VeloBins: Learning Velocity and Its Uncertainty via Bins and Error-Conditioned Gaussian Labels for Aerial Inertial Odometry
Authors: Maulana Bisyir Azhari, Seungwook Lee, Donghun Han, Sung Jun Park, David Hyunchul Shim
Abstract
Inertial odometry (IO) is critical for aerial robots, where aggressive maneuvers and poor lighting degrade visual sensors. Recent learning-based IO methods improve traditional integration-based approaches by learning motion priors from IMU and platform-specific sensors, then fusing the predictions within an extended Kalman filter. However, learning velocity through regression is difficult, while jointly estimating uncertainty with a separate decoder and negative log-likelihood (NLL) loss further complicates training and can lead to over-confident estimates. We introduce VeloBins, which reformulates velocity regression as classification over discretized velocity bins. We decode both the velocity from the bin distribution's expectation and the uncertainty from its variance, removing the need for a separate uncertainty decoder. We further supervise the uncertainty explicitly using an error-conditioned Gaussian label centered at the ground-truth velocity, with a standard deviation set to the velocity error. We evaluate VeloBins on four aerial datasets, ranging from free-form aggressive flights and a 27 g nano-quadrotor to drone racing at over 21~m/s. VeloBins achieves the lowest average errors on all four datasets, reducing velocity, relative trajectory, and absolute trajectory errors by 3-27%, 8-40%, and 6-53%, respectively, compared with the strongest baseline. Notably, the proposed supervision achieves the lowest NLL and best filter consistency despite never optimizing an NLL loss. The code will be available upon acceptance.
The training of learned inertial odometry depends on dense, high-precision position ground truth from motion capture, visual-inertial odometry or SLAM, which is costly and hard to acquire at scale. We propose DINS-IO, which learns inertial odometry directly from raw IMU streams without position labels. Our key insight is that the strapdown INS velocity recursion is a strong, fully differentiable consistency prior: the predicted velocity, rotated into the navigation frame, must agree with the integrated specific force up to an unknown initial velocity and a constant accelerometer bias. We cast this constraint as a sliding-window least-squares problem with a globally shared bias, solve it in closed form, and use the solver residual as a self-supervised loss whose gradient flows back to the network through the analytic solution. To supply this per-sample constraint, we design a high-frequency network that emits dense body-frame velocity at the IMU rate. Since the self-supervised network learns consistent motion but its velocity is not yet metrically calibrated, we calibrate it to true metric velocity from a few labeled trajectories by directly supervising the predicted body-frame velocity and adapting only low-rank (LoRA) patches. On standard benchmarks, DINS-IO pretrained self-supervised and fine-tuned with a small fraction of labels matches or surpasses fully supervised baselines.
Robust inertial odometry is essential for various carriers when external sensing is unreliable. Learning-based methods reduce integration drift by capturing local motion priors, but these methods often remain tied to a particular carrier, limiting generalization across heterogeneous platforms. We present MosaicIMU, a carrier-conditioned Mixture-of-Experts (MoE) pretraining-and-adaptation framework for generalizable neural inertial odometry. MosaicIMU uses a prototype-based router to compose carrier-specific expert features, decodes local velocity and uncertainty constraints, and integrates them with a history-aware EKF. For unseen domain adaptation, it freezes the pretrained base model and learns a new lightweight expert residual branch. For edge-deployment, it further reuses the router to select informative online samples for efficient incremental updates. Experiments show that MosaicIMU consistently outperforms learning-based baselines, reducing average ATE and RTE-10s by 40% and 34%, respectively. These results highlight that MosaicIMU provides a scalable pretraining-to-deployment paradigm for generalizable and adaptive neural inertial odometry.
In this study, the learning-based inertial odometry problem is investigated using raw IMU measurements obtained from the EuRoC MAV benchmark dataset. Instead of absolute position regression-a formulation that may lead to large constant errors-the models are trained to estimate the incremental displacement (Δp) over a fixed 50 ms sliding window, and the full trajectory is reconstructed through numerical integration. A standard Multi-Layer Perceptron (MLP) is compared with a Kolmogorov-Arnold Network (KAN) equipped with learnable B-spline activations. Although KAN has 6.9 times fewer parameters than MLP (8,444 versus 57,859), it produces a 44% lower error in terms of final cumulative drift on the test trajectory (9.61 m versus 17.23 m). In addition, KAN exhibits more stable behavior in terms of long-term error accumulation, with lower P_50 and P_90 cumulative drift values. These findings indicate that learnable B-spline-based activations have the potential to reduce error accumulation in the inertial odometry problem.