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REVIEW 3 major objections 6 minor 24 references

Comparative analysis of whole-body center-of-mass estimation methods in dynamic and static activities using marker-based systems

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Three marker-based CoM estimators separate cleanly by task dynamics: pelvis-only estimates fail in dynamic activities, whole-body kinematics are accurate, and force-plate fusion adds no measurable benefit.

desk verdict PM-vs-WM is a solid, useful result; the WMG-vs-WM null is circular because the Kalman filter was tuned to match WM. read the letter →

arxiv 2411.18774 v1 pith:BMV7DL4D submitted 2024-11-27 q-bio.QM

Jingshu Peng , Mohsen Alizadeh Noghani , Edgar Bolívar-Nieto This is my paper · ORCID
classification q-bio.QM
keywords centerofmassestimationexternalforceresidualKalmanfiltergroundreactionforcesmarker-basedmotioncapturewhole-bodykinematicspelvismarkersetbalanceassessment
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 asks which marker-based way of estimating the whole-body center of mass (CoM) and its velocity is accurate enough for balance and movement research. It compares a pelvis-only markerset, a whole-body marker model, and a Kalman filter that fuses whole-body kinematics with ground reaction forces, using the root-mean-square external force residual as the score. In static activities all three methods are statistically indistinguishable; in dynamic activities the pelvis-only method has 96% to 104% higher residuals than the two whole-body methods, with very large effect sizes. The whole-body method and the GRF-fused filter differ by only 0.28% in RMS residual, so the paper concludes the Kalman fusion does not improve whole-body kinematics. If correct, the comparison gives a practical default—whole-body markers—and shows force-plate data are not needed for CoM state estimation in the tested tasks.

What carries the argument

The load-bearing object is the external force residual r(t) = F_ext(t) − m a_est(t), where F_ext is the net external force from the force plates minus gravity, m is body mass, and a_est is CoM acceleration obtained by differentiating the estimated position or velocity; RMS of this residual is the performance metric. The third method is a Kalman filter with state x ∈ $R^{6}$ containing 3D CoM position and velocity, control input u built from GRF-derived acceleration, and measurement y from the whole-body marker position. Its process and measurement covariance matrices Vw and Vv were tuned by a genetic algorithm that minimizes the difference between the Kalman output and the low-pass-filtered whole-body markerset estimate, so the filter's similarity to the whole-body method is partly built into the comparison.

What would settle it

Re-tune the Kalman filter's covariance matrices Vw and Vv from an independent source—force-plate noise statistics, or cross-validation on activities not used for tuning—and recompute the RMS external force residual in dynamic trials; if the re-tuned GRF-fused estimate beats the whole-body markerset estimate, the paper's central conclusion fails.

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Extended reading notes

Core claim

On its own terms, the paper establishes that method choice matters mainly when the body moves. With ten healthy participants performing 14 Berg Balance Scale-derived activities, the measured external force residual F_ext(t) − m a_est(t) is roughly double for the pelvis-markerset estimate than for either whole-body method in every dynamic activity, and this gap is statistically significant with Cohen's d near 3.0. Static activities show no significant method effect because the CoM stays near the pelvis. The whole-body markerset and the whole-body-plus-GRFs Kalman filter produce nearly equal residuals, so the paper asserts that, at least for the filter's tuning, adding GRFs through a Kalman filter does not improve CoM position or velocity estimates. The authors therefore recommend the whole-body markerset as the default method and restrict the pelvis-only method to static tasks or situations where pelvis markers track whole-body motion.

Load-bearing premise

The comparison's key assumption is that the Kalman filter's noise coefficients were chosen fairly, but they were tuned to reproduce the low-pass-filtered whole-body marker estimate, which biases the force-plate-fusion method toward matching the method it is compared against.

Editorial extensions

If this is right

  • In dynamic balance and mobility tasks, pelvis-only marker estimates of CoM position and velocity should be avoided when whole-body marker data are available; they produce roughly twice the external force residual.
  • Whole-body marker kinematics deliver consistent CoM estimates across all 14 activities, making them a good default when a full markerset is present.
  • Adding GRF measurements through the tested Kalman filter does not improve the whole-body kinematics estimate, so the added instrumentation and modeling complexity may not be justified for this purpose.
  • For quiet-stance and low-motion conditions, the pelvis-only method remains an acceptable low-cost option.

Reading between the lines

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

  • Editorial inference: because the Kalman filter was tuned to match the whole-body markerset estimate on the same data used for evaluation, the claim that GRF fusion adds nothing should be treated as conditional on that tuning; an independent noise model or held-out tuning could change the comparison.
  • Editorial inference: the external-force residual could serve as a general, force-plate-based validation protocol for other CoM estimators, including inertial-sensor or robot-state estimators, whenever the ground reaction forces are measured.
  • Editorial inference: the tested activities do not include running, jumping, or impact tasks, so the recommendation may not extend to higher-bandwidth motions where double integration of GRFs is known to drift differently.
  • Editorial inference: the 96–104% residual gap suggests that using pelvis-only markers in dynamic fall-risk assessments could materially change extrapolated-CoM margin-of-stability values, a hypothesis the paper does not test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript compares three center-of-mass (CoM) estimation methods—pelvic marker centroid (PM), whole-body inverse kinematics (WM), and a Kalman filter that fuses WM with ground reaction forces (WMG)—across 14 activities performed by 10 subjects. Accuracy is quantified by the root mean square (RMS) of the external force residual defined in Eq. (4). The authors report no differences between methods in static activities, substantially larger PM residuals in dynamic activities (Cohen's d ≈ 2.9–3.0), and nearly identical WMG and WM residuals. Based on these results, they recommend WM for general use and caution against PM for dynamic CoM estimation.

Significance. If the PM-versus-WM comparison is accepted, the paper provides a useful multi-activity benchmark: the data set covers 14 balance-relevant activities, the statistical analysis reports effect sizes and confidence intervals, and the PM disadvantage in dynamic tasks is large and consistent. The WMG-versus-WM comparison, however, is not an independent test of whether GRF fusion improves CoM estimation, because the Kalman filter covariances were tuned to minimize the difference between WMG and low-pass-filtered WM. The practical recommendation that GRF fusion does not help is therefore conditional on a reanalysis or a restricted claim. The study is valuable mainly for the PM-versus-WM result and for documenting a reproducible comparison protocol.

major comments (3)
  1. [§2.2 (after Eq. 3)] The Kalman filter covariance matrices Vw and Vv were specified by a genetic algorithm that minimized the difference between the WMG output and the low-pass-filtered WM estimate (6 Hz cutoff). The later observation in §3 that WMG and WM have nearly identical RMS residuals (0.28% difference, d=0.01) is therefore an expected consequence of the tuning objective, not an independent evaluation of whether GRF fusion improves CoM estimation. To support the central negative claim in the Abstract and §4.2, the filter should be tuned on an independent criterion (for example, minimizing the external force residual on held-out trials) or the claim must be weakened to 'no improvement under this tuning protocol'.
  2. [§2.2, Eq. (4)] The external force residual is not a fully independent accuracy metric for WMG. WMG uses the measured GRFs as the control input u in Eq. (1), and Eq. (4) evaluates the same measured Fext against the estimated acceleration; a low residual for WMG can reflect that the filter follows the GRF-derived acceleration directly rather than that the kinematic estimate is accurate. This confound should be acknowledged and, if possible, addressed with a metric that does not feed the same measured GRFs into both the estimator and the error signal.
  3. [§3, position results] The reported WMG−WM post-hoc comparison (p<0.001, d=0.01, 95% CI (−0.82, 0.85)) is internally inconsistent: a 95% confidence interval that spans zero cannot accompany p<0.001 for the same comparison. This contradiction bears directly on the central WMG-versus-WM conclusion and must be resolved; if the CI is correct, the p-value should be non-significant, and if the p-value is correct, the CI or d is misreported.
minor comments (6)
  1. [§2.1, Table 1] The classification of activities into Static and Dynamic is described as qualitative, based on the magnitude of displacement of body segments; please define an operational criterion or report the displacement range used for the split.
  2. [§2.2, Eq. (5)] The smoothing parameter α=300 is said to be found through experimentation; please provide the selection criterion or a sensitivity analysis showing that the main results are robust to this choice.
  3. [§2.2, after Eq. (3)] The genetic algorithm that sets Vw and Vv is described in one sentence; algorithmic details such as population size, number of generations, cost function, and convergence criteria are needed for reproducibility.
  4. [§2.1] The One Leg, Squat, and Shoe Lace trials were split into two parts, but the effect of this split on Kalman filter initialization and on the smoothing optimization in Eq. (5) is not explained; please clarify whether the parts were processed separately or concatenated.
  5. [§3, velocity results] For the velocity comparisons, the point estimates d=3.04 and d=2.99 are positive while their reported 95% CIs are negative; this sign inconsistency should be corrected.
  6. [Fig. 2] The y-axis limits differ across panels, and within panels the axis limits are set to the maximum RMS among methods; please state explicitly that between-panel comparisons of bar heights are not meaningful.

Circularity Check

1 steps flagged · score 7.0 of 10

The WMG-vs-WM null result is a fitting artifact: the Kalman filter was tuned to match WM, so the conclusion that GRF fusion does not improve CoM estimation is predetermined.

  1. fitted input called prediction [Section 2.2 (CoM state estimation), after Eq. 3; Results Section 3; Discussion Section 4.2]
    "A genetic algorithm that minimized the difference between the WMG and low-pass-filtered WM estimates (with a cutoff frequency of 6 Hz) specified the process and measurement covariance matrices, Vw and Vv."

    The Kalman filter's only free parameters, Vw and Vv, are fit to minimize the difference between the WMG output and the low-pass-filtered Whole-Body Markerset estimate. The paper then reports that WMG and WM have nearly identical RMS external-force residuals (0.28% higher average, d=0.01, 95% CI covering zero) and concludes that incorporating GRFs through the presented Kalman filter does not improve CoM estimation. That null result is the optimization objective itself: the filter was forced to match WM, so the observed agreement is a fitting artifact, not an independent empirical finding. The filter was never tuned to the external-force residual or to any independent ground truth, so the recommendation against GRF fusion is not supported by the comparison as run.

full rationale

The PM-versus-WM comparison is self-contained and non-circular: the Pelvis Markerset estimate is a simple four-marker average, it was not used in any fitting or tuning step, and the large 96-104% RMS-residual gap in dynamic activities (d approximately 2.9-3.0) is an empirical contrast between that kinematic proxy and the two whole-body pipelines. If the paper only recommended whole-body marker-based estimation over pelvis-only estimation, the circularity score would be low. The circularity is localized to the WMG-versus-WM claim. Section 2.2 states that a genetic algorithm specified Vw and Vv by minimizing the difference between WMG and the low-pass-filtered WM estimate. Therefore the later result that WMG differs from WM by only 0.28% RMS (d=0.01) is the direct output of that fitting objective. The abstract and conclusion convert this fitted agreement into the substantive claim that fusing GRFs through the Kalman filter does not improve whole-body CoM estimation. That is a fitted input called a prediction. The PM-vs-WM result is still independent, which is why the score is 7 rather than 9 or 10.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claim depends on several standard biomechanics assumptions and on two fitted parameters: the Kalman filter noise matrices, whose fitting target biases the GRF-fusion conclusion, and the smoothing weight alpha. The activity classification is an ad hoc modeling choice.

free parameters (4)
  • Kalman filter covariance matrices Vw and Vv = not reported; selected by genetic algorithm
    Tuned in Section 2.2 to minimize the difference between WMG and low-pass-filtered WM, biasing the WMG-versus-WM comparison.
  • Smoothing parameter alpha = 300
    Chosen 'through experimentation' (Section 2.2) to balance signal fit and jerk/snap penalty; affects all methods.
  • Marker data low-pass filter cutoff = 6 Hz
    Set in Section 2.1 without sensitivity analysis; used for all marker data.
  • Force plate data low-pass filter cutoff = 20 Hz
    Set in Section 2.1; used before downsampling.
assumptions (5)
  • standard math Newton's second law applied to the whole body: the net external force equals total body mass times CoM acceleration.
    Basis for the external force residual in Eq. 4; assumes force plates measure net external force and the body can be modeled as a point mass at the CoM.
  • domain assumption The anthropometric tables of Dumas et al. (2007) provide valid segment masses and CoM locations.
    Used to define segment inertial parameters in the OpenSim model (Section 2.2).
  • domain assumption The OpenSim musculoskeletal model and BodyKinematics tool produce accurate segment kinematics.
    Used to compute whole-body CoM position and velocity from marker data (Section 2.2).
  • ad hoc to paper Activities can be qualitatively separated into Static and Dynamic based on magnitude of segment displacement.
    The classification in Section 2.1 and Table 1 is not based on a quantitative criterion or validated threshold.
  • domain assumption The Kalman filter noise model with zero-mean Gaussian noise matches the actual sensor errors.
    Assumed in Section 2.2 to set up the filter equations.

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Cite this review

Pith. "Pith review of Comparative analysis of whole-body center-of-mass estimation methods in dynamic and static activities using marker-based systems." pith.science (2026). https://pith.science/paper/BMV7DL4D

@misc{pith2026241118774,
  author       = {Pith},
  title        = {Pith review of: Comparative analysis of whole-body center-of-mass estimation methods in dynamic and static activities using marker-based systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BMV7DL4D}},
  note         = {Machine review of arXiv:2411.18774}
}
abstract

Accurate estimation of the whole-body center of mass (CoM) is essential for assessing human stability and postural control. However, selecting the most accurate estimation method is challenging due to the complexity of human movement, diverse nature of activities, and varying availability of equipment, such as marker-based systems and ground reaction force (GRF) sensors. This study compares three CoM estimation methods -- "Pelvis Markerset", "Whole-Body Markerset", and "Whole-Body Markerset & GRFs" -- across static activities, such as standing with eyes closed, and dynamic activities, such as picking up an object from the ground. Using the root mean square (RMS) of "external force residual" (the difference between measured ground reaction forces and estimated CoM accelerations multiplied by total body mass) as a performance metric, we found that while all methods performed similarly under static conditions, the "Pelvis Markerset" method showed 96% to 104% higher RMS external force residual values during dynamic activities compared to the two whole-body methods ($p<0.001$, Cohen's $d$:2.90-3.04). The accuracy of "Whole-Body Markerset & GRFs" (i.e., Kalman filter) was similar to "Whole-Body Markerset", suggesting that incorporating the GRFs through the presented Kalman filter does not improve the estimates from whole-body kinematics. Based on these findings, we recommend the "Whole-Body Markerset" as it performs well and does not require information from GRFs. The "Pelvis Markerset" method can be used in static activities or when markersets around the pelvis reflect whole-body kinematics. This method is not recommended for CoM state estimation in highly dynamic scenarios and when whole-body markersets are available.

Figures

Figures reproduced from arXiv: 2411.18774 by the authors.

Figure 1
Figure 1. (a) The anterior and posterior views of the Biomech (57) markerset. The calibration markers are highlighted in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. (a,c) RMS of force residual for Static and Dynamic activities, when estimating position and velocity. The * [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Works this paper leans on

24 extracted references · 20 canonical work pages

  1. [8]

    and Young et al

    Adjustments to McConville et al. and Young et al. body segment inertial parameters. Journal of Biomechanics 40, 543–553. doi: 10.1016/j.jbiomech.2006.02.013. Hasan, S.S., Robin, D.W., Szurkus, D.C., Ashmead, D.H., Peterson, S.W., Shiavi, R.G.,

    work page doi:10.1016/j.jbiomech.2006.02.013 2006

  2. [13]

    Estimation of the center of mass of humanoid robot, in: 2007 International Conference on Control, Automation and Systems, IEEE, Seoul, South Korea. pp. 2705–2709. doi:10.1109/ICCAS.2007.4406826. OptiTrack,

    work page arXiv 2007

  3. [16]

    Journal of Biomechanics 35, 707–712

    Body segment inertial parameter estimation for the general population of older adults. Journal of Biomechanics 35, 707–712. doi: 10.1016/S0021-9290(01)00250-0 . Rajagopal, A., Dembia, C.L., DeMers, M.S., Delp, D.D., Hicks, J.L., Delp, S.L.,

    work page doi:10.1016/s0021-9290(01)00250-0

  4. [18]

    Robotics and Autonomous Systems 73, 16–23

    An adaptive control strategy for postural stability using a wearable robot. Robotics and Autonomous Systems 73, 16–23. doi: 10.1016/j.robot.2014.11.014. Saini, M., Kerrigan, D.C., Thirunarayan, M.A., Du ff-Raffaele, M.,

    work page doi:10.1016/j.robot.2014.11.014 2014

  5. [20]

    IEEE Transactions on Biomedical Engineering 56, 1189–1195

    Ambulatory Estimation of Center of Mass Displace- ment During Walking. IEEE Transactions on Biomedical Engineering 56, 1189–1195. doi: 10.1109/TBME.2008. 2011059. Seth, A., Sherman, M., Reinbolt, J.A., Delp, S.L.,

    doi:10.1109/tbme.2008 2008

  6. [22]

    Procedia IUTAM 2, 241–261

    Simbody: Multibody dynamics for biomedical research. Procedia IUTAM 2, 241–261. doi: 10.1016/j.piutam.2011.04.023. Winter, D.,

    work page doi:10.1016/j.piutam.2011.04.023 2011

  7. [23]

    Center of mass estimator for humanoids and its application in modelling error compensation, fall detection and prevention, in: 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), IEEE, Seoul, South Korea. pp. 67–73. doi:10.1109/HUMANOIDS.2015.7363533. Yazdani, M., Gamble, G., Henderson, G., Hecht-Nielsen, R.,

    work page arXiv 2015

  8. [1996]

    Part I: Methods

    Simultaneous measure- ment of body center of pressure and center of gravity during upright stance. Part I: Methods. Gait & Posture 4, 1–10. doi:10.1016/0966-6362(95)01030-0 . Hof, A., Gazendam, M., Sinke, W.,

    work page doi:10.1016/0966-6362(95)01030-0

Show all 24 references
  1. [1997]

    Journal of Biomechanics 30, 347–354

    Center of mass velocity-position predictions for balance control. Journal of Biomechanics 30, 347–354. doi: 10.1016/S0021-9290(96)00165-0 . Pavol, M.J., Owings, T.M., Grabiner, M.D.,

    doi

  2. [1998]

    Journal of Biomechanical Engineering 120, 133–139

    The Vertical Displacement of the Center of Mass During Walking: A Comparison of Four Measurement Methods. Journal of Biomechanical Engineering 120, 133–139. doi: 10.1115/1.2834293. Schepers, H., Van Asseldonk, E., Buurke, J., Veltink, P.,

    doi

  3. [2001]

    Archives of Physical Medicine and Rehabilitation 82, 80–85

    Postural control in the elderly: An analysis of test-retest and interrater reliability of the COP-COM variable. Archives of Physical Medicine and Rehabilitation 82, 80–85. doi:10.1053/apmr.2001.18678. Cotton, S., Murray, A., Fraisse, P.,

    2001

  4. [2002]

    Journal of Biomechanics 35, 117–124

    Simultaneous positive and negative external mechanical work in human walking. Journal of Biomechanics 35, 117–124. doi: 10.1016/S0021-9290(01)00169-5 . Dumas, R., Ch `eze, L., Verriest, J.P.,

    doi

  5. [2005]

    Journal of Biomechanics 38, 1–8

    The condition for dynamic stability. Journal of Biomechanics 38, 1–8. doi:10.1016/j.jbiomech.2004.03.025. Hof, A.L.,

    2004 doi

  6. [2007]

    IEEE Transactions on Biomedical Engineering 54, 1940–1950

    OpenSim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement. IEEE Transactions on Biomedical Engineering 54, 1940–1950. doi: 10.1109/TBME.2007.901024. Donelan, J., Kram, R., Kuo, A.D.,

    1940

  7. [2008]

    Human Movement Science 27, 112–125

    The ‘extrapolated center of mass’ concept suggests a simple control of balance in walking. Human Movement Science 27, 112–125. doi:10.1016/j.humov.2007.08.003. 8 Kagawa, T., Ishikawa, H., Kato, T., Sung, C., Uno, Y .,

    2007 doi

  8. [2009]

    IEEE/ASME Transactions on Mechatronics 14, 707–712

    Estimation of the Center of Mass: From Humanoid Robots to Human Beings. IEEE/ASME Transactions on Mechatronics 14, 707–712. doi:10.1109/TMECH.2009.2032687. Delp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, D.G.,

    2009

  9. [2011]

    Procedia IUTAM 2, 212–232

    OpenSim: A musculoskeletal modeling and simulation frame- work for in silico investigations and exchange. Procedia IUTAM 2, 212–232. doi: 10.1016/j.piutam.2011.04

    2011 doi

  10. [2012]

    Neural Networks 27, 74–80

    A simple control policy for achieving minimum jerk trajectories. Neural Networks 27, 74–80. doi: 10.1016/j.neunet.2011.11.005. 9

    2011 doi

  11. [2015]

    IEEE Transactions on Robotics 31, 415–424

    Optimization-Based Motion Planning in Joint Space for Walking Assistance With Wearable Robot. IEEE Transactions on Robotics 31, 415–424. doi: 10.1109/TRO.2015. 2409434. Kwon, S., Oh, Y .,

    2015 doi

  12. [2016]

    IEEE Transactions on Biomedical Engineering 63, 2068–2079

    Full-Body Musculoskeletal Model for Muscle-Driven Simulation of Human Gait. IEEE Transactions on Biomedical Engineering 63, 2068–2079. doi:10.1109/TBME.2016.2586891. Rajasekaran, V ., Aranda, J., Casals, A., Pons, J.L.,

    2016

  13. [2018]

    Journal of Biomechanics 71, 217–224

    A comparison of methods to determine center of mass during pregnancy. Journal of Biomechanics 71, 217–224. doi: 10.1016/j.jbiomech.2018.02.004. Cohen, J.,

    2018 doi

  14. [2022]

    https://docs.optitrack.com/ movement-sciences/movement-sciences-markersets/biomech-57

    Biomech 57 markerset - movement sciences documentation. https://docs.optitrack.com/ movement-sciences/movement-sciences-markersets/biomech-57 . Accessed: 2024-10-25. Pai, Y .C., Patton, J.,

    2024

  15. [2023]

    Journal of Biomechanics 146, 111415

    Comparison of ground reaction force and marker-based methods to estimate mediolateral center of mass displacement and margins of stability during walking. Journal of Biomechanics 146, 111415. doi: 10.1016/j.jbiomech.2022.111415. Catena, R.D., Connolly, C.P., McGeorge, K.M., Ca...

    2022

  16. [2024]

    doi: 10.48550/ARXIV.2411.16891

    Predicting center of mass position in non-cyclic activities: The influence of acceleration, prediction horizon, and ground reaction forces. doi: 10.48550/ARXIV.2411.16891. Berg, K.O., Wood-Dauphinee, S.L., Williams, J.I., Maki, B.,

    doi arXiv

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Reviewed August 12, 2026 · model on record in the stance chip above.