NEURAL INERTIAL ODOMETRY

PLATOPreintegration-Based Likelihood Maximization
from Accurate Trajectory Observations
for Neural Inertial Odometry

Haoying Li¹Qihang Liu²Yifan Peng¹Keyan Miao³Junfeng Wu¹

¹ School of Data Science, The Chinese University of Hong Kong, Shenzhen

² School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen

³ Department of Engineering Science, University of Oxford

Explore the method AquaLux dataset Method figure

Learn the IMU measurement model. Propagate motion through visual outages.

OVERVIEW

Learning bias dynamics and uncertainty.

Neural inertial odometry has demonstrated strong potential for motion estimation in challenging environments, yet inertial-only preintegration remains sensitive to IMU bias and uncertainty. PLATO is a unified framework for jointly learning IMU bias dynamics, modeled by a neural ordinary differential equation, and gyroscope and accelerometer noise covariances.

Optimization exploits the sparse structure of the negative log-likelihood. IMU noise-parameter gradients are computed by forward differentiation, while a tailored double-adjoint scheme couples a discrete invariant-error adjoint with a continuous-time adjoint for the bias model. Experiments on EuRoC and AquaLux evaluate inertial preintegration and downstream visual-inertial odometry under intermittent visual degradation.

Likelihood-based learningNeural ODE bias dynamicsUncertainty-aware preintegration

METHOD

A unified likelihood.
Structured, efficient gradients.

Trajectory observations supervise training. The learned bias model operates on IMU inputs at deployment.

Trajectory observations

Ground-truth trajectories and noisy visual-odometry poses provide supervision through their observation models and assumed uncertainties.

Sparse marginal likelihood

Jointly learn bias dynamics and IMU noise statistics by exploiting the sparse information structure of the latent inertial trajectory.

Double-adjoint optimization

Couple an outer invariant-error adjoint with an inner continuous-time bias adjoint. Noise updates use forward covariance sensitivities.

NEURAL BIAS DYNAMICS

A neural ODE models the temporal evolution of accelerometer and gyroscope biases.

MARGINAL NEGATIVE LOG-LIKELIHOOD

Residuals are weighted by the marginal covariance .

Camera-ready training strategy showing bias and covariance updates with structured gradients — The training schedule alternates bias-dynamics and covariance updates after MSE initialization.

EXPERIMENTS

From EuRoC to underwater VIO.

Mean results reported in the camera-ready manuscript. Lower errors are better; protocols and supervision are shown explicitly.

Mean AOE / APE over five EuRoC test sequences
Method	Supervision	Raw integration		OpenVINS
Method	Supervision	AOE (°)	APE (m)	AOE (°)	APE (m)
HL-CBD	GT	3.393	683.675	1.310	0.180
PLATO	GT	3.076	631.279	0.756	0.095
PLATO	VO	3.036	644.071	0.822	0.106

The same OpenVINS backend is used for these downstream results. The manuscript also reports LBP-InVIO as a literature reference with a different backend; it is not included in this controlled-backend summary.

Mean errors over five AquaLux test sequences in the paper’s protocol
Method	Supervision	Preintegration		OpenVINS
Method	Supervision	Rot. RMSE (°)	Pos. RMSE (m)	Rot. RMSE (°)	Pos. RMSE (m)
Raw IMU	—	40.828	3018.438	9.284	1.868
HL-CBD	GT	4.681	354.871	14.524	0.379
PLATO	VO	3.976	313.094	6.224	0.171

This table uses the short-horizon HL-CBD configuration. With a matched 1.6 s horizon, HL-CBD achieves 5.135° / 194.928 m and PLATO 3.976° / 313.094 m in preintegration: PLATO retains lower rotation error, while HL-CBD has lower position error. The supervision sources remain GT and VO.

The paper’s historical evaluation protocol and the current dataset preview are distinct. The preview separately flags Test_005, Test_009 and Test_011 for reference calibration quality.

Peak GPU memory and runtime relative to full-graph AD · RTX 5060 Ti
Window	Full-graph AD (MB)	Double adjoint (MB)	Memory saved	Runtime overhead
16	525.6	351.3	33.2%	24.2%
32	745.5	366.9	50.8%	5.7%
64	1069.3	279.8	73.8%	4.2%
128	2067.2	457.0	77.9%	2.3%

The double-adjoint scheme trades additional computation for lower peak memory. In a separate long-horizon AquaLux profile on an RTX 5090 with batch size 1000, peak memory falls from 22,554.6 to 2,256 MiB.

Underwater robot, representative AquaLux trajectories and visual outages, and a Test_019 VIO comparison from the camera-ready manuscript — Underwater platform, representative trajectories and visual outages, and VIO comparison from the camera-ready manuscript.

Scope and limitations. PLATO is trained offline. The covariance model is isotropic; under noisy trajectory supervision, it acts as an effective likelihood weight rather than an independently calibrated physical sensor covariance. Cross-IMU transfer and out-of-distribution evaluation remain future work.

20recorded sequences

2.09Bstereo events

≈1kHzIMU sampling rate

36light-off intervals

AQUALUX / THE DATASET

Meet AquaLux.

A controlled look at underwater visual failure. Real recordings, paired motion patterns, and the sensors to study what happens next.

Good lighting for learning.
Lights out for testing.

Ten training sequences have generally reliable visual conditions. Ten test sequences include controlled light-off intervals, while inertial sensing and motion capture continue recording.

10 TRAIN10 TEST

Both splits come from the same collection session. The split probes lighting robustness; it does not establish generalization to new sites or devices.

SENSOR INVENTORY20 recordings

Stereo events2,085,742,726 individual events

Asynchronous

Grayscale frames124,725 left + right image messages

346 × 260
≈40 Hz

Inertial measurements1,556,685 IMU measurements

≈999 Hz

Motion captureMarker exports + IMU-body trajectories

120 Hznominal

AQUALUX / INTERACTIVE EXPLORER

Follow the motion.

Choose a recording. Rotate its trajectory, inspect its lighting, and scrub through actual recorded sensor data.

Drag to rotate · Scroll to zoom

Light onLight offCurrent position

— / — s

DURATION—

IMU SAMPLES—

LIGHT-OFF TIME—

RAW SIZE—

Frame brightnessMean pixel value · 0–255

IMU signal

WHAT A VISUAL OUTAGE LOOKS LIKE

The same scene.
A very different signal.

Real left-camera frames from Test_001. Light-off labels use mean brightness below 5, merge gaps up to 0.5 s, and retain intervals of at least 1 s.

9.78%of test image-stream time
falls within retained light-off intervals

Actual grayscale frame from Test_001 with normal lighting — Lighting availableTest_001

Actual grayscale frame from Test_001 during a light-off interval — Lighting unavailableTest_001

THE COMPLETE COLLECTION

Twenty paths. Two conditions.

Overview of all 10 training trajectories — All ten training recordings under generally good lighting. These overview figures come from the historical dataset visualization; the interactive explorer uses the versioned, time-corrected reference.

DATA ACCESS

Start with the data.

AquaLux v0.1.0 · Dataset preview
Hosted on Hugging Face.

HUGGING FACE DATASET

Get AquaLux

Full dataset available on Hugging Face · 20 recordings.

Original sensor recordings, reference trajectories, calibration and light-off annotations. Browse the file inventory on Hugging Face.

DATASET CARD

Know your signals

Sensor units, coordinate frames, clock conventions, splits, and annotation semantics.

Reference conventions

Released trajectories use sensor timestamps and the IMU body frame. Apply the supplied quality masks and keep continuous segments separate. The recorded clock offset is already applied.

Preview status

This is a dataset preview. Licensing and contact metadata are pending. Reference trajectories are mocap-derived candidates; physical accuracy and hardware synchronization have not been independently established. Test_005, Test_009 and Test_011 are excluded from default reference evaluation, while their raw recordings remain available.

PLATOPreintegration-Based Likelihood Maximization from Accurate Trajectory Observations for Neural Inertial Odometry