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arxiv: 2605.07412 · v2 · pith:XSHKFFFC · submitted 2026-05-08 · cs.LG · cs.AI

Tracking Large-scale Shared Bikes with Inertial Motion Learning in GNSS Blocked Environments

Feng Liu (1) , Kejia Li (1) , Zhiwei Yang (2) , Chunwei Yang (2) , Qun Li (2) , Guobin Wu (2) , Qiang Ni (3) , Ruipeng Gao (1) ((1) Beijing Jiaotong University
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(2) DiDi Company (3) Lancaster University)
This is my paper

Reviewed by Pith2026-06-30 23:21 UTCgrok-4.3pith:XSHKFFFCopen to challenge →

classification cs.LG cs.AI
keywords inertial navigationmixture of expertsbike trackingGNSS denied environmentsmechanical constraintswheel speed estimationshared mobilitypedalling patterns
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The pith

Integrating pedalling mechanics with a mixture-of-experts model enables accurate inertial tracking of bikes where GNSS fails.

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

This paper aims to solve bike localization in areas without reliable GNSS signals by combining low-cost inertial sensors with two key additions. It models the mechanical connection between a rider's pedalling and the bike's wheel speed to provide ongoing calibration that counters drift. It also employs a mixture-of-experts neural network to handle multiple learning tasks while estimating uncertainty in the trajectory. If successful, this would allow large-scale tracking of shared bike fleets using only accelerometers and gyroscopes, avoiding the cost and privacy issues of cameras or lidars.

Core claim

The authors establish that the intrinsic relationship between periodic pedalling behaviors and acceleration variations can be converted into wheel speed measurements for dynamic calibration of inertial navigation. When this mechanical constraint is integrated into a mixture-of-experts framework that weights expert modules via a gating mechanism, the system achieves at least 12% improvement in accuracy over baselines on real shared-bike data, with 95-percentile wheel speed errors below 0.5 m/s.

What carries the argument

Mixture-of-experts model with gating mechanism for multi-task learning and uncertainty-aware estimation, augmented by mechanical constraints derived from pedal-to-wheel transmission.

If this is right

  • Trajectory estimation becomes uncertainty-aware, improving robustness in complex environments.
  • The approach supports deployment at scale since it relies only on low-cost inertial sensors.
  • Dynamic calibration from pedalling reduces cumulative drifts typical in pure inertial systems.
  • Performance holds on real-world data from varied riding conditions in the DiDi platform.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar mechanical constraints might apply to other human-powered vehicles for calibration.
  • The method could be tested on electric bikes where pedalling patterns differ.
  • Integration with map matching could further enhance accuracy in known urban layouts.
  • This opens possibilities for privacy-preserving fleet management without visual sensors.

Load-bearing premise

Periodic pedalling behaviors observed in acceleration can be reliably converted into accurate wheel-speed values for dynamic calibration across varied riders, bikes, and road conditions.

What would settle it

Collecting wheel speed ground truth on a diverse set of riders and road surfaces and finding that the estimated wheel speeds exceed 0.5 m/s error at the 95th percentile would disprove the calibration method's reliability.

Figures

Figures reproduced from arXiv: 2605.07412 by (2) DiDi Company, (3) Lancaster University), Chunwei Yang (2), Feng Liu (1), Guobin Wu (2), Kejia Li (1), Qiang Ni (3), Qun Li (2), Ruipeng Gao (1) ((1) Beijing Jiaotong University, Zhiwei Yang (2).

Figure 1
Figure 1. Figure 1: Satellite signals may be blocked or even unavailable in many bike [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed inertial tracking framework for shared [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Model architecture comparison between the conventional multi-head [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of task-specific gating and top-2 expert fusion in MTIM [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Overall architecture of the MTIMNet. An encoder extracts features [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Demonstration of the pedal action and one-way clutch mechanism. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Calculation process of pedalling cycles. From top to bottom: forward [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The MWI and autocorrelation sequences of forward accelerations in [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Top view of the Customized Dataset collection area. [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: ATE and AYE for different methods on the Customized Dataset. The MTIMNet model outperforms baselines on both test-seen and test-unseen sets. [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Example trajectories produced by different models. Results from the MTIMNet model are closer to the ground truth. [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of MTIMNet with the best baseline in terms of [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 16
Figure 16. Figure 16: Task-expert analysis of the proposed MTIMNet. (a) Average gating [PITH_FULL_IMAGE:figures/full_fig_p010_16.png] view at source ↗
Figure 14
Figure 14. Figure 14: Performance comparison of MTIMNet with different model structures [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 17
Figure 17. Figure 17: Performance of pseudo wheel speed estimation under different riding [PITH_FULL_IMAGE:figures/full_fig_p011_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Comparison of pseudo wheel speed estimation with RTK velocity [PITH_FULL_IMAGE:figures/full_fig_p011_18.png] view at source ↗
read the original abstract

Although Global Navigation Satellite Systems (GNSS) provide a general solution for bike tracking outdoors, there still exist complex riding environments where only inertial navigation systems work, such as urban canyons. Despite decades of research, localization using only low-cost inertial sensors still faces challenges such as cumulative drifts and poor robustness caused by filtering methods. Furthermore, sensors such as visual and LiDAR could provide reliable measurements, but they are not suitable for large-scale deployment. In this paper, we propose an inertial tracking framework that integrates bicycle mechanical constraints with a mixture-of-experts model. Specifically, we leverage multiple expert modules to capture shared representations and weight them through the gating mechanism, thus improving multi-task learning performance and enabling uncertainty-aware trajectory estimation. Furthermore, based on the mechanical transmission between the pedal and the rear wheel of a bike, we explore the intrinsic relationship between the rider's periodic pedalling behaviors and acceleration variations, and convert such patterns into bike's wheel speed for dynamic calibration. Experiments with real-world riding data from shared bikes of the DiDi ride-hailing platform demonstrate that our system improves the accuracy of baselines by at least 12%, with wheel speed errors below 0.5 m/s at 95-percentile.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The manuscript proposes an inertial tracking framework for shared bikes in GNSS-blocked environments. It combines bicycle mechanical constraints (converting periodic pedaling acceleration patterns into wheel-speed estimates via the pedal-to-rear-wheel transmission) with a mixture-of-experts model that uses expert modules and a gating mechanism for multi-task learning and uncertainty-aware trajectory estimation. Experiments on real-world DiDi ride-hailing shared-bike data are reported to yield at least 12% accuracy improvement over baselines and wheel-speed errors below 0.5 m/s at the 95th percentile.

Significance. If the performance claims hold under rigorous validation, the work could offer a practical, low-cost solution for large-scale bike tracking without visual or LiDAR sensors. The integration of domain-specific mechanical constraints with learned MoE components is a potentially efficient way to mitigate INS drift, and the uncertainty-aware estimation is a positive feature for real-world deployment.

major comments (3)
  1. [Abstract] Abstract: The quantitative claims ('improves the accuracy of baselines by at least 12%', 'wheel speed errors below 0.5 m/s at 95-percentile') are stated without any description of the experimental protocol, baseline definitions, dataset size or characteristics, data exclusion rules, or error analysis. This absence prevents verification that the data support the central performance claims.
  2. [Abstract] Abstract: The mechanical-constraint component rests on converting pedaling patterns into wheel speed 'based on the mechanical transmission between the pedal and the rear wheel,' which implicitly assumes a fixed transmission ratio. DiDi shared bikes typically employ multi-gear transmissions; without gear detection, variable-ratio modeling, or per-bike calibration, the derived wheel-speed values (and thus the dynamic calibration) are likely incorrect under gear shifts or across bike models, directly affecting the reported accuracy gains.
  3. [Abstract] Abstract: The MoE gating and expert weights are learned from the same riding data used to generate the mechanical-constraint wheel-speed targets. This creates a potential circular dependence in which the reported performance numbers may partly reflect consistency between the learned model and the calibration method rather than independent generalization.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on the abstract and the potential limitations in our approach. We address each major comment below and will make revisions where they strengthen the manuscript without misrepresenting our contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The quantitative claims ('improves the accuracy of baselines by at least 12%', 'wheel speed errors below 0.5 m/s at 95-percentile') are stated without any description of the experimental protocol, baseline definitions, dataset size or characteristics, data exclusion rules, or error analysis. This absence prevents verification that the data support the central performance claims.

    Authors: We agree that the abstract would benefit from additional context on the experiments to support the claims. In the revised version, we will expand the abstract to briefly reference the real-world DiDi ride-hailing dataset, the specific baselines compared (standard INS methods and other learning-based approaches), and the evaluation on trajectory and wheel-speed metrics. Full details on protocol, dataset characteristics, size, exclusion criteria, and error analysis are already present in the Experiments section; the abstract revision will point readers there while respecting length limits. revision: yes

  2. Referee: [Abstract] Abstract: The mechanical-constraint component rests on converting pedaling patterns into wheel speed 'based on the mechanical transmission between the pedal and the rear wheel,' which implicitly assumes a fixed transmission ratio. DiDi shared bikes typically employ multi-gear transmissions; without gear detection, variable-ratio modeling, or per-bike calibration, the derived wheel-speed values (and thus the dynamic calibration) are likely incorrect under gear shifts or across bike models, directly affecting the reported accuracy gains.

    Authors: The derivation uses the fixed mechanical relationship observed in the DiDi fleet bikes under typical operating conditions captured in our dataset. We recognize that variable gear ratios could introduce inaccuracies not explicitly modeled. In the revision, we will add a limitations discussion on gear shifts and note that future work could incorporate gear detection; the current results reflect performance on the collected real-world data where the constraint provides useful calibration signals. revision: partial

  3. Referee: [Abstract] Abstract: The MoE gating and expert weights are learned from the same riding data used to generate the mechanical-constraint wheel-speed targets. This creates a potential circular dependence in which the reported performance numbers may partly reflect consistency between the learned model and the calibration method rather than independent generalization.

    Authors: The mechanical constraints supply wheel-speed targets for supervising the calibration task within the multi-task MoE framework. Trajectory estimation performance is evaluated independently against GNSS ground truth collected in open-sky segments, separate from the constraint-derived targets. We will revise the manuscript to explicitly clarify this training-evaluation separation and the use of held-out validation to demonstrate that gains arise from improved fusion and uncertainty modeling rather than circularity alone. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's framework combines a domain-knowledge mechanical constraint (pedal-to-rear-wheel transmission used to map periodic acceleration patterns to wheel speed for calibration) with a standard mixture-of-experts architecture for multi-task learning and uncertainty estimation. No equations or sections are provided that show any prediction or result reducing by construction to fitted parameters, self-citations, or renamed inputs. The reported accuracy gains are empirical outcomes on held-out real-world DiDi riding data rather than tautological outputs of the method itself. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the domain assumption that pedaling acceleration patterns map directly to wheel speed and on the learned parameters of the mixture-of-experts model; no new physical entities are introduced.

free parameters (1)
  • MoE gating and expert weights
    Parameters of the mixture-of-experts model are learned from riding data and directly affect trajectory and wheel-speed estimates.
axioms (1)
  • domain assumption Bicycle mechanical transmission links periodic pedaling behavior to rear-wheel speed, allowing acceleration patterns to be converted into wheel-speed estimates for calibration.
    Invoked in the abstract as the basis for the dynamic calibration component.

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