\textbf{PLATO}: \emph{Preintegration Learning from Accurate Trajectory Observations} for Neural Inertial Odometry

Haoying Li; Qihang Liu; Yifan Peng; Keyan Miao; Junfeng Wu

cs.ROSep 6, 2026

\textbf{PLATO}: \emph{Preintegration Learning from Accurate Trajectory Observations} for Neural Inertial Odometry

Authors: Haoying Li, Qihang Liu, Yifan Peng, Keyan Miao, Junfeng Wu

Abstract

Neural inertial odometry has demonstrated strong potential for motion estimation in challenging environments, yet inertial-only preintegration remains sensitive to IMU bias and uncertainty. To this end, this paper introduces \textbf{PLATO}:\emph{Preintegration Learning from Accurate Trajectory Observations}, a likelihood-based framework that leverages accurate trajectory observations to jointly learn IMU bias dynamics modeled by a neural ordinary differential equation(NODE) and gyroscope and accelerometer noise covariances. Optimization exploits the sparse structure of the negative log-likelihood, with IMU noise-parameter gradients computed by forward differentiation. A tailored double-adjoint scheme couples a discrete invariant-error adjoint with a continuous-time adjoint for the bias NODE, enabling memory-efficient likelihood optimization over the nested bias-dynamics and IMU-preintegration rollouts. Validation on EuRoC shows improved performance, and underwater robot experiments demonstrate applicability under intermittent lighting failures and visual degradation.

Figures & tables

Figure 1: PLATO framework for ATO-supervised neural inertial preintegration.

Figure 2: Training strategy and structured gradient computation.

Figure 3: (a) Overview of the AquaLux dataset. (b) An OpenVINS testing example under intermittent visual outages. The lower plot reports the cumulative position RMSE over time, showing that uncompensated IMU propagation accumulates larger errors after each light-off interval.

Seq.	Raw Integration (AOE $\downarrow$ (deg) / APE $\downarrow$ (m))			OpenVINS (AOE $\downarrow$ (deg) / APE $\downarrow$ (m))
Seq.	(GT) HL-CBD [ 17 ]	(GT) Ours	(VO) Ours	(GT) HL-CBD [ 17 ]	(GT) LBP-InVIO [ 1 ]	(GT) Ours	(VO) Ours
MH02 (149.960 s)	$1.410/161.816$	$\textbf{1.027}/\textbf{85.002}$	$\underline{1.200}/\underline{140.480}$	$1.010/0.220$	$-$	$\underline{0.734}/\underline{0.083}$	$\textbf{0.680}/\textbf{0.079}$
MH04 (98.760 s)	$1.677/\textbf{92.715}$	$\underline{1.371}/\underline{100.679}$	$\textbf{1.331}/106.841$	$\underline{0.650}/0.310$	$-$	$\textbf{0.433}/\textbf{0.192}$	$0.799/\underline{0.249}$
V101 (115.450 s)	$3.536/1486.906$	$\underline{3.177}/\textbf{1310.107}$	$\textbf{3.075}/\underline{1313.105}$	$1.440/0.110$	$-$	$\underline{0.568}/\underline{0.044}$	$\textbf{0.565}/\textbf{0.043}$
V103 (104.655 s)	$5.086/886.348$	$\underline{4.855}/\underline{881.565}$	$\textbf{4.682}/\textbf{855.191}$	$\textbf{0.850}/\underline{0.120}$	$1.584/0.140$	$\underline{1.141}/\textbf{0.111}$	$1.147/\textbf{0.111}$
V202 (144.700 s)	$5.255/790.589$	$\underline{4.948}/\textbf{779.040}$	$\textbf{4.894}/\underline{804.737}$	$2.600/0.160$	$2.198/0.125$	$\textbf{0.903}/\textbf{0.048}$	$\underline{0.919}/\underline{0.050}$

Table 1: EuRoC test-set results for raw integration and OpenVINS. Best and second-best results are marked in bold and underlined , respectively. The supervision source is shown in parentheses.

Objective ablation			Peak GPU memory $\downarrow$
Metric	(GT) MSE	(GT) NLL	$W$	AD (MB)	Double adjoint (MB)	$W$	AD (MB)	Double adjoint (MB)
AOE $\downarrow$ (deg)	0.764	0.756	16	525.6	351.3	64	1069.3	279.8
APE $\downarrow$ (m)	0.102	0.095	32	745.5	366.9	128	2067.2	457.0

Table 2: Left: OpenVINS ablation. Right: peak GPU memory for different window sizes.

Seq.	Light-off ratio (%)	Preintegration (Rot. RMSE $\downarrow$ (deg) / Pos. RMSE $\downarrow$ (m))			OpenVINS (Rot. RMSE $\downarrow$ (deg) / Pos. RMSE $\downarrow$ (m))
Seq.	Light-off ratio (%)	Raw	(GT) HL-CBD [ 17 ]	(VO) Ours	Raw	HL-CBD [ 17 ]	(VO) Ours
Test_001	$10.427$	$36.991/2362.635$	$3.275/187.850$	$\textbf{3.161}/\textbf{152.040}$	$8.456/0.854$	$3.976/\textbf{0.145}$	$\textbf{3.185}/0.149$
Test_005	$10.295$	$39.327/2715.495$	$3.789/204.714$	$\textbf{2.988}/\textbf{168.111}$	$\textbf{4.443}/0.749$	$5.285/\textbf{0.251}$	$5.711/0.264$
Test_007	$9.276$	$39.610/2788.245$	$\textbf{6.182}/472.936$	$6.213/\textbf{436.972}$	$10.635/7.339$	$\textbf{10.000}/\textbf{0.134}$	$10.880/0.180$
Test_017	$8.562$	$46.918/4273.670$	$4.849/499.592$	$\textbf{3.357}/\textbf{444.660}$	$4.479/0.177$	$4.119/0.126$	$\textbf{3.232}/\textbf{0.106}$
Test_019	$10.366$	$41.295/2952.144$	$5.308/409.265$	$\textbf{4.160}/\textbf{363.689}$	$18.408/0.220$	$49.239/1.238$	$\textbf{8.115}/\textbf{0.158}$

Table 3: AquaLux test-set results for preintegration and OpenVINS.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Training sequences provided in AquaLux .

Figure 5: Testing sequences provided in AquaLux .

Panel of Figure 7 — Figure 7: Numerical verification of the invariant-adjoint bias gradients.

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Inertial Odometry Domain Adaptation Mixture-of-Experts Models Inertial Navigation

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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.

Abstract

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