KISS-IMU: Self-supervised Inertial Odometry with Motion-balanced Learning and Uncertainty-aware Inference

Geonmo Yang; Hogyun Kim; Jiwon Choi; Juhui Lee; Younggun Cho

KISS-IMU: Self-supervised Inertial Odometry with Motion-balanced Learning and Uncertainty-aware Inference

T0 review · 3 major / 0 minor · reviewed 2026-07-15 · grok-4.5

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Pith's one-line read An IMU-only network can learn odometry without ground truth by training on selective LiDAR registration and pose-graph poses, then stay accurate by balancing rare motions and weighting by its own uncertainty.

desk verdict Useful self-supervised IMU recipe with real multi-platform evidence; the main soft spot is partial circularity in training-time PGO pseudo-labels, not a collapse of the result. read the letter →

arxiv 2603.06205 v2 pith:AA5PQFQO submitted 2026-03-06 cs.RO

Jiwon Choi , Hogyun Kim , Geonmo Yang , Juhui Lee , Younggun Cho This is my paper · ORCID

classification cs.RO

keywords inertialodometryself-supervisedlearningIMUmotion-balancedtraininguncertainty-awareinferenceposegraphoptimizationLiDARregistrationquadrupedrobots

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Most learned inertial odometry systems need expensive, high-precision ground-truth trajectories, which limits them to labs or carefully instrumented routes and hurts generalization. This paper shows that a pure IMU network can instead be trained from pseudo-labels produced by ordinary LiDAR ICP registration and pose-graph optimization, with no motion-capture system and no second learnable modality. Two design choices make the approach work: a Gaussian-mixture model reweights training so rare but critical maneuvers are not drowned out by common straight-line motion, and at inference the network’s predicted uncertainties adaptively reweight IMU versus LiDAR constraints inside the pose graph. Experiments on wheeled and quadruped platforms, including harsh outdoor terrain where ground truth is unobtainable, claim competitive or better absolute and relative pose accuracy than supervised baselines even when only 20 percent of a single training sequence is used. The practical upshot is that IMU-based odometry can be scaled to new robots and environments without the usual labeling bottleneck.

What carries the argument

Selective pseudo-labeling (symmetric-overlap choice between ICP and PGO) plus GMM motion-balanced loss reweighting and uncertainty-aware adaptive PGO at inference; together they replace ground-truth supervision while keeping learning stable across motion patterns and inference strong under varying sensor confidence.

What would settle it

Train the identical IMU network on the same sequences with true motion-capture labels versus the paper’s selective ICP/PGO pseudo-labels; if the pseudo-label model systematically underperforms or collapses on sequences where ICP overlap is low, the self-supervision claim fails.

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Extended reading notes

Core claim

A neural IMU corrector and uncertainty estimator can be trained self-supervised solely from selective LiDAR-derived relative poses (ICP or pose-graph optimization chosen by symmetric overlap score) and, when training is reweighted by a Gaussian mixture over motion descriptors and inference uses the learned covariances for adaptive pose-graph weights, produces competitive generalization on unseen sequences and platforms without ground truth or jointly trained visual or LiDAR networks.

Load-bearing premise

The chosen LiDAR ICP or pose-graph relative pose is accurate and unbiased enough to supervise the IMU network, even though the pose graph already mixes in IMU constraints and ICP can fail in featureless geometry.

Editorial extensions

If this is right

Learned IMU odometry can be trained and deployed on platforms and terrains where centimeter-level ground truth cannot be collected.
Only the IMU network needs learning; LiDAR is used as a disposable geometric teacher, so the trained IMU model can later run alone or with other sensors.
Balancing motion components via GMM reweighting can improve generalization with far less training data than simply collecting more of the dominant motion.
The same selective-pseudo-label and adaptive-weight recipe can be plugged into other existing IMU networks without redesigning their architectures.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the pseudo-label quality remains high under aggressive quadruped gaits, the same pipeline could support online or lifelong IMU adaptation without ever returning to a motion-capture facility.
The GMM motion descriptor may transfer across platforms once standardized, enabling a shared motion vocabulary for multi-robot IMU pre-training.
Degenerate geometry that simultaneously fools both ICP and the training-time PGO would still produce silent label noise; an explicit degeneracy detector would be a natural next safeguard.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing worth knowing is that they train only an IMU correction/uncertainty network from selective LiDAR ICP/PGO relative poses—no ground truth, no jointly learned visual or LiDAR network—and get competitive or better generalization on unseen sequences and platforms, including with 20% of one training sequence and a no-GT In-House quadruped case.

What is actually new is the packaging, not the individual parts. Preintegration, ICP, PGO, GMM motion clustering (TartanIMU-style), uncertainty losses (AirIMU-style), and class-balanced reweighting already exist. The combination is a clean self-supervised IO pipeline: geometry-derived pseudo-labels supervise a pure IMU net, GMM reweights rare motions for “stable” training, and learned covariances drive adaptive PGO weights at inference for “strong” fusion. They only learn the IMU; LiDAR is a fixed supervisor. That design choice is honest and practical.

They do the empirical work well. Botanic Garden, DiTer++ (quadruped), and a harsh In-House crater dataset; 100/60/20% data ablations; component ablations (GMM, adaptive weights); trajectory plots; APE significance tests. The feasibility table is the right argument for self-supervision: supervised baselines cannot even be trained when mocap is impossible. Motion-balance figures and Wasserstein distances between sequences make the generalization story concrete rather than hand-wavy.

The soft spot the stress-test flags is real but not fatal. Training PGO (Eqs. 6–7) already includes IMU preintegration residuals from the network’s current corrections. When s_PGO wins the overlap selection, the pseudo-label is partly a joint optimum, so the network is not purely learning from external geometry. Overlap selection and fixed information weights reduce but do not remove that loop. Gains over Baseline*/AirIMU* may therefore mix geometric teaching with self-consistency. That is the load-bearing assumption; it does not invalidate the system result, but it means the “LiDAR-only supervision” claim is only partially true. Minor other notes: free parameters (G, β, ε, w’s, κ/τ’s) are not fully ablated, and the deliberately harsh single-sequence/30-epoch protocol (TLIO at 100) complicates fairness.

Math and citation pattern look solid—standard preintegration, sensible losses, related work covers the right IO and motion-analysis papers. This is for people who care about deployable IMU learning without mocap. I would send it to peer review; the circularity needs tighter discussion or an ICP-only ablation, not a desk reject. Worth engaging if you work on self-supervised state estimation.

Referee Report

3 major / 0 minor

Summary. KISS-IMU proposes a self-supervised inertial odometry pipeline that trains only an IMU correction/uncertainty network using pseudo-labels from LiDAR ICP and pose-graph optimization (PGO), without ground-truth poses or a jointly learned visual/LiDAR network. Relative poses between consecutive scans are obtained by ICP or by a short-horizon PGO that fuses ICP and IMU preintegration; the source with higher symmetric overlap is retained as the supervisory label. Training reweights samples via a GMM over hand-crafted IMU-window features to balance rare and dominant motions, and inference uses learned covariances plus LiDAR overlap to adaptively weight IMU and ICP factors in PGO. Experiments on Botanic Garden, DiTer++ (quadruped), and an In-House planetary-analog dataset report competitive RPE/APE versus TLIO, AirIMU, and AirIO under deliberately limited training (single sequence, 20–100% data, 30 epochs), with ablations of GMM balancing and adaptive weighting and a feasibility argument where ground truth is unavailable.

Significance. If the supervision is sufficiently external and the gains hold under stronger controls, the work is practically significant: it targets a real bottleneck (GT-dependent IO) and demonstrates deployability on dynamic quadrupeds and feature-poor outdoor terrain where motion-capture supervision is infeasible. The separation of a pure IMU network from a non-learned LiDAR supervisor, the GMM motion-balancing idea, and the uncertainty-aware inference PGO are useful design patterns for scalable robot learning. Multi-dataset tables, data-fraction ablations, component ablations, and statistical APE tests give the empirical claims more weight than typical short IO papers. The main significance risk is whether reported gains partly reflect self-consistency of IMU-in-the-loop PGO rather than pure geometric teaching; resolving that would strengthen the contribution for the field.

major comments (3)

Sec. III-B and Eqs. (6)–(7): training-time PGO already includes IMU preintegration residuals C_ΔR_IMU, C_Δv_IMU, C_Δp_IMU built from the network’s corrected measurements (Eqs. 2–3). When s_PGO > s_ICP, the selected pseudo-label ΔT_i,i+1 is therefore a joint optimum that already incorporates the current network state, and the pose/velocity losses (Eqs. 9–14) then supervise the network partly against its own (or weakly constrained) estimates. Symmetric-overlap selection (Eq. 8) chooses the higher-scoring source but does not remove IMU factors from the PGO that produced that source. This soft circularity is load-bearing for the claim of ground-truth-free, geometry-derived, non-joint supervision. Please (i) report selection frequencies of ICP vs PGO on each dataset/split, (ii) add an ICP-only pseudo-label ablation (no IMU terms in the supervisor), and (iii) discuss residual self-reinforcemen
Sec. IV-A.3 and Table I: the training protocol deliberately uses a single sequence and only 30 epochs (TLIO 100) to stress generalization. That is a useful stress test, but it weakens the claim of competitive or superior generalization relative to supervised SOTA under standard training budgets. Either retrain all learning baselines under matched full-data multi-sequence protocols with recommended epochs, or reframe the contribution more narrowly as “data-efficient / GT-free under scarce labels” rather than broad superiority. Also clarify why TLIO alone is given 100 epochs and whether that choice affects ranking on seen sequences.
Table II and Fig. 8 (In-House): feasibility without GT is an important practical point, but the only evidence is qualitative mapping. Without any quantitative proxy (e.g., loop-closure consistency, multi-session map alignment, or comparison against a strong LiDAR-inertial baseline such as FAST-LIO2/Point-LIO on the same logs), the extreme-condition claim remains anecdotal. Add at least one quantitative consistency metric or a comparison to a classical LIO system on In-House.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity in training supervision: PGO pseudo-labels (when selected) already incorporate the IMU network's own preintegrated corrections, so the network is partly trained against a joint optimum that depends on its current outputs.

self definitional [Sec. III-B, Eqs. (6a–d), (7), and selective fusion via Eq. (8)]
"To obtain more reliable pseudo-labels, we formulate a PGO that jointly considers LiDAR and IMU constraints... C_training := C_ΔT_ICP + C_ΔR_IMU + C_Δv_IMU + C_Δp_IMU ... We evaluate both s_ICP = s_overlap(ΔT_ICP) and s_PGO = s_overlap(ΔT_PGO), selecting the transformation with the higher overlap score as our pseudo-label. ... These pseudo-label states {R^W_{i+1}, v^W_{i+1}, p^W_{i+1}} serve as supervision for the IMU-predicted states in our loss functions"

The IMU residual terms inside C_training are exactly the preintegrated quantities (Eqs. 3) obtained from the network's corrected measurements (Eq. 2). When s_PGO wins the selection, the chosen ΔT_pseudo is therefore a joint optimum that already depends on the current network parameters θ. The subsequent pose/velocity/uncertainty losses (Eqs. 9–14) then update θ against a target that is partly a function of θ itself. This is self-definitional supervision rather than pure external geometric teaching; the selective overlap only chooses the source, it does not remove the IMU terms from the PGO that generated it.

full rationale

The paper's central claim of pure self-supervised IMU learning from geometry-derived (LiDAR ICP/PGO) pseudo-labels without ground truth or jointly learned modalities is only partially true. The training PGO cost explicitly mixes ICP geometric terms with IMU preintegration residuals that are produced by the same network being optimized; when the higher-overlap source is the PGO solution, the supervisory relative pose is therefore a function of the network's current corrections. Symmetric-overlap selection and fixed information weights mitigate but do not eliminate the dependence. GMM motion reweighting and inference-time adaptive weighting are independent of this loop and introduce no additional circularity. The result is soft self-reinforcement risk rather than definitional equivalence or a fitted-parameter-as-prediction, so the score is moderate (4). No load-bearing self-citation uniqueness claims or renamed known results appear. The method remains self-contained against external benchmarks once the supervision loop is acknowledged.

Assumptions & free parameters 7 free parameters · 5 assumptions · 3 invented entities

The central claim rests on standard IMU preintegration and ICP/PGO machinery plus several hand-chosen training and fusion knobs. No new physical entities are postulated; the main invented constructs are the selective pseudo-label pipeline and the GMM motion-reweighting scheme for IO. Pseudo-label quality and the partial use of IMU inside training PGO are the critical domain assumptions.

free parameters (7)

GMM component count G
Chosen via BIC on training motion descriptors; reported G=7 on DiTer++ Forest. Controls motion clustering granularity and thus reweighting.
class-balance β for motion reweighting
Controls strength of rare-motion upweighting (w_g = (1-β)/(1-β^{N_g})); value not specified numerically in text.
uncertainty loss scale ε
Scales covariance-aware terms in L_total (Eq. 11); free training hyperparameter.
training PGO scalar weights w1–w4
Fixed diagonal information weights for ICP and IMU factors during pseudo-label PGO; held constant but not numerically reported.
inference scaling factors κ_r, κ_p, τ_R, τ_v, τ_p
Hand-set multipliers in adaptive C_inference (Eq. 15); affect how strongly LiDAR vs IMU constraints are trusted.
IMU window duration Δt_w
Typically 0.2 s for motion descriptors and RPE intervals; design choice that defines what counts as a motion sample.
training protocol (single sequence, 30 epochs; TLIO 100)
Deliberately constrained schedule used for all main comparisons; shapes reported generalization gaps.

assumptions (5)

domain assumption Standard manifold IMU preintegration and error-state covariance propagation correctly map corrected measurements and learned η into relative ΔR, Δv, Δp and Σ (Forster et al.; AirIMU-style).
Sec. III-A Eqs. 3–5; entire supervision and uncertainty path depends on this model.
domain assumption ICP (or small_gicp/KISS-ICP-style registration) plus symmetric overlap scoring yields a geometrically trustworthy relative pose often enough to supervise IMU learning without ground truth.
Sec. III-B; core of the self-supervised claim.
ad hoc to paper A GMM on hand-crafted IMU window features captures motion modes whose reweighting improves generalization rather than distorting the loss.
Sec. III-C; motivated by TartanIMU/class-balanced loss but applied specifically as IO sample weights.
ad hoc to paper Selecting max(s_ICP, s_PGO) prevents the network from systematically reinforcing its own errors despite IMU factors inside training PGO.
Sec. III-B selective fusion paragraph; mitigates but does not prove independence of labels.
domain assumption Levenberg–Marquardt PGO with fixed or adaptive diagonal information matrices is an adequate fusion backend for both pseudo-label generation and inference.
Sec. III-B/D; PyPose LM used throughout.

invented entities (3)

KISS-IMU selective pseudo-label supervisor (ICP vs PGO by symmetric overlap)
purpose: Replace ground-truth poses with geometry-derived relative poses for pure IMU network training.
Pipeline is assembled from known tools but defined as the paper’s self-supervision mechanism; independent evidence is only the empirical tables, not an external theorem.
GMM motion-aware sample weights w_GMM for IO loss
purpose: Balance rare vs dominant motions during self-supervised training to stabilize learning.
Adaptation of class-balanced weighting to IMU motion clusters; support is ablation/t-SNE, not external validation of the entity itself.
Sensor confidence-aware adaptive PGO cost C_inference
purpose: Strengthen inference by reweighting LiDAR and IMU factors from overlap and learned Σ^{-1}.
Inference-time construct combining known quantities; evaluated via Ours vs Ours†/‡ ablations.

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Cite this review

Pith. "Pith review of KISS-IMU: Self-supervised Inertial Odometry with Motion-balanced Learning and Uncertainty-aware Inference." pith.science (2026). https://pith.science/paper/AA5PQFQO

@misc{pith2026260306205,
  author       = {Pith},
  title        = {Pith review of: KISS-IMU: Self-supervised Inertial Odometry with Motion-balanced Learning and Uncertainty-aware Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AA5PQFQO}},
  note         = {Machine review of arXiv:2603.06205}
}

read the original abstract

Inertial measurement units (IMUs), which provide high-frequency linear acceleration and angular velocity measurements, serve as fundamental sensing modalities in robotic systems. Recent advances in deep neural networks have led to remarkable progress in inertial odometry. However, the heavy reliance on ground truth data during training fundamentally limits scalability and generalization to unseen and diverse environments. We propose KISS-IMU, a novel self-supervised inertial odometry framework that eliminates ground truth dependency by leveraging simple LiDAR-based ICP registration and pose graph optimization as a supervisory signal. Our approach embodies two key principles: keeping the IMU stable through motion-aware balanced training and keeping the IMU strong through uncertainty-driven adaptive weighting during inference. To evaluate performance across diverse motion patterns and scenarios, we conducted comprehensive experiments on various real-world platforms, including quadruped robots. Importantly, we train only the IMU network in a self-supervised manner, with LiDAR serving solely as a lightweight supervisory signal rather than requiring additional learnable processes. This design enables the framework to ensure robustness without relying on joint multi-modal learning or ground truth supervision. The supplementary materials are available at https://sparolab.github.io/research/kiss_imu.

Figures

Figures reproduced from arXiv: 2603.06205 by the authors.

**Figure 1.** KISS-IMU performance on unseen LAWN sequence (trained on Forest, both from DiTer++). (a) Training without a Gaussian mixture model (GMM) weighting: Imbalanced motion components bias learning toward dominant patterns, causing trajectory drift and poor generalization. (b) Training with GMM weighting: Our balanced motion components mitigate bias and improve generalization. Red boxes in (a) indicate failures in regions … view at source ↗

**Figure 2.** Our inertial odometry (IO) framework follows the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Our proposed network architecture. A CNN-GRU encoder [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: t-SNE visualization of motion pattern clustering with quantita [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: Motion pattern analysis using GMM across [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Trajectory comparison on unseen sequences (a) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Motion component weighting before (imbalanced) and after [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: Mapping results comparison on In-House dataset. (a) Aerial view of crater-filled planetary terrain with Unitree B2 quadruped robot. (b) Our mapping results. The proposed method maintains consistent mapping quality despite challenging environmental and motion conditions…

**Figure 9.** Figure 9: Absolute pose error (APE) box plots on unseen sequences: [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed July 15, 2026 · model on record in the stance chip above.

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