Debiasing 6-DOF IMU via Hierarchical Learning of Continuous Bias Dynamics

TL;DR

Low-cost IMUs suffer time-varying biases that degrade state estimation. The authors model explicit bias dynamics as a neural ordinary differential equation (NODE) on a Lie group, with continuous control inputs from measurements and pose-ground-truth supervision, enabling online debiasing without bias ground truth. A hierarchical training scheme with Lie-algebra embeddings and a cubic Hermite spline for inputs yields improved orientation and velocity estimates, demonstrated on EUROC, TUM-VI, and a Fetch dataset in IMU-only and VIO scenarios. This approach provides robust, device-specific IMU debiasing that enhances downstream odometry under challenging conditions and motions.

Abstract

This paper develops a deep learning approach to the online debiasing of IMU gyroscopes and accelerometers. Most existing methods rely on implicitly learning a bias term to compensate for raw IMU data. Explicit bias learning has recently shown its potential as a more interpretable and motion-independent alternative. However, it remains underexplored and faces challenges, particularly the need for ground truth bias data, which is rarely available. To address this, we propose a neural ordinary differential equation (NODE) framework that explicitly models continuous bias dynamics, requiring only pose ground truth, often available in datasets. This is achieved by extending the canonical NODE framework to the matrix Lie group for IMU kinematics with a hierarchical training strategy. The validation on two public datasets and one real-world experiment demonstrates significant accuracy improvements in IMU measurements, reducing errors in both pure IMU integration and visual-inertial odometry.

Figures (9)

• Figure 1: Training process for the explicit evolution of bias. The subscript notation $u_{n:k}$ represents $u_n,u_{n+1},...,u_k$. The existing method buchanan2022deepbias models bias evolution using a discrete approach, which requires ground-truth bias values during training. In contrast, our method employs a continuous model to capture bias dynamics and does not rely on ground-truth bias for training.
• Figure 2: The framework for learning bias dynamics. The bias dynamics are modeled by NODE, trained in a hierarchical manner. We first train the gyroscope component, followed by the accelerometer component. At each stage, the IMU raw data is represented as a continuous spline and serves as control input to the bias dynamics. Given initial conditions, the pose and bias along the trajectory are obtained through integration, with only the pose contributing to the loss function. The ODE on the manifold $\mathrm{SO}(3)$ is reformulated as a Lie algebra ODE, enabling an efficient solution via canonical NODE.
• Figure 3: Absolute error and relative error.
• Figure 4: The Euler angles obtained by only integrating the IMU data. The results are very close to the ground truth, which implies that the debiased gyroscope yields good performance.
• Figure 5: The coordinates of the errors, $\mathrm{Log}(R_{gt}^\mathsf{T}\hat{R})$. The estimates are obtained by only integrating the IMU data. The unit is converted to a degree. Closer to zero yields better results.

Theorems & Definitions (3)

• Remark 1
• Theorem 1
• Remark 2