Learned Inertial Odometry for Autonomous Drone Racing

What this paper solves

Visual-inertial odometry fails during aggressive drone flight: motion blur and rapid rotation cause visual feature tracking to break down. IMU-only dead reckoning accumulates drift rapidly from integrated accelerometer and gyroscope bias. This paper trains a neural network to perform inertial odometry by predicting velocity from raw IMU measurements, bypassing camera input entirely.

The result is a localization system that works under the exact conditions where visual methods fail: aggressive maneuvers, motion blur, textureless walls, and rapid lighting changes. It provides a GPS-denied odometry baseline using only the IMU that every platform already carries.

Key mathematical framework

IMU kinematics and the drift problem

Raw IMU integration for position estimate accumulates errors quadratically in time. Given accelerometer measurement $\tilde{a}=a+b_a+n_a$ (true acceleration plus bias plus noise) and gyroscope measurement $\tilde{\omega }=\omega +b_g+n_g$, dead reckoning computes:

Bias $b_a$ is unknown and time-varying. Any error in the bias estimate grows as $O(t^2)$ in position, making raw IMU integration unusable beyond a few seconds.

Learned velocity prediction

Rather than integrating acceleration directly, the network predicts body-frame velocity from a window of recent IMU measurements. Let ${\mathcal{I}}_k=\{({\tilde{a}}_t,{\tilde{\omega }}_t){\}}_{t=k-W}^k$be the IMU window of length $W$. The network maps this to a velocity estimate:

Velocity prediction is less sensitive to bias than acceleration integration because the network can implicitly learn the mean bias from training data. Position is recovered by integrating the predicted velocity:

Attitude $R_k$ is provided by gyroscope integration with online bias estimation, which is accurate over short time windows.

Training loss

The network is trained to minimize velocity prediction error on a dataset of aggressive flight trajectories with ground-truth from a motion capture system:

where $v_k^{B,\ast }$ is the ground-truth body-frame velocity from motion capture. The network architecture is a temporal convolutional network that captures the IMU dynamics relevant for velocity estimation across the window length.

Empirical results

• Accuracy: 0.1 m/s velocity RMSE on aggressive flight trajectories where VIO fails, achieving 10x lower drift than raw IMU integration
• Robustness: Maintains odometry through maneuvers that cause motion blur and VIO tracking failure, including Power Loop and Barrel Roll
• Sensor requirement: IMU only. No camera, no lidar, no GPS. The system operates on the sensor already embedded in every flight controller
• Latency: Real-time on an NVIDIA Jetson AGX Xavier at the IMU integration rate (200-400 Hz)

What this means for robotic automation

Learned inertial odometry demonstrates that the IMU (the one sensor present in every autonomous platform regardless of cost) contains enough information for useful velocity estimation when processed by a learned model rather than integrated analytically. This is a sensor-minimal result: no camera, no map, no external reference.

The dead-reckoning limitation remains: velocity integration still accumulates position error over long timescales. But for short-horizon tasks where the system periodically receives absolute position corrections (from gate detection, anomaly observation, or any other localization event), inertial odometry provides a reliable high-frequency bridge between corrections. The learned model is what makes that bridge accurate enough to be useful at agile flight speeds.