iMoT: Inertial Motion Transformer for Inertial Navigation

Duc Viet Le; Linh Duy Tran; Paul J.M Havinga; Son Minh Nguyen

REVIEW 3 major objections 5 minor 1 cited by

iMoT: Inertial Motion Transformer for Inertial Navigation

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A transformer that encodes each IMU channel as a time-series token and models velocity uncertainty with learnable query motion particles reports lower trajectory errors than prior learned inertial odometry on four benchmark datasets, with…

desk verdict A real architectural contribution with a solid ablation, but the paper's own Table 2 contradicts its 'consistently outperforms' claim; it deserves peer review after the overstatement and reproducibility gaps are fixed. read the letter →

arxiv 2412.12190 v1 pith:YETFM5XW submitted 2024-12-13 cs.LG cs.AIcs.RO

Son Minh Nguyen , Linh Duy Tran , Duc Viet Le , Paul J.M Havinga This is my paper · ORCID

classification cs.LGcs.AIcs.RO

keywords inertialnavigationodometrytransformerIMUquerymotionparticlesprogressiveseriesdecoupleradaptivepositionalencodingdynamicscoringmechanism

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

This paper proposes iMoT, a Transformer-based inertial odometry method that estimates position from accelerometer and gyroscope readings by learning to emphasize critical motion events and by modeling the uncertainty of each instantaneous velocity segment with a set of learnable query motion particles. The authors claim that the method consistently outperforms existing learned inertial odometry systems on four public datasets, RIDI, RoNIN, OxIOD, and IDOL, and that the advantage is largest on unseen subjects in dynamic, natural placements such as phones freely held or pocketed. On the RoNIN dataset's unseen-subject split, iMoT reports an absolute trajectory error (ATE) of 5.31 m, compared to 6.89 m for CTIN and 6.77 m for TLIO. The paper's central assertion is that separating each sensor series into seasonal and trend-cycle components, adapting positional encodings per modality, and refining query motion particles through cross-modal attention are what make this improvement possible. A careful reader would care because learned inertial odometry is one of the few positioning approaches that works indoors, in smoke, or without radio signals, where drift has historically made it unusable.

What carries the argument

The central machinery is a set of four interlocking modules inside a Transformer encoder-decoder. Progressive Series Decoupler (PSD) applies a centered moving average (orders $k_1=9$ and $k_2=3$) at the start of each encoder layer to split each sensor series $A$ into a trend-cycle component $A_t$ and a residual seasonal component $A_s$, making turns and stillness stand out. Adaptive Positional Encoding (APE) multiplies base sinusoidal embeddings by modality-specific MLP scaling factors, so acceleration and angular-velocity tokens receive position information matched to their temporal content. Adaptive Spatial Sync (ASC) runs a 1x3 convolution plus a channel-attention branch at each residual connection to fuse cross-channel information that pure temporal attention would miss. In the decoder, 128 learnable query motion particles act as positional embeddings that are added to content features, passed through self- and cross-attention over both modalities, and refined by shared-weight MLP velocity corrections. Dynamic Scoring Mechanism (DSM) replaces the ground-truth-dependent inverse-distance scores with an MLP that pools all particles into the final velocity estimate, removing the need for entropy regularization during testing.

What would settle it

Run iMoT on the RoNIN unseen-subject split with the PSD kernel orders changed to $k_1=5$, $k_2=2$ and to $k_1=15$, $k_2=5$, and with PSD removed; if the ATE no longer stays near 5.31 m or the PSD ablation gain shrinks far below the reported 8.29%, the decomposition is a dataset-tuned artifact rather than a general mechanism.

Watch

Extended reading notes

Core claim

In the paper's own terms, the discovery is that motion context in IMU sequences is best encoded by treating each channel's entire time series as a token and then progressively decomposing it, layer by layer, into seasonal and trend-cycle components, so that attention can focus on critical events such as turns, stops, and gait cycles. The decoder then represents the uncertainty of each velocity segment by a set of 128 query motion particles, each acting as a learnable positional embedding that probes cross-modal features from acceleration and rotation tokens; the particles are updated both by gradients and by layer-by-layer velocity corrections, and a dynamic scoring mechanism pools them into a final velocity estimate. With this design, iMoT reports the lowest ATE among compared methods on the unseen-subject splits of RIDI (1.49 m), RoNIN (5.31 m), OxIOD (0.90 m), and IDOL (3.00 m). The authors attribute the gains specifically to the combination of the decoupler, the adaptive positional encoding, the spatial sync, and the particle set with dynamic scoring, rather than to any single module.

Load-bearing premise

The load-bearing premise is that the fixed moving-average decomposition in Eq. 1, with kernel orders $k_1=9$ and $k_2=3$, separates critical motion events such as turns, stops, and gait cycles from noise for every attachment and gait in the test sets.

Editorial extensions

If this is right

On the RoNIN unseen-subject split, iMoT reports an ATE of 5.31 m, a 22.93% reduction over CTIN (6.89 m) and a 21.57% reduction over TLIO (6.77 m).
Ablation on RoNIN attributes a 13.89% ATE reduction to PSD alone, and a further 3.99% reduction to adding the query-particle decoder with DSM on top of the three basic modules.
Because the model uses only IMU input and no external infrastructure, the reported accuracy applies to indoor and GPS-denied contexts where vision or radio positioning fails.
The reported 7.79 GFLOP/s at 200 Hz sampling, lower than RoResNet18's 9.16 GFLOP/s despite more parameters, suggests embedded deployment is feasible if the parameter count is acceptable.
Across IDOL, the method reports a 15.43% improvement in T-RTE and a 12.50% improvement in D-RTE over RoResNet18, the second-best method in that comparison.

Reading between the lines

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

An extension the paper leaves implicit is a sensitivity sweep over PSD's moving-average kernel orders, since the claim that PSD highlights motion events generally would be stronger if accuracy is stable across a small range of odd and even kernel pairs.
The query-motion-particle set behaves like a learned mixture over motion modes; one testable extension is to inspect per-particle attention to check whether distinct particles specialize to turns, straight-line walking, or stairs, which the paper does not report.
The PSD decomposition could plausibly transfer to other inertial-attachment problems such as wrist, ankle, or vehicle IMUs, but only if the kernel orders are re-tuned; the paper evaluates pocket, hand, bag, body, and trolley placements but not those.
The dynamic scoring mechanism removes the test-time need for ground-truth velocities, so an editorially proposed stress test is to port the trained model to an unseen device model or sampling rate and measure how much the ATE changes.

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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

First thing to know: this is a genuine architectural contribution with a serious ablation, but the authors' claim that iMoT 'consistently outperforms' SoTA is contradicted by their own Table 2. The paper is worth engaging, but the overstatement needs fixing.

What's actually new: the combination of Progressive Series Decoupler, Adaptive Positional Encoding, Adaptive Spatial Sync, learnable query motion particles, and Dynamic Scoring Mechanism. The 15-configuration ablation on RoNIN gives credible evidence that each component contributes, especially PSD (13.89% ATE reduction) and DSM (which turns the query particles from a liability into a gain). The compute numbers (7.79 GFLOPS at 200 Hz) are useful. Code is linked.

Soft spots, in order of importance. First, the internal contradiction. The 'State-of-The-Art Performance' section says 'consistently outperforms other SoTA approaches,' but Table 2 shows RoResNet18 winning RIDI Seen ATE (1.64 vs 1.68) and OxIOD Unseen T-RTE (1.15 vs 1.32). To the authors' credit, an appendix openly discusses this and offers plausible explanations (outlier distribution, reduced motion variability in OxIOD). That does not rescue the phrase 'consistently.' The claim should be qualified to 'on dynamic benchmarks' or 'in most evaluated cells.' Second, no error bars, multiple seeds, or significance tests. The 5.31 vs 6.89 m ATE advantage on RoNIN is large and consistent with the cross-dataset pattern, but we can't rule out run-to-run variation. Third, the appendix's PDE formula divides by a sum of zero distances (d(x_t - x_t)); it is clearly a typo, but the metric was used in the paper's boxplots, so it should be corrected. Fourth, the linked repo lacks a commit hash, configuration files, and explicit data splits. For a paper where everything hinges on benchmark numbers, that is a real reproducibility gap.

Where does that leave the central claim? The paper's own data supports a weaker claim: iMoT is a strong new method, typically best on dynamic, high-uncertainty benchmarks, with modest losses in a couple of controlled cells. That is still a publishable contribution.

Who is this for: researchers in learned inertial odometry, sensor fusion, and transformer-based time-series modeling. It deserves a serious referee with expertise in the benchmarks; it should not be desk-rejected, but it needs a revision that fixes the overclaim and reports variance.

Recommendation: send to peer review, conditional on the authors toning down the SOTA claim and addressing reproducibility.

Referee Report

3 major / 5 minor

Summary. iMoT is a Transformer encoder-decoder for inertial odometry from IMU acceleration and angular velocity sequences. The encoder introduces a Progressive Series Decoupler (PSD) that splits each modality into trend and seasonal components, an Adaptive Positional Encoding (APE) that scales sinusoidal position embeddings by modality content, and an Adaptive Spatial Sync (ASC) module for cross-channel feature mixing. The decoder maintains P learnable query motion particles that are refined internally and via cross-attention to the encoded motion and rotation tokens, then pooled by a Dynamic Scoring Mechanism (DSM). The paper reports a 15-configuration ablation on RoNIN and compares against SINS, PDR, RIDI, RoLSTM, RoTCN, RoResNet18, CTIN, and TLIO on RIDI, RoNIN, OxIOD, and IDOL, using ATE, T-RTE, D-RTE, and PDE metrics. The central claim is that iMoT consistently outperforms state-of-the-art methods, particularly in unseen-subject generalization.

Significance. The work is a substantial engineering contribution: it releases code, evaluates across four benchmark datasets, includes a detailed ablation study, and provides a computation-cost analysis showing lower FLOPs than some baselines despite a larger parameter count. If the claimed improvements are reproducible, especially the RoNIN unseen-subject ATE reduction (5.31 m vs 6.77 m for TLIO and 6.89 m for CTIN), the method would advance learned inertial navigation. However, the paper's headline claim of consistent superiority is not fully supported by its own tables, and the lack of statistical uncertainty estimates makes it difficult to judge whether small margins are meaningful. The presence of an appendix that explicitly acknowledges counterexamples to the main claim makes the overstatement a load-bearing issue rather than a cosmetic one.

major comments (3)

[State-of-The-Art Performance, Table 2, and appendix 'Explanation for the inferiority in State-of-The-Art Performance…] The claim in Section 'State-of-The-Art Performance' that 'our proposed method consistently outperforms other SoTA approaches' is contradicted by the paper's own Table 2. In the RIDI seen-subject ATE row, iMoT reports 1.68 m versus 1.64 m for RoResNet18, and in OxIOD unseen-subject T-RTE, iMoT reports 1.32 m versus 1.15 m for RoResNet18. The appendix explicitly admits that RoResNet18 demonstrates 'slightly better T-RTE and comparable D-RTE results relative to our method.' Since 'consistently outperforms' is the paper's central SOTA claim, this is an internal inconsistency. The paper must either qualify the claim (e.g., by reporting a win/loss/tie breakdown over metric-dataset cells) or provide statistical evidence that these losses fall within run-to-run noise. As written, the conclusion is not supported by the reported data.
[All experimental sections] No error bars, confidence intervals, or significance tests are reported for any entry in Table 1 or Table 2. Several comparisons are within very small margins or tie exactly (e.g., RoNIN Seen D-RTE is 0.26 for iMoT and RoResNet18; OxIOD Seen D-RTE is 0.21 for iMoT, RoResNet18, and TLIO). Without multiple random seeds or paired tests, the assertion that iMoT 'significantly outperforms' baselines is not established. In addition, hyperparameters such as the PSD kernel orders k1=9, k2=3, the particle count P=128, and the DSM weighting factor are tuned on RoNIN, so the claim of consistent improvement across datasets would be strengthened by reporting module ablations on at least one additional dataset, rather than only on RoNIN.
[Final paragraph of 'State-of-The-Art Performance' and appendix 'Explanation for the inferiority in State-of-The-Art…] The main text states that iMoT 'exhibits the lowest position drift error (PDE %) with the highest confidence and fewest outliers,' while the appendix states that the PDE plot shows 'our method's lower mean error but a higher percentile of outliers compared to RoResNet18.' These two statements cannot both be true. This is load-bearing because the main text uses the PDE/outlier behavior as evidence of robustness, and the appendix's own explanation contradicts it. The authors should correct the inconsistency or clarify what 'outliers' means in each place, and report the actual outlier fractions from the PDE boxplots.

minor comments (5)

[Ablation Study, Table 1] The text says 'we develop 14 configurations,' but Table 1 lists 15 configurations (i) through (xv). Please correct the count.
[Dynamic Scoring Mechanism, Eqs. (8)-(10)] The paper defines an entropy loss Jent in Eq. (9) but then states that the MLP-based dynamic scoring 'eliminating the need for the entropy loss Jent' and that iMoT is optimized using only Jvel. Please clarify whether Jent is used in any reported configuration or only in intermediate ablation variants that use average pooling.
[Table 1 header] The third metric column is labeled 'D-TRE' in Table 1 but should be 'D-RTE' to match the rest of the paper.
[Figure 1] The blue and magenta signal flows are described in the caption, but several arrows in the figure are not clearly associated with either flow, making it hard to trace the path of controlling signals through the decoder. Please add a more explicit legend or annotate the arrows.
[Adaptive Spatial Sync, Section 'Proposed Method' and Figure 3] The phrase 'an 1 x 3 convolution operated along 3D direction' is ambiguous. Please specify which tensor axes are convolved (temporal vs channel) and clarify what '3D direction' means in this context.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: iMoT is an empirical benchmark paper whose components are trained and evaluated against external ground-truth trajectories, with no equation reducing to a fitted constant or self-citation.

full rationale

This paper does not present a formal derivation chain in which a predicted quantity is equivalent to an input by construction. The core method is a transformer encoder-decoder with learnable modules: Progressive Series Decoupler (PSD) uses a fixed moving-average decomposition (Eq. 1) with kernel orders k1=9 and k2=3, Adaptive Positional Encoding (APE) learns scaling factors from tokens, Adaptive Spatial Sync (ASC) applies convolutions and channel weighting, and the decoder uses learnable query motion particles refined by MLPs. None of these components is defined in terms of the evaluation metric or the final trajectory output; all are trained with a supervised velocity loss (Eq. 8) against ground-truth velocity particles, which is standard supervised learning rather than circularity. The only occurrences of ground-truth data are in the training loss and in the final evaluation metrics (ATE, T-RTE, D-RTE, PDE), and the model is tested on held-out subjects and sequences. Hyperparameters such as kernel sizes, particle count, and token dimension are tuned empirically on the benchmark, but this is ordinary model selection, not a fitted parameter being renamed as a prediction. The paper contains no load-bearing self-citation chain and invokes no uniqueness theorem from the authors' prior work. The appendix's candid admission that RoResNet18 achieves slightly better T-RTE and comparable D-RTE in some OxIOD and RIDI configurations is an internal consistency issue with the phrase 'consistently outperforms', not a circular-reasoning defect. The derivation and evaluation pipeline are self-contained against external ground-truth benchmarks, so the appropriate circularity score is 0.

Assumptions & free parameters 5 free parameters · 3 assumptions · 1 invented entities

The central claim is an empirical architecture-performance claim, so the ledger is dominated by modeling assumptions rather than physical postulates. The key assumptions are that moving-average decomposition isolates meaningful motion events, that 128 query particles cover the motion mode distribution, and that benchmark preprocessing is consistent across compared methods. No new physical entities are introduced; query motion particles are internal latent constructs.

free parameters (5)

PSD moving-average kernel order k1 = 9
Hand-set in Implementation Details; controls the trend/seasonal split in Eq. 1 and no sensitivity analysis is reported.
PSD moving-average kernel order k2 = 3
Hand-set in Implementation Details; must be less than k1 and share parity, but no search is described.
Number of query motion particles P = 128
Selected by ablation on RoNIN (Fig. 4) and described as optimal for that dataset.
DSM weighting factor gamma = not reported
Introduced in Eq. 8 to control the influence of distant particles on the mean particle; no value or sensitivity study is given.
Token dimension = 100 at 100 Hz, 200 at 200 Hz
Chosen based on the sampling rate of each dataset; a standard implementation choice.

assumptions (3)

domain assumption Centered moving-average decomposition (Eq. 1) separates IMU series into trend and seasonal components that correspond to meaningful motion events.
The PSD module relies on this decomposition; the kernel sizes are hand-set and no evidence is given that the decomposition is physically meaningful across all tested placements.
domain assumption A set of P learnable query motion particles can represent the distribution of possible instantaneous velocity segments.
The decoder design assumes that 128 particles cover the relevant motion modes; no uncertainty calibration or coverage analysis is provided.
domain assumption Benchmark ground-truth trajectories and train/test splits are consistent and comparable across all methods in Table 2.
Fairness of the SOTA comparison depends on identical preprocessing, alignment, and data splits, but the exact split protocol is not specified.

invented entities (1)

Query motion particles
purpose: Learned latent hypotheses about the current velocity segment, used as adaptive positional queries in decoder cross-attention to model motion uncertainty.
Internal latent variables with no physical counterpart and no external falsifiable prediction; their only evidence is benchmark accuracy.

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Cite this review

Pith. "Pith review of iMoT: Inertial Motion Transformer for Inertial Navigation." pith.science (2026). https://pith.science/paper/YETFM5XW

@misc{pith2026241212190,
  author       = {Pith},
  title        = {Pith review of: iMoT: Inertial Motion Transformer for Inertial Navigation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YETFM5XW}},
  note         = {Machine review of arXiv:2412.12190}
}

read the original abstract

We propose iMoT, an innovative Transformer-based inertial odometry method that retrieves cross-modal information from motion and rotation modalities for accurate positional estimation. Unlike prior work, during the encoding of the motion context, we introduce Progressive Series Decoupler at the beginning of each encoder layer to stand out critical motion events inherent in acceleration and angular velocity signals. To better aggregate cross-modal interactions, we present Adaptive Positional Encoding, which dynamically modifies positional embeddings for temporal discrepancies between different modalities. During decoding, we introduce a small set of learnable query motion particles as priors to model motion uncertainties within velocity segments. Each query motion particle is intended to draw cross-modal features dedicated to a specific motion mode, all taken together allowing the model to refine its understanding of motion dynamics effectively. Lastly, we design a dynamic scoring mechanism to stabilize iMoT's optimization by considering all aligned motion particles at the final decoding step, ensuring robust and accurate velocity segment estimation. Extensive evaluations on various inertial datasets demonstrate that iMoT significantly outperforms state-of-the-art methods in delivering superior robustness and accuracy in trajectory reconstruction.

Figures

Figures reproduced from arXiv: 2412.12190 by the authors.

**Figure 2.** Progressive Series Decoupler. Progressive Series Decoupler To promote the capture of necessary motion events during encoding, Progressive Series Decoupler (PSD) is introduced at the facade of each encoder layer, breaking down complex temporal patterns of motion and rotation series into two more interpretable components, namely seasonal signals and trend-cycle signals. That is, seasonal signals carry prominent info… view at source ↗

**Figure 3.** Adaptive Spatial Sync. Decoder A given instantaneous velocity segment varies across individuals and is influenced by their unique gaits, giving rise to uncertainties in motion. To address this, we introduce P motion pairs of query motion particles vˆ ∈ R P ×2 and their query content features C ∈ R P ×T into decoder layers, as illustrated in Fig.1. Each pair represents a specific motion mode, collectively modeling m… view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: Ablation Study on the number of query motion [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Cumulative Error Distributions (CDF) with three types of metric types, and boxplot of PDE on RoNIN dataset. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Quantitative Assessment between iMoT and RoResnet18 for Subject 54 on Trajectory 3 in the RoNIN Dataset. Best [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 7.** Figure 7: Quantitative Assessment between iMoT and RoResnet18 for Subject 24 on Trajectory 1 in the RoNIN Dataset. Best [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: Cumulative Error Distributions (CDF) with three types of metric types, and boxplot of PDE on IDOL dataset. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: Cumulative Error Distributions (CDF) with three types of metric types, and boxplot of PDE on OxIOD dataset. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Cumulative Error Distributions (CDF) with three types of metric types, and boxplot of PDE on RIDI dataset. [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

**Figure 11.** Figure 11: Selected visualizations of trajectories for iMoT, CTIN, and RoResNet18 on the IDOL. [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

**Figure 12.** Figure 12: Selected visualizations of trajectories for iMoT, CTIN, and RoResNet18 on the OxIOD. [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]

**Figure 13.** Figure 13: Selected visualizations of trajectories for iMoT, CTIN, and RoResNet18 on the RIDI. [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

**Figure 14.** Figure 14: Selected visualizations of trajectories for iMoT, CTIN, and RoResNet18 on the RoNIN. [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

FDIO: Frequency Decomposed Inertial Odometry
cs.CV 2025-11 conditional novelty 5.0 of 10

Splitting pedestrian IMU signals into smooth and jumpy frequency bands — Mamba on the smooth band, multi-scale convolutions on the jumpy band — cuts average trajectory error by roughly a third versus the RoNIN ResNet ...

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

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Carion, N.; Massa, F.; Synnaeve, G.; Usunier, N.; Kirillov, A.; and Zagoruyko, S. 2020. End-to-end object detection with transformers. In European conference on computer vision, 213--229. Springer

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