SSIO: Self-Supervised Inertial Odometry

Yuheng Qiu; Yutian Chen; Carlton Cort; Weison Huang; Shibo Zhao; Pieter Abbeel; Rocky Duan; Koushil Sreenath

cs.ROOct 19, 2026

SSIO: Self-Supervised Inertial Odometry

Authors: Yuheng Qiu, Yutian Chen, Carlton Cort, Weison Huang, Shibo Zhao, Pieter Abbeel, Rocky Duan, Koushil Sreenath,

Organizations: Amazon FAR · Carnegie Mellon University · UC Berkeley · Stanford University ·

Abstract

Learning inertial odometry for a new platform usually requires ground-truth trajectories. We show that an inertial odometry model can instead be trained from scratch by a myopic teacher that integrates the IMU over each short window independently, a scheme we call integration self-supervision. Interestingly, although supervised only by short-window velocity changes, the student learns to directly predict velocity, and does so more accurately than its integration teacher. Pose graph distillation then refines the model with sequence-consistent targets from a pose graph over many windows. Training on a new platform therefore no longer requires collecting ground-truth trajectories, but only calibrating the IMU and recording data during normal operation. Across six datasets spanning pedestrians, drones, quadrupeds, and a humanoid, the same recipe with no velocity or position labels trains models that come within 0.07~m/s average velocity error of a same-architecture supervised baseline.

Figures & tables

Fig. 2 : Integration Self-Supervision trains the motion network to match the body-frame velocity change predicted by the frozen integration teacher under a squared velocity-change loss, supervising only the velocity mean. Pose Graph Distillation (PGD) builds a full-sequence pose graph from the teacher’s IMU factors and the network’s velocity factors. The graph posterior $\mathbf{v}^{\mathrm{opt}}$ then supervises the network through an L2 loss. Velocity Regularization , $\mathcal{L}^{\mathrm{reg}}$ , is used over detected static frames.

Fig. 3 : Motion network architecture used for both stages of self-supervised training and the supervised AirIO † baseline.

Supervised Learning
	TLIO		EuRoC		Blackbird		MIPO		GrandTour		Humanoid
Method	AVE $\downarrow$	ATE $\downarrow$	AVE $\downarrow$	ATE $\downarrow$	AVE $\downarrow$	ATE $\downarrow$	AVE $\downarrow$	ATE $\downarrow$	AVE $\downarrow$	ATE $\downarrow$	AVE $\downarrow$	ATE $\downarrow$
AirIMU [ 22 ]	20.83	–	13.42	–	46.95	–	1.958	39.07	2.448	334.8	0.618	–
RoNIN [ 17 ]	0.160	2.420	0.661	9.011	0.948	16.49	0.157	0.429	0.102	3.894	0.163	1.989
TLIO [ 19 ]	0.161	2.872	0.656	8.541	0.972	15.54	0.160	0.487	0.106	4.327	0.163	1.737
AirIO [ 23 ]	0.081	1.890	0.335	3.720	0.318	6.100	0.120	0.310	0.068	3.190	0.087	1.260

TABLE II : Self-Supervised Learning from Scratch. We report AVE (m/s) and ATE (m) across six datasets. Supervised rows are trained with ground-truth labels and serve as reference; ours are trained from random initialization without velocity or position labels.

Dataset	Time	Length	Max Speed
TLIO [ 19 ]	31.6 h	42.3 km	6.0 m/s
EuRoC [ 6 ]	22.5 min	892 m	2.9 m/s
Blackbird [ 1 ]	5.0 h	28.4 km	8.7 m/s
MIPO [ 28 ]	58.6 min	1.4 km	6.6 m/s
GrandTour [ 12 ]	5.65 h	10.3 km	1.5 m/s
Humanoid	1.31 h	1.9 km	3.9 m/s

TABLE I : Evaluation datasets. Six datasets on six distinct embodiments, spanning different IMU grades and motion patterns.

Fig. 5 : Supervision window ablation on TLIO. Velocity-change error $\|\Delta\hat{\mathbf{v}}^{\mathrm{net}}_{ij}-\Delta\mathbf{v}^{\star}_{ij}\|_{2}$ [m/s] over evaluation and training horizons, where $\Delta\mathbf{v}^{\star}_{ij}$ is the ground-truth body-frame velocity change; red cells underperform and blue cells outperform the integrator.

Fig. 6 : Cross-dataset transfer over five datasets. Each cell reports AVE for a model trained on one dataset and evaluated on another. Models trained on the target dataset outperform transferred models, showing the importance of training on the target distribution. The traces show a representative TLIO–Blackbird mismatch.

Dataset (source)	Reference tilt	Estimated tilt	Tilt error
TLIO (gyro)	0.109 / 3.21	0.133 / 3.81 (+22%)	$<1^{\circ}$
MIPO (AHRS)	0.182 / 1.63	0.235 / 1.41 (+29%)	$0.9^{\circ}$

TABLE IV : Attitude source in the teacher. Test AVE (m/s) / ATE (m) of Ours with the reference tilt and with a tilt estimated from the IMU alone: the gyroscope integrated from the sequence start on TLIO, the onboard AHRS on MIPO. Parentheses: AVE change relative to the reference column.

Fig. 9 : Raw-IMU Stationary Window Detector performance vs. GT stationary windows for two ANYmal GrandTour sequences, ETH-3 (top) and EIG-1 (bottom).

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	TLIO	EuRoC	Blackbird	MIPO	GrandTour (quadruped)		Humanoid
	(pedestrian)	(drone)	(drone)	(quadruped)	IMU-only	joints
Batch size	512	64	512	256	256	256	512
Supervision horizon [s]	5.12	1.22	2.43	0.41	3.65	3.65	1.22
Learning rate	1e-3	1e-3	1e-3	5e-5	5e-5	5e-5	1e-3
Epochs	40	150	120	240	120	60	128
Regularization weight $\lambda_{\mathrm{reg}}$	0.25	0.1	0.1	0.01	1.0	0.1	1.0

Appendix

TABLE VI : Integration self-supervision training configuration. Supervision horizon is the velocity-increment window length used during integration self-supervision.

Keyframes $N$	Dense (Cholesky)	Sparse (BSR + cuDSS)	Speedup
128	63.4 ms	35.3 ms	$1.8\times$
512	OOM	167.9 ms	n/a
1024	OOM	438.7 ms	n/a

Appendix

TABLE VII : Pose-graph solve cost at batch size

B=128

on a single NVIDIA RTX 5090 (

32

GB), mean over

20

solves. Both backends return the same solution; OOM marks configurations whose dense memory exceeds the device.

Fig. 12 : Position and velocity on six sequences from the GrandTour Test set.

Fig. 13 : Position and velocity on six sequences from the TLIO Test set.

Fig. 14 : Position and velocity on six sequences from the EuRoC Test set.

Inertial Odometry

Inertial odometry estimates position and orientation over time from motion sensors, often combining inertial data with other measurements.

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DINS-IO: Learned Inertial Odometry via Differentiable INS Consistency

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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.

Abstract

Inertial Odometry

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