Pith Number

pith:DL6KEKBA

pith:2026:DL6KEKBAYMQO2J4UPBHGEZNYOY

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Galilean State Estimation for Inertial Navigation Systems with Unknown Time Delay

Giulio Delama, Martin Scheiber, Robert Mahony, Stephan Weiss, Tarek Hamel, Yixiao Ge

An equivariant filter using Galilean symmetry estimates both navigation states and unknown time delays consistently.

arxiv:2605.13266 v1 · 2026-05-13 · cs.RO

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Record completeness

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Claims

C1strongest claim

An Equivariant Filter (EqF) is derived for the coupled estimation of navigation states and time delay. Results show that the EqF preserves accuracy and consistency, while the EKF lacks consistency and its performance degrades significantly with increasing measurement delays.

C2weakest assumption

Galilean symmetry can be leveraged to provide a joint representation of space and time that remains consistent for time-delayed INS measurements, allowing derivation of the EqF without post-hoc parameter tuning or data exclusions.

C3one line summary

A Galilean-equivariant filter jointly estimates INS navigation states and unknown GNSS time delays, preserving accuracy and consistency better than EKF in UAV flights and simulations with delays up to 500 ms.

References

27 extracted · 27 resolved · 1 Pith anchors

[1] Equivariant IMU Preintegration With Biases: A Galilean Group Approach.IEEE Robotics and Automation Letters, 10(1):724–731, 2025 2025 · doi:10.1109/lra.2024.3511424

[2] Kalman filtering approach to multi-rate information fusion in the presence of irregular sampling rate and variable measurement delay.Journal of Process Control, 53:15–25, 5 2017 2017 · doi:10.1016/j.jprocont.2017.02.010

[3] Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation With Online Calibration.IEEE Robotics and Automation Letters, 7(4):12118–12125, 10 2022 2022 · doi:10.1109/lra.2022.3210867

[4] In: 2022 International Conference on Robotics and Automation (ICRA), pp 2022 · doi:10.1109/icra46639.2022.9811778

[5] MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation.IEEE Robotics and Automation Letters, 1 2023 2023 · doi:10.1109/lra.2023.3335775

Receipt and verification

First computed	2026-05-18T02:44:49.311953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1afca22820c320ed2794784e6265b87603dffcd6f256163c304fe21ec00a97e1

Aliases

arxiv: 2605.13266 · arxiv_version: 2605.13266v1 · doi: 10.48550/arxiv.2605.13266 · pith_short_12: DL6KEKBAYMQO · pith_short_16: DL6KEKBAYMQO2J4U · pith_short_8: DL6KEKBA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DL6KEKBAYMQO2J4UPBHGEZNYOY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 1afca22820c320ed2794784e6265b87603dffcd6f256163c304fe21ec00a97e1

Canonical record JSON

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    "abstract_canon_sha256": "56f146421ad897e21b83514c1015e76b95dd03d067ec47c106894a417e295886",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.RO",
    "submitted_at": "2026-05-13T09:46:18Z",
    "title_canon_sha256": "458abea44d1f689bcda0d3af271e78d6d3eb68a7a421031243ffeb90382a2eb5"
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