IMU alone can produce results difficult to distinguish from ground truth, showing the importance of correct calibration.
  • The proposed method outperforms OriNet and improves the accurate calibrated IMU baseline by a factor of 2 to 4.Median errors reach 1.34 deg /min on EuRoC and 0.68 deg /min on TUM-VI.
  • The IMU-only method remains accurate under high-motion dynamics and competes with VINS-Mono and Open-VINS after training on only a few minutes of data.
  • Comparisons among VIO algorithms remain difficult because each method's performance depends on the dataset and algorithm setting.
  • Corrections of only a few deg/s make calibrated and corrected gyro signals visually indistinguishable while substantially improving orientation estimates.

2) The Proposed Method is Well Suited to Yaw Estimation:

The method is particularly effective for yaw estimation, a challenging long-term odometry quantity because visual-inertial systems can recover roll and pitch more directly. Its results compete with VIO while using only inertial data and limited corrections.

  • 2) The Proposed Method is Well Suited to Yaw Estimation:: Yaw estimates are particularly accurate according to the reported results.
  • 2) The Proposed Method is Well Suited to Yaw Estimation:: VIO methods can recover roll and pitch using accelerometers, but yaw estimates drift with time.
  • 2) The Proposed Method is Well Suited to Yaw Estimation:: The dead-reckoning method estimates orientation without testing-time information that recovers roll and pitch or future information from loop closure.
  • 2) The Proposed Method is Well Suited to Yaw Estimation:: Accurate yaw estimates could support yaw-independent VIO methods such as.
  • 2) The Proposed Method is Well Suited to Yaw Estimation:: The proposed method competes with VIO algorithms on orientation estimates while applying gyro corrections as low as 1 deg/s maximum.

3) Ground Truth Time-Alignement:

The approach depends critically on suitable, accurately aligned training data and selected network design choices. The paper identifies dataset quality as its main limitation and reports that the proposed architecture outperforms tested alternatives.

  • 3) Ground Truth Time-Alignement:: A proper dataset is required, and the authors identify this requirement as the approach's main limitation.
  • 3) Ground Truth Time-Alignement:: Smooth activation functions such as GELU and ELU perform well, whereas ReLU-based networks are more prone to overfitting.
  • 3) Ground Truth Time-Alignement:: Increasing network depth, channel count, or kernel size does not systematically improve results.
  • 3) Ground Truth Time-Alignement:: Batch normalization improves both training speed and accuracy.
  • 3) Ground Truth Time-Alignement:: Removing accelerometers increases ROE errors by 50% relative to the proposed IMU configuration.This ablation indicates that accelerometers contribute useful information.
  • 3) Ground Truth Time-Alignement:: Replacing dilated convolutions with an LSTM increases ROE errors by around 40% and requires more training time.

1) Optimizer:

The paper highlights practical training choices and concludes that its learned gyroscope-denoising method achieves accurate attitude estimation while remaining efficient and fast to train. It also identifies generalization across devices and platforms as an unresolved challenge.

  • Optimizer: Cosine warm restarts substantially improve optimization and help identify an appropriate learning rate.
  • Optimizer: Dropout and weight decay are crucial for avoiding overfitting, with suitable values quickly tuned by basic grid search.
  • Optimizer: Rotation-matrix and quaternion loss implementations achieve similar accuracy and execution time once numerical issues, such as quaternion normalization, are addressed.
  • Limitations: Generalization from one dataset to another device or platform remains challenging and is left for future work.
  • Conclusion: The method produces accurate attitude estimates with a low-cost IMU, outperforms state-of-the-art inertial methods, and competes with visual-inertial methods without vision.
  • Limitations: Future directions include learning from multiple IMUs, using moderately accurate ground truth, and denoising accelerometers through relative preintegration increments.
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