AirIMU: Learning Uncertainty Propagation for Inertial Odometry

TL;DR

AirIMU tackles non-deterministic IMU noise in inertial odometry by a hybrid approach that couples a data-driven uncertainty model with a model-based, differentiable IMU integrator. It introduces differentiable pre-integration and covariance propagation to supervise long-horizon state and uncertainty, enabling end-to-end learning and robust GPS fusion via IMU-GPS PGO. Across a broad spectrum of IMUs and platforms—including hand-held, vehicle, and helicopter missions—AirIMU achieves substantial gains in IMU pre-integration accuracy and fusion performance, with a notable 31.6% improvement in GPS-PGO ATE and enhanced long-term stability when jointly training uncertainty with noise correction. The work provides an open, scalable toolkit for differentiable IMU integration and covariance propagation within PyPose, supporting future multi-sensor inertial navigation research and deployment."

Abstract

Inertial odometry (IO) using strap-down inertial measurement units (IMUs) is critical in many robotic applications where precise orientation and position tracking are essential. Prior kinematic motion model-based IO methods often use a simplified linearized IMU noise model and thus usually encounter difficulties in modeling non-deterministic errors arising from environmental disturbances and mechanical defects. In contrast, data-driven IO methods struggle to accurately model the sensor motions, often leading to generalizability and interoperability issues. To address these challenges, we present AirIMU, a hybrid approach to estimate the uncertainty, especially the non-deterministic errors, by data-driven methods and increase the generalization abilities using model-based methods. We demonstrate the adaptability of AirIMU using a full spectrum of IMUs, from low-cost automotive grades to high-end navigation grades. We also validate its effectiveness on various platforms, including hand-held devices, vehicles, and a helicopter that covers a trajectory of 262 kilometers. In the ablation study, we validate the effectiveness of our learned uncertainty in an IMU-GPS pose graph optimization experiment, achieving a 31.6\% improvement in accuracy. Experiments demonstrate that jointly training the IMU noise correction and uncertainty estimation synergistically benefits both tasks.

Figures (11)

• Figure 1: Left: Traditional methods with empirically set uncertainty parameters often fail to capture noise inherent in the sensor accurately. Middle: AirIMU corrects the IMU noise and predicts the corresponding uncertainty of the integration. Notably, its covariance propagation is differentiable, promoting efficient training. Right: Learning-based methods predict velocity and the corresponding covariance but lack interpretability and generalizability across different data domains.
• Figure 2: We evaluate our algorithm on IMUs with different prices and drift rates. Sensor quality is evaluated based on the gyroscope’s in-run bias stability metric. Our evaluation spans the full spectrum of IMUs, including automotive-grade, industrial-grade, tactical-grade, and navigation-grade IMUs.
• Figure 3: Right: We employ a CNN-GRU encoder to capture IMU features ($f$) from raw IMU accelerometer ($a_k$) and gyroscope ($w_k$) measurements. Subsequently, these features are decoded to obtain IMU corrections ($\sigma_{acc}$, $\sigma_{gyro}$). Left: We add the raw measurements with learned corrections, generating corrected IMU measurements ($\hat{a}_k$ and $\hat{w}_k$). The learned uncertainties ($\eta$) are propagated to estimate the corresponding covariance matrix ($\Sigma$).
• Figure 4: This graph presents the parallel scan we use to accelerate the cumulative product in our IMU integration. Given a sequence of gyroscope input from $R_1$ to $R_n$, the algorithm iterates through $\log(n)$ layers. In each layer $i$, it updates the last $N-2^i$ elements by multiplying the first $2^i$ elements. In this algorithm, each layer is a parallel batch that supports parallel computation.
• Figure 5: Pose graph optimization of a GPS signal with IMU pre-integration. The state of the graph is defined as $x_{i}$ constrained by two different observations: IMU ($\Delta p$, $\Delta v$ and $\Delta r$) and GPS ($\hat{p}_i$). We back-propagate the gradient through the IMU pre-integration and covariance propagation to learn the integration and noise model.