A Lightweight Cubature Kalman Filter for Attitude and Heading Reference Systems Using Simplified Prediction Equations

Lei Jing; Shunsei Yamagishi

arxiv: 2602.12283 · v1 · pith:TVXJEHB2new · submitted 2026-01-12 · 📡 eess.SY · cs.HC· cs.RO· cs.SY

A Lightweight Cubature Kalman Filter for Attitude and Heading Reference Systems Using Simplified Prediction Equations

Shunsei Yamagishi , Lei Jing This is my paper

Pith reviewed 2026-05-21 15:29 UTC · model grok-4.3

classification 📡 eess.SY cs.HCcs.ROcs.SY

keywords Cubature Kalman FilterAttitude and heading reference systemComputational efficiencySimplified prediction equationsKalman filteringOrientation estimationEmbedded systems

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The pith

The Kaisoku Cubature Kalman Filter simplifies CKF prediction equations to cut floating-point operations while keeping identical attitude estimation accuracy.

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

This paper presents the Kaisoku Cubature Kalman Filter as a version of the Cubature Kalman Filter with lighter computation for Attitude and Heading Reference Systems. The authors obtain the new equations by first expanding the summation terms inside the standard CKF prediction step and then algebraically simplifying the resulting expressions. They claim these steps leave the underlying mathematical relations unchanged. Experiments on both high-performance and low-cost hardware show the new filter runs 15 to 19 percent faster than the original while producing the same orientation estimates.

Core claim

The paper establishes that the prediction equations of the Cubature Kalman Filter can be rewritten in a reduced form by expanding the summation terms and canceling redundant operations. This produces the KCKF, which the authors state requires fewer floating-point operations than the CKF yet yields mathematically equivalent state estimates. Controlled tests confirm that computation time falls by roughly 19 percent on a high-performance computer and 15 percent on a low-cost single-board computer, with no measurable change in attitude estimation accuracy.

What carries the argument

The simplified prediction equations formed by expanding and algebraically reducing the summation terms inside the CKF time-update step.

If this is right

The KCKF can run on microcontrollers with limited processing cycles for real-time orientation tracking.
Lower operation count translates directly to reduced energy use in battery-powered AHRS devices.
The same expansion-and-simplification approach may apply to other sigma-point filters that rely on similar weighted sums.
Attitude estimation accuracy remains unchanged from the standard CKF across the tested motion profiles.

Where Pith is reading between the lines

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

Similar algebraic reductions could be searched for in the update steps of other nonlinear filters used in navigation.
On extremely constrained hardware the time savings might allow an increase in filter update rate without exceeding processor limits.
Software libraries for inertial sensing could incorporate the KCKF equations as a drop-in replacement to improve efficiency.

Load-bearing premise

The algebraic simplification of the expanded summation terms in the CKF prediction equations produces results that are mathematically identical to the original equations.

What would settle it

A direct numerical comparison of the attitude quaternion outputs from the original CKF and the KCKF on identical sensor data sequences, checking whether the estimates differ beyond ordinary floating-point rounding.

Figures

Figures reproduced from arXiv: 2602.12283 by Lei Jing, Shunsei Yamagishi.

**Figure 1.** Figure 1: The algorithm of the CKF Prediction Update Output: 𝒒"!|! Normalize: 𝑘 ← 𝑘 + 1 Proposed lightweight formulas Inputs: 𝒒"#|#,𝑷#|#𝜎$ %, 𝜎&'' % , 𝜎(&) % , 𝜔*,!, 𝜔,,!, 𝜔-,!, 𝑎*,!, 𝑎,,!, 𝑎-,!, 𝑚*,!, 𝑚,,!, 𝑚-,! [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Figure 2: The algorithm of the KCKF [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: MTW2-3A7G6 mounted on a shoe value, because XKF3hm provides high accuracy as an attitude estimator of the AHRS. Formula 27 is used to evaluate the RMSEs of the Euler angles. RMSE = vuut 1 n Xn i=0 e 2 i (27) , where e 2 i = min[(ˆyi − y ref i ) 2 , {yˆi − (y ref i ± 360◦ )} 2 ] (28) n, yˆi denotes the length of the data, estimates by each attitude estimator. y ref i denotes reference value estimated by XKF… view at source ↗

**Figure 5.** Figure 5: The estimation results of attitudes by each attitude estimator in Data [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 7.** Figure 7: Comparing the KCKF with the CKF and EKF (MacBook Pro 2021 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: Comparing the KCKF with the KUKF and UKF (MacBook Pro 2021 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 11.** Figure 11: Comparing the KCKF with the CKF and EKF (Raspberry Pi 4 [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗

**Figure 12.** Figure 12: Comparing the KCKF with the KUKF and UKF (Raspberry Pi 4 [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗

**Figure 13.** Figure 13: Comparing the KCKF with the Guo’s FKF and Wu’s RMr-GDALKF [PITH_FULL_IMAGE:figures/full_fig_p008_13.png] view at source ↗

**Figure 14.** Figure 14: A bar chart of the average computation time [PITH_FULL_IMAGE:figures/full_fig_p009_14.png] view at source ↗

read the original abstract

Attitude and Heading Reference Systems (AHRSs) are broadly applied wherever reliable orientation and motion sensing is required. In this paper, we present an improved Cubature Kalman Filter (CKF) with lower computational cost while maintaining estimation accuracy, which is named "Kaisoku Cubature Kalman Filter (KCKF)". The computationally efficient equations of the KCKF are derived by simplifying those of the CKF, while preserving equivalent mathematical relations. The lightweight prediction equations in the KCKF are derived by expanding the summation terms in the CKF and simplifying the result. This paper shows that the KCKF requires fewer floating-point operations (FLOPs) than the CKF. The controlled experimental results show that the KCKF reduces the computation time by approximately 19% compared to the CKF on a high-performance computer, whereas the KCKF reduces the computation time by approximately 15% compared to the CKF on a low-cost single-board computer. In addition, the KCKF maintains the attitude estimation accuracy of the CKF.

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.

Desk Editor's Note private letter to a colleague

The paper gives a concrete algebraic simplification of the CKF prediction step that trims 15-19% off runtime for AHRS while keeping accuracy the same in the reported tests.

read the letter

The main takeaway is that this work turns the standard cubature-point summations in the CKF into a shorter set of prediction equations for the mean and covariance, then shows the new version runs faster on both desktop and single-board hardware without changing the attitude estimates in their experiments. That is the actual contribution: a drop-in lighter prediction block derived by expanding and regrouping terms rather than by approximation or tuning. The timing numbers are the clearest part of the evidence, with the 19% and 15% reductions measured under controlled conditions on two different platforms. The accuracy claim rests on the assertion that the simplified expressions remain mathematically identical to the original CKF, which the authors say follows directly from the algebra. If the full derivation in the paper really starts from the usual cubature formulas and arrives at the KCKF equations without dropping or reweighting any terms, then the equivalence holds and the speed gain is free. The experiments appear to support that outcome in practice. The soft spot is exactly where the stress test points: the paper needs to make the expansion and cancellation steps fully traceable so a reader can confirm no numerical difference sneaks in. Without that, the accuracy-maintenance claim stays an assertion rather than a demonstrated identity. A secondary gap is the lack of head-to-head numbers against other established ways to lighten Kalman filters, such as square-root implementations or reduced-point variants, though the paper stays narrowly focused on the CKF case. This is useful reading for anyone already running CKF on embedded orientation hardware and looking for a quick reduction in FLOPs. The math is checkable, the benchmarks are straightforward, and the scope is modest enough that a referee could evaluate it in one pass. I would send it to peer review.

Referee Report

1 major / 2 minor

Summary. The paper proposes the Kaisoku Cubature Kalman Filter (KCKF), a computationally lighter variant of the standard Cubature Kalman Filter (CKF) tailored for Attitude and Heading Reference Systems (AHRS). It derives simplified prediction equations by expanding the cubature-point summation terms in the CKF and algebraically simplifying the results, asserting that equivalent mathematical relations are preserved. The work claims this yields fewer floating-point operations, with controlled experiments demonstrating approximately 19% and 15% reductions in computation time on high-performance and low-cost hardware, respectively, while maintaining identical attitude estimation accuracy.

Significance. If the claimed algebraic equivalence holds exactly, the KCKF would provide a practical, low-effort optimization for real-time AHRS on embedded platforms, extending the usability of CKF without accuracy trade-offs. The hardware-specific timing experiments constitute a concrete strength, offering reproducible evidence of speedup. However, the significance is limited by the absence of a verifiable derivation, which is required to confirm that no terms are inadvertently altered or dropped.

major comments (1)

[derivation of the KCKF prediction equations] Derivation of lightweight prediction equations: The central claim that expanding the summation terms in the CKF prediction step (for predicted state mean and covariance) followed by algebraic simplification produces mathematically identical expressions is asserted in the abstract and methods but not demonstrated with a traceable, step-by-step derivation from the standard CKF formulas. This is load-bearing for both the FLOP-reduction and accuracy-maintenance claims; without it, equivalence cannot be independently verified and any regrouping error would invalidate the experimental conclusions.

minor comments (2)

[abstract] The abstract refers to 'Kaisoku Cubature Kalman Filter' without explaining the origin or meaning of 'Kaisoku'; a brief etymology or definition in the introduction would improve clarity.
[methods] The manuscript would benefit from an explicit table or pseudocode comparing the original CKF prediction equations side-by-side with the simplified KCKF versions, including operation counts for each term.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript on the Kaisoku Cubature Kalman Filter (KCKF). The referee correctly identifies that the central claim of mathematical equivalence between the simplified KCKF prediction equations and the standard CKF requires explicit verification. We address this point below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

Referee: Derivation of lightweight prediction equations: The central claim that expanding the summation terms in the CKF prediction step (for predicted state mean and covariance) followed by algebraic simplification produces mathematically identical expressions is asserted in the abstract and methods but not demonstrated with a traceable, step-by-step derivation from the standard CKF formulas. This is load-bearing for both the FLOP-reduction and accuracy-maintenance claims; without it, equivalence cannot be independently verified and any regrouping error would invalidate the experimental conclusions.

Authors: We agree with the referee that a traceable, step-by-step derivation is necessary for independent verification of the claimed algebraic equivalence. The manuscript states that the KCKF equations are obtained by expanding the cubature-point summation terms in the standard CKF prediction step and then algebraically simplifying the results while preserving equivalent mathematical relations, but we acknowledge that this process was not shown in full detail. In the revised manuscript we will add a dedicated subsection (or appendix) that starts from the standard CKF equations for the predicted state mean and covariance, expands the sums explicitly over the 2n cubature points, applies the algebraic regrouping steps (combining like terms and using the zero-mean and unit-variance properties of the cubature points), and arrives at the simplified expressions. Each manipulation will be shown with intermediate equations so that readers can confirm no terms are dropped or altered. This addition will directly support the reported FLOP reductions and the experimental observation that attitude accuracy remains identical. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation is a direct algebraic reduction of standard CKF summations

full rationale

The paper derives the KCKF prediction equations explicitly by expanding the cubature-point summation terms present in the conventional CKF and then algebraically simplifying the expanded expressions while asserting that the resulting relations remain mathematically equivalent. This process is a standard symbolic manipulation of existing formulas rather than a self-definitional loop, a fitted parameter renamed as a prediction, or any load-bearing self-citation. No uniqueness theorem, prior ansatz, or author-overlapping citation is invoked to justify the equivalence; the central claim therefore rests on the algebraic identity itself, which is independent of the present paper's fitted values or experimental results. The derivation chain is self-contained against the external benchmark of the original CKF equations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that algebraic simplification after expansion leaves the filter's statistical properties unchanged; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption Expanding the summation terms in the CKF prediction equations and then simplifying yields mathematically equivalent expressions.
This equivalence is the foundation for claiming identical accuracy with lower cost.

pith-pipeline@v0.9.0 · 5725 in / 1218 out tokens · 39028 ms · 2026-05-21T15:29:30.063009+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

[1]

The extended kalman filter with reduced computation time for pedestrian dead reckoning,

S. Yamagishi and L. Jing, “The extended kalman filter with reduced computation time for pedestrian dead reckoning,”IEEE Sensors Letters, vol. 7, no. 12, pp. 1–4, 2023

work page 2023
[2]

The unscented kalman filter with reduced computation time for estimating the attitude of the attitude and heading reference system,

——, “The unscented kalman filter with reduced computation time for estimating the attitude of the attitude and heading reference system,” IEEE Journal of Indoor and Seamless Positioning and Navigation, vol. 2, pp. 320–332, 2024

work page 2024
[3]

Pedestrian trajectory projection based on adaptive interpolation factor linear interpolation quaternion attitude estimation method,

L.-F. Shi, Y .-F. Dai, H. Yin, and Y . Shi, “Pedestrian trajectory projection based on adaptive interpolation factor linear interpolation quaternion attitude estimation method,”IEEE Transactions on Instrumentation and Measurement, vol. 74, pp. 1–9, 2025

work page 2025
[4]

Effects of imu sensor- to-segment misalignment and orientation error on 3-d knee joint angle estimation,

B. Fan, Q. Li, T. Tan, P. Kang, and P. B. Shull, “Effects of imu sensor- to-segment misalignment and orientation error on 3-d knee joint angle estimation,”IEEE Sensors Journal, vol. 22, no. 3, pp. 2543–2552, 2022

work page 2022
[5]

Magnetic-free quaternion-based robust unscented kalman filter for upper limb kinematic analysis,

L. Truppa, E. Bergamini, P. Garofalo, G. Vannozzi, A. M. Sabatini, and A. Mannini, “Magnetic-free quaternion-based robust unscented kalman filter for upper limb kinematic analysis,”IEEE Sensors Journal, vol. 23, no. 3, pp. 3212–3219, 2023

work page 2023
[6]

Imu shoulder angle estimation: Effects of sensor-to-segment misalignment and sensor ori- entation error,

K. Zhu, J. Li, D. Li, B. Fan, and P. B. Shull, “Imu shoulder angle estimation: Effects of sensor-to-segment misalignment and sensor ori- entation error,”IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 31, pp. 4481–4491, 2023

work page 2023
[7]

Measurement of hand joint angle using inertial-based motion capture system,

C. Lu, Z. Dai, and L. Jing, “Measurement of hand joint angle using inertial-based motion capture system,”IEEE Transactions on Instrumen- tation and Measurement, vol. 72, pp. 1–11, 2023

work page 2023
[8]

A least squares estimate of satellite attitude,

G. Wahba, “A least squares estimate of satellite attitude,”SIAM Rev., vol. 7, no. 3, p. 409, Jul. 1965. [Online]. Available: https://doi.org/10.1137/1007077

work page doi:10.1137/1007077 1965
[9]

Novel marg-sensor orientation estimation algorithm using fast kalman filter,

S. Guo, J. Wu, Z. Wang, and J. Qian, “Novel marg-sensor orientation estimation algorithm using fast kalman filter,”Journal of Sensors, vol. 2017, no. 1, p. 8542153, 2017. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1155/2017/8542153

work page doi:10.1155/2017/8542153 2017
[10]

Lightweight extended kalman filter for marg sensors attitude estimation,

Z. Dai and L. Jing, “Lightweight extended kalman filter for marg sensors attitude estimation,”IEEE Sensors Journal, vol. 21, no. 13, pp. 14 749– 14 758, 2021. 11

work page 2021
[11]

Attitude estimation of quadrotor uav based on qukf,

T. Liang, K. Yang, Q. Han, C. Li, J. Li, Q. Deng, S. Chen, and X. Tuo, “Attitude estimation of quadrotor uav based on qukf,”IEEE Access, vol. 11, pp. 111 133–111 141, 2023

work page 2023
[12]

Unscented kalman filter and magnetic angular rate update (maru) for an improved pedestrian dead-reckoning,

F. Zampella, M. Khider, P. Robertson, and A. Jim ´enez, “Unscented kalman filter and magnetic angular rate update (maru) for an improved pedestrian dead-reckoning,” inProceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium, 2012, pp. 129–139

work page 2012
[13]

Improved attitude and heading accuracy with double quaternion parameters estimation and magnetic disturbance rejection,

A. Wondosen, J.-S. Jeong, S.-K. Kim, Y . Debele, and B.-S. Kang, “Improved attitude and heading accuracy with double quaternion parameters estimation and magnetic disturbance rejection,”Sensors, vol. 21, no. 16, 2021. [Online]. Available: https://www.mdpi.com/ 1424-8220/21/16/5475

work page 2021
[14]

Quaternion-based robust attitude estimation using an adaptive unscented kalman filter,

A. C. B. Chiella, B. O. S. Teixeira, and G. A. S. Pereira, “Quaternion-based robust attitude estimation using an adaptive unscented kalman filter,”Sensors, vol. 19, no. 10, 2019. [Online]. Available: https://www.mdpi.com/1424-8220/19/10/2372

work page 2019
[15]

Marg attitude estimation using gradient-descent linear kalman filter,

J. Wu, “Marg attitude estimation using gradient-descent linear kalman filter,”IEEE Transactions on Automation Science and Engineering, vol. 17, no. 4, pp. 1777–1790, 2020

work page 2020
[16]

Attitude and heading estimation for indoor positioning based on the adaptive cubature kalman filter,

J. Geng, L. Xia, and D. Wu, “Attitude and heading estimation for indoor positioning based on the adaptive cubature kalman filter,”Micromachines, vol. 12, no. 1, 2021. [Online]. Available: https://www.mdpi.com/2072-666X/12/1/79

work page 2021
[17]

Attitude heading reference algorithm based on transformed cubature kalman filter,

Y . jun Yu, X. Zhang, and M. S. A. Khan, “Attitude heading reference algorithm based on transformed cubature kalman filter,”Measurement and Control, vol. 53, no. 7-8, pp. 1446–1453, 2020. [Online]. Available: https://doi.org/10.1177/0020294020944941

work page doi:10.1177/0020294020944941 2020
[18]

Integrated attitude estimate algorithm for ins/magnetometer system based on data fusion of dual mimu inertial array,

L. Xue, J. Lu, G. Cai, B. Yang, X. Wang, and H. Chang, “Integrated attitude estimate algorithm for ins/magnetometer system based on data fusion of dual mimu inertial array,”IEEE Sensors Journal, vol. 25, no. 13, pp. 25 410–25 419, 2025

work page 2025
[19]

An observation model from linear interpolation for quaternion-based attitude estimation,

X. Chen, Z. Xie, Y . Eun, A. Bettens, and X. Wu, “An observation model from linear interpolation for quaternion-based attitude estimation,”IEEE Transactions on Instrumentation and Measurement, vol. 72, pp. 1–12, 2023

work page 2023
[20]

Low cost imu attitude estimation algorithm based on measurement adaptive reduced dcm,

X. Wei, Y . Zhang, S. Fan, W. Gao, F. Shen, X. Ming, and Y . Wang, “Low cost imu attitude estimation algorithm based on measurement adaptive reduced dcm,”IEEE Sensors Journal, vol. 25, no. 1, pp. 1428–1439, 2025

work page 2025
[21]

Nonlinear complementary filters on the special orthogonal group,

R. Mahony, T. Hamel, and J.-M. Pflimlin, “Nonlinear complementary filters on the special orthogonal group,”IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1203–1218, 2008

work page 2008
[22]

Fast complementary filter for attitude estimation using low-cost marg sensors,

J. Wu, Z. Zhou, J. Chen, H. Fourati, and R. Li, “Fast complementary filter for attitude estimation using low-cost marg sensors,”IEEE Sensors Journal, vol. 16, no. 18, pp. 6997–7007, 2016

work page 2016
[23]

A fast complementary filter for avoiding the magnetometer measurements from influencing the calculation of pitch and roll,

H. Rong, C. Peng, Y . Chen, J. Lv, Y . Zhu, and L. Zou, “A fast complementary filter for avoiding the magnetometer measurements from influencing the calculation of pitch and roll,”IEEE Sensors Journal, vol. 25, no. 7, pp. 11 521–11 531, 2025

work page 2025
[24]

A time-efficient complementary kalman gain filter derived from extended kalman filter and used for magnetic and inertial measurement units,

H. Rong, C. Peng, Y . Chen, J. Lv, and L. Zou, “A time-efficient complementary kalman gain filter derived from extended kalman filter and used for magnetic and inertial measurement units,”IEEE Sensors Journal, vol. 22, no. 23, pp. 23 077–23 087, 2022

work page 2022
[25]

Estimation of imu and marg orientation using a gradient descent algorithm,

S. O. H. Madgwick, A. J. L. Harrison, and R. Vaidyanathan, “Estimation of imu and marg orientation using a gradient descent algorithm,” in2011 IEEE International Conference on Rehabilitation Robotics, 2011, pp. 1– 7

work page 2011
[26]

Pedestrian dead reckoning using pocket-worn smartphone,

H. Zhao, L. Zhang, S. Qiu, Z. Wang, N. Yang, and J. Xu, “Pedestrian dead reckoning using pocket-worn smartphone,”IEEE Access, vol. 7, pp. 91 063–91 073, 2019

work page 2019
[27]

Improved formulation of the imu and marg orientation gradient descent algorithm for motion tracking in human-machine interfaces,

M. Admiraal, S. Wilson, and R. Vaidyanathan, “Improved formulation of the imu and marg orientation gradient descent algorithm for motion tracking in human-machine interfaces,” in2017 IEEE International Con- ference on Multisensor Fusion and Integration for Intelligent Systems (MFI), 2017, pp. 403–410

work page 2017
[28]

Optimization of gradient descent parameters in attitude estimation algorithms,

K. Sever, L. M. Golu ˇsin, and J. Lon ˇcar, “Optimization of gradient descent parameters in attitude estimation algorithms,”Sensors, vol. 23, no. 4, 2023. [Online]. Available: https://www.mdpi.com/1424-8220/23/ 4/2298

work page 2023
[29]

Three-axis attitude determination from vector observations,

M. D. SHUSTER and S. D. OH, “Three-axis attitude determination from vector observations,”Journal of Guidance and Control, vol. 4, no. 1, pp. 70–77, 1981. [Online]. Available: https://doi.org/10.2514/3.19717

work page doi:10.2514/3.19717 1981
[30]

A simplified quaternion- based algorithm for orientation estimation from earth gravity and mag- netic field measurements,

X. Yun, E. R. Bachmann, and R. B. McGhee, “A simplified quaternion- based algorithm for orientation estimation from earth gravity and mag- netic field measurements,”IEEE Transactions on Instrumentation and Measurement, vol. 57, no. 3, pp. 638–650, 2008

work page 2008
[31]

New extension of the Kalman filter to nonlinear systems,

S. J. Julier and J. K. Uhlmann, “New extension of the Kalman filter to nonlinear systems,” inSignal Processing, Sensor Fusion, and Target Recognition VI, I. Kadar, Ed., vol. 3068, International Society for Optics and Photonics. SPIE, 1997, pp. 182 – 193. [Online]. Available: https://doi.org/10.1117/12.280797

work page doi:10.1117/12.280797 1997
[32]

Cubature kalman filters,

I. Arasaratnam and S. Haykin, “Cubature kalman filters,”IEEE Trans- actions on Automatic Control, vol. 54, no. 6, pp. 1254–1269, 2009

work page 2009
[33]

A slam algorithm based on adaptive cubature kalman filter,

F. Yu, Q. Sun, C. Lv, Y . Ben, and Y . Fu, “A slam algorithm based on adaptive cubature kalman filter,”Mathematical Problems in Engineering, vol. 2014, no. 1, p. 171958, 2014. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1155/2014/171958

work page doi:10.1155/2014/171958 2014
[34]

Mobile agents based load balancing method for parallel applications,

H. Thant, K. M. San, K. M. L. Tun, T. Naing, and N. Thein, “Mobile agents based load balancing method for parallel applications,” in6th Asia-Pacific Symposium on Information and Telecommunication Tech- nologies, 2005, pp. 77–82

work page 2005
[35]

Movella dot & dot pro/mtw2 awinda product documentation,

M. Inc., “Movella dot & dot pro/mtw2 awinda product documentation,” accessed: Jun. 4, 2025. [Online]. Available: https://wsdocs.movella. com/hardware-overview

work page 2025
[36]

The unscented kalman filter for non- linear estimation,

E. Wan and R. Van Der Merwe, “The unscented kalman filter for non- linear estimation,” inProceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), 2000, pp. 153–158

work page 2000
[37]

Macbook pro (14-inch, 2021) - technical specifications,

A. Inc., “Macbook pro (14-inch, 2021) - technical specifications,” accessed: Nov. 15, 2025. [Online]. Available: https://support.apple.com/ en-gb/111902

work page 2021
[38]

Raspberry pi 4 model b,

R. P. Foundation, “Raspberry pi 4 model b,” accessed: Nov. 15, 2025. [Online]. Available: https://www.raspberrypi.com/products/ raspberry-pi-4-model-b/

work page 2025
[39]

The fast attitude estimation method based on quaternion and generalized multivectors,

J. Song, Z. Shi, and H. Wang, “The fast attitude estimation method based on quaternion and generalized multivectors,”IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1–10, 2021. Shunsei Yamagishireceived the B.S. degree and the M.S. degree in computer science and engineering from The University of Aizu, Japan, in 2022 and 2024, respectiv...

work page 2021

[1] [1]

The extended kalman filter with reduced computation time for pedestrian dead reckoning,

S. Yamagishi and L. Jing, “The extended kalman filter with reduced computation time for pedestrian dead reckoning,”IEEE Sensors Letters, vol. 7, no. 12, pp. 1–4, 2023

work page 2023

[2] [2]

The unscented kalman filter with reduced computation time for estimating the attitude of the attitude and heading reference system,

——, “The unscented kalman filter with reduced computation time for estimating the attitude of the attitude and heading reference system,” IEEE Journal of Indoor and Seamless Positioning and Navigation, vol. 2, pp. 320–332, 2024

work page 2024

[3] [3]

Pedestrian trajectory projection based on adaptive interpolation factor linear interpolation quaternion attitude estimation method,

L.-F. Shi, Y .-F. Dai, H. Yin, and Y . Shi, “Pedestrian trajectory projection based on adaptive interpolation factor linear interpolation quaternion attitude estimation method,”IEEE Transactions on Instrumentation and Measurement, vol. 74, pp. 1–9, 2025

work page 2025

[4] [4]

Effects of imu sensor- to-segment misalignment and orientation error on 3-d knee joint angle estimation,

B. Fan, Q. Li, T. Tan, P. Kang, and P. B. Shull, “Effects of imu sensor- to-segment misalignment and orientation error on 3-d knee joint angle estimation,”IEEE Sensors Journal, vol. 22, no. 3, pp. 2543–2552, 2022

work page 2022

[5] [5]

Magnetic-free quaternion-based robust unscented kalman filter for upper limb kinematic analysis,

L. Truppa, E. Bergamini, P. Garofalo, G. Vannozzi, A. M. Sabatini, and A. Mannini, “Magnetic-free quaternion-based robust unscented kalman filter for upper limb kinematic analysis,”IEEE Sensors Journal, vol. 23, no. 3, pp. 3212–3219, 2023

work page 2023

[6] [6]

Imu shoulder angle estimation: Effects of sensor-to-segment misalignment and sensor ori- entation error,

K. Zhu, J. Li, D. Li, B. Fan, and P. B. Shull, “Imu shoulder angle estimation: Effects of sensor-to-segment misalignment and sensor ori- entation error,”IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 31, pp. 4481–4491, 2023

work page 2023

[7] [7]

Measurement of hand joint angle using inertial-based motion capture system,

C. Lu, Z. Dai, and L. Jing, “Measurement of hand joint angle using inertial-based motion capture system,”IEEE Transactions on Instrumen- tation and Measurement, vol. 72, pp. 1–11, 2023

work page 2023

[8] [8]

A least squares estimate of satellite attitude,

G. Wahba, “A least squares estimate of satellite attitude,”SIAM Rev., vol. 7, no. 3, p. 409, Jul. 1965. [Online]. Available: https://doi.org/10.1137/1007077

work page doi:10.1137/1007077 1965

[9] [9]

Novel marg-sensor orientation estimation algorithm using fast kalman filter,

S. Guo, J. Wu, Z. Wang, and J. Qian, “Novel marg-sensor orientation estimation algorithm using fast kalman filter,”Journal of Sensors, vol. 2017, no. 1, p. 8542153, 2017. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1155/2017/8542153

work page doi:10.1155/2017/8542153 2017

[10] [10]

Lightweight extended kalman filter for marg sensors attitude estimation,

Z. Dai and L. Jing, “Lightweight extended kalman filter for marg sensors attitude estimation,”IEEE Sensors Journal, vol. 21, no. 13, pp. 14 749– 14 758, 2021. 11

work page 2021

[11] [11]

Attitude estimation of quadrotor uav based on qukf,

T. Liang, K. Yang, Q. Han, C. Li, J. Li, Q. Deng, S. Chen, and X. Tuo, “Attitude estimation of quadrotor uav based on qukf,”IEEE Access, vol. 11, pp. 111 133–111 141, 2023

work page 2023

[12] [12]

Unscented kalman filter and magnetic angular rate update (maru) for an improved pedestrian dead-reckoning,

F. Zampella, M. Khider, P. Robertson, and A. Jim ´enez, “Unscented kalman filter and magnetic angular rate update (maru) for an improved pedestrian dead-reckoning,” inProceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium, 2012, pp. 129–139

work page 2012

[13] [13]

Improved attitude and heading accuracy with double quaternion parameters estimation and magnetic disturbance rejection,

A. Wondosen, J.-S. Jeong, S.-K. Kim, Y . Debele, and B.-S. Kang, “Improved attitude and heading accuracy with double quaternion parameters estimation and magnetic disturbance rejection,”Sensors, vol. 21, no. 16, 2021. [Online]. Available: https://www.mdpi.com/ 1424-8220/21/16/5475

work page 2021

[14] [14]

Quaternion-based robust attitude estimation using an adaptive unscented kalman filter,

A. C. B. Chiella, B. O. S. Teixeira, and G. A. S. Pereira, “Quaternion-based robust attitude estimation using an adaptive unscented kalman filter,”Sensors, vol. 19, no. 10, 2019. [Online]. Available: https://www.mdpi.com/1424-8220/19/10/2372

work page 2019

[15] [15]

Marg attitude estimation using gradient-descent linear kalman filter,

J. Wu, “Marg attitude estimation using gradient-descent linear kalman filter,”IEEE Transactions on Automation Science and Engineering, vol. 17, no. 4, pp. 1777–1790, 2020

work page 2020

[16] [16]

Attitude and heading estimation for indoor positioning based on the adaptive cubature kalman filter,

J. Geng, L. Xia, and D. Wu, “Attitude and heading estimation for indoor positioning based on the adaptive cubature kalman filter,”Micromachines, vol. 12, no. 1, 2021. [Online]. Available: https://www.mdpi.com/2072-666X/12/1/79

work page 2021

[17] [17]

Attitude heading reference algorithm based on transformed cubature kalman filter,

Y . jun Yu, X. Zhang, and M. S. A. Khan, “Attitude heading reference algorithm based on transformed cubature kalman filter,”Measurement and Control, vol. 53, no. 7-8, pp. 1446–1453, 2020. [Online]. Available: https://doi.org/10.1177/0020294020944941

work page doi:10.1177/0020294020944941 2020

[18] [18]

Integrated attitude estimate algorithm for ins/magnetometer system based on data fusion of dual mimu inertial array,

L. Xue, J. Lu, G. Cai, B. Yang, X. Wang, and H. Chang, “Integrated attitude estimate algorithm for ins/magnetometer system based on data fusion of dual mimu inertial array,”IEEE Sensors Journal, vol. 25, no. 13, pp. 25 410–25 419, 2025

work page 2025

[19] [19]

An observation model from linear interpolation for quaternion-based attitude estimation,

X. Chen, Z. Xie, Y . Eun, A. Bettens, and X. Wu, “An observation model from linear interpolation for quaternion-based attitude estimation,”IEEE Transactions on Instrumentation and Measurement, vol. 72, pp. 1–12, 2023

work page 2023

[20] [20]

Low cost imu attitude estimation algorithm based on measurement adaptive reduced dcm,

X. Wei, Y . Zhang, S. Fan, W. Gao, F. Shen, X. Ming, and Y . Wang, “Low cost imu attitude estimation algorithm based on measurement adaptive reduced dcm,”IEEE Sensors Journal, vol. 25, no. 1, pp. 1428–1439, 2025

work page 2025

[21] [21]

Nonlinear complementary filters on the special orthogonal group,

R. Mahony, T. Hamel, and J.-M. Pflimlin, “Nonlinear complementary filters on the special orthogonal group,”IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1203–1218, 2008

work page 2008

[22] [22]

Fast complementary filter for attitude estimation using low-cost marg sensors,

J. Wu, Z. Zhou, J. Chen, H. Fourati, and R. Li, “Fast complementary filter for attitude estimation using low-cost marg sensors,”IEEE Sensors Journal, vol. 16, no. 18, pp. 6997–7007, 2016

work page 2016

[23] [23]

A fast complementary filter for avoiding the magnetometer measurements from influencing the calculation of pitch and roll,

H. Rong, C. Peng, Y . Chen, J. Lv, Y . Zhu, and L. Zou, “A fast complementary filter for avoiding the magnetometer measurements from influencing the calculation of pitch and roll,”IEEE Sensors Journal, vol. 25, no. 7, pp. 11 521–11 531, 2025

work page 2025

[24] [24]

A time-efficient complementary kalman gain filter derived from extended kalman filter and used for magnetic and inertial measurement units,

H. Rong, C. Peng, Y . Chen, J. Lv, and L. Zou, “A time-efficient complementary kalman gain filter derived from extended kalman filter and used for magnetic and inertial measurement units,”IEEE Sensors Journal, vol. 22, no. 23, pp. 23 077–23 087, 2022

work page 2022

[25] [25]

Estimation of imu and marg orientation using a gradient descent algorithm,

S. O. H. Madgwick, A. J. L. Harrison, and R. Vaidyanathan, “Estimation of imu and marg orientation using a gradient descent algorithm,” in2011 IEEE International Conference on Rehabilitation Robotics, 2011, pp. 1– 7

work page 2011

[26] [26]

Pedestrian dead reckoning using pocket-worn smartphone,

H. Zhao, L. Zhang, S. Qiu, Z. Wang, N. Yang, and J. Xu, “Pedestrian dead reckoning using pocket-worn smartphone,”IEEE Access, vol. 7, pp. 91 063–91 073, 2019

work page 2019

[27] [27]

Improved formulation of the imu and marg orientation gradient descent algorithm for motion tracking in human-machine interfaces,

M. Admiraal, S. Wilson, and R. Vaidyanathan, “Improved formulation of the imu and marg orientation gradient descent algorithm for motion tracking in human-machine interfaces,” in2017 IEEE International Con- ference on Multisensor Fusion and Integration for Intelligent Systems (MFI), 2017, pp. 403–410

work page 2017

[28] [28]

Optimization of gradient descent parameters in attitude estimation algorithms,

K. Sever, L. M. Golu ˇsin, and J. Lon ˇcar, “Optimization of gradient descent parameters in attitude estimation algorithms,”Sensors, vol. 23, no. 4, 2023. [Online]. Available: https://www.mdpi.com/1424-8220/23/ 4/2298

work page 2023

[29] [29]

Three-axis attitude determination from vector observations,

M. D. SHUSTER and S. D. OH, “Three-axis attitude determination from vector observations,”Journal of Guidance and Control, vol. 4, no. 1, pp. 70–77, 1981. [Online]. Available: https://doi.org/10.2514/3.19717

work page doi:10.2514/3.19717 1981

[30] [30]

A simplified quaternion- based algorithm for orientation estimation from earth gravity and mag- netic field measurements,

X. Yun, E. R. Bachmann, and R. B. McGhee, “A simplified quaternion- based algorithm for orientation estimation from earth gravity and mag- netic field measurements,”IEEE Transactions on Instrumentation and Measurement, vol. 57, no. 3, pp. 638–650, 2008

work page 2008

[31] [31]

New extension of the Kalman filter to nonlinear systems,

S. J. Julier and J. K. Uhlmann, “New extension of the Kalman filter to nonlinear systems,” inSignal Processing, Sensor Fusion, and Target Recognition VI, I. Kadar, Ed., vol. 3068, International Society for Optics and Photonics. SPIE, 1997, pp. 182 – 193. [Online]. Available: https://doi.org/10.1117/12.280797

work page doi:10.1117/12.280797 1997

[32] [32]

Cubature kalman filters,

I. Arasaratnam and S. Haykin, “Cubature kalman filters,”IEEE Trans- actions on Automatic Control, vol. 54, no. 6, pp. 1254–1269, 2009

work page 2009

[33] [33]

A slam algorithm based on adaptive cubature kalman filter,

F. Yu, Q. Sun, C. Lv, Y . Ben, and Y . Fu, “A slam algorithm based on adaptive cubature kalman filter,”Mathematical Problems in Engineering, vol. 2014, no. 1, p. 171958, 2014. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1155/2014/171958

work page doi:10.1155/2014/171958 2014

[34] [34]

Mobile agents based load balancing method for parallel applications,

H. Thant, K. M. San, K. M. L. Tun, T. Naing, and N. Thein, “Mobile agents based load balancing method for parallel applications,” in6th Asia-Pacific Symposium on Information and Telecommunication Tech- nologies, 2005, pp. 77–82

work page 2005

[35] [35]

Movella dot & dot pro/mtw2 awinda product documentation,

M. Inc., “Movella dot & dot pro/mtw2 awinda product documentation,” accessed: Jun. 4, 2025. [Online]. Available: https://wsdocs.movella. com/hardware-overview

work page 2025

[36] [36]

The unscented kalman filter for non- linear estimation,

E. Wan and R. Van Der Merwe, “The unscented kalman filter for non- linear estimation,” inProceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), 2000, pp. 153–158

work page 2000

[37] [37]

Macbook pro (14-inch, 2021) - technical specifications,

A. Inc., “Macbook pro (14-inch, 2021) - technical specifications,” accessed: Nov. 15, 2025. [Online]. Available: https://support.apple.com/ en-gb/111902

work page 2021

[38] [38]

Raspberry pi 4 model b,

R. P. Foundation, “Raspberry pi 4 model b,” accessed: Nov. 15, 2025. [Online]. Available: https://www.raspberrypi.com/products/ raspberry-pi-4-model-b/

work page 2025

[39] [39]

The fast attitude estimation method based on quaternion and generalized multivectors,

J. Song, Z. Shi, and H. Wang, “The fast attitude estimation method based on quaternion and generalized multivectors,”IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1–10, 2021. Shunsei Yamagishireceived the B.S. degree and the M.S. degree in computer science and engineering from The University of Aizu, Japan, in 2022 and 2024, respectiv...

work page 2021