Improved estimation of the whole-body center of mass, a step ahead in biomechanical analyses of balance control.  

The paper presents a clear and comprehensive description of a Kalman filter-based method to enhance the estimation of center of mass kinematics. The core concept of the method is that center of mass estimated derived from rigid-body models and motion capture violate Newton's laws of motion, which can be solved by optimally combining measured external forces and kinematics. The inclusion of code implementation and the demonstration of the method's impact on foot placement control analyses are highly appreciated. I have one minor comment/suggestion regarding the methods section:

In lines 265–276, the authors describe a method to compute the discrepancy between kinematic and kinetic positions over a gait cycle. Could the authors clarify why this analysis was conducted for an average gait cycle rather than for each cycle individually? Addressing this point would help readers understand the rationale behind this choice and its implications for the analysis.

The paper present the use of Kalman filter to estimate the COM. The method is compared to model based methods and validated against the the COM acceleration during the flight phase of running.

Overall the paper is clear and complete.

I only have small comments:

1. The use of kalman filter method should be added to the title and abstract. Optimal merging, for me, recall more optimization methods than kalman filter.
2. In the methods section, it's not clear how the model were personalized.
3. In table 3, it's not clear if the data is in meters or mm. It's written in meters but then the percentage is with respect to something in mm.
4. Figure 3 and 4 have the same figure.

The manuscript presents a novel approach for determining the position of the whole-body center of mass (CoM) by combining kinematic and kinetic data through the use of a Kalman filter. The authors effectively address the inherent limitations in both kinematic and kinetic methods when used in isolation, proposing a solution that reduces errors in CoM estimation, especially during dynamic activities such as running. The study shows that the combination of kinematic and kinetic information can significantly reduce the error in estimating CoM positions, with the proposed method being applicable across different kinematic models. The paper is well-written and structured, with the problem statement clearly outlined and the methodology appropriately justified. The manuscript's integration of statistical methods, such as bootstrapping and the Mann-Whitney U test, shows a thoughtful approach to handling the small sample size.

Below you can find my detailed review of each section of the manuscript:

Title and Abstract:
- The title of the manuscript seems to clearly reflect the topic of the manuscript.
- The abstract summarizes the key findings, including the error reduction achieved with the Kalman filter method, and clearly communicates the study's contributions.

Introduction:
- The introduction outlines the challenges in CoM estimation and proposes combining kinematic and kinetic data to improve accuracy. The hypotheses are logically presented.
- The literature review presented in the introduction, addresses the different types of CoM estimation methods properly, however, it comes to my concern that among the "Kinetic" methods the "LowPass filtering of the Center of Pressure" method (Caron et al., 1997), was left unmentioned. Moreover, a relatively recent and popular CoM estimation technique named "Statically Equivalent Serial Chain" (Cotton et al., 2009) was also left unmentioned in the literature section. This technique also utilizes both kinetic and kinematic information for CoM estimation. I would recommend this section to be modified accordingly.

Methods:
- The methods are detailed enough, including the use of a publicly available database and clearly defined protocols for data processing and analysis. 
- Regarding the sample size, this can be considered a major limitation for this study (as mentioned in the limitation section), as only using 2 subjects, cannot reflect the generalizability of the study, I strongly recommend increasing the number of the participants (could be through incorporating data from another dataset).
- Regarding the statistical analysis, the use of Mann-Whitney U test and bootstrapping for confidence intervals, are appropriate and described in detail. Although the study could benefit from a larger sample size for more robust conclusions, there is no mention of a formal power analysis, which is typically used to determine whether a study has sufficient sample size to detect meaningful effects.

Results:
- The results are correctly described and interpreted. They support the hypothesis that combining kinematic and kinetic data reduces error in CoM estimation.

Discussion:
- The conclusions are supported by the results and do not overstate the findings. The author does acknowledge the need for further research to validate the method with larger datasets. However, the discussion could have been more focused on the practical implications of the proposed method. For instance, how could this Kalman filter-based approach be integrated into existing motion capture systems? How would it improve upon current methods in clinical gait analysis or athletic performance monitoring? The study would benefit from more concrete examples or applications. 
- Another concern which should be pointed out, is that the study focuses heavily on the use of a Kalman filter to combine kinematic and kinetic data, without exploring alternative filtering or data fusion techniques. The assumption of linearity and Gaussian noise makes the Kalman filter suboptimal for handling non-linear dynamics or complex noise models, which may be more prevalent in biomechanical data. The author could have explored or at least discussed other potential methods.
- Moreover, the lack of direct ground truth for horizontal CoM Coordinates should also be emphasized. Although the GRF are regarded as almost ground truth, it should be mentioned that it is still not optimal.

Summary of the review:

While this study provides an innovative solution to the problem of CoM estimation by combining kinematic and kinetic data through a Kalman filter, there are several areas where the work could be significantly improved. The small sample size, assumptions about Gaussian noise, and lack of exploration of alternative methods weaken the overall rigor of the study. Additionally, more discussion around computational complexity and practical applications would greatly enhance the manuscript’s relevance. Addressing these points would result in a more robust, generalizable, and practically useful contribution to the field, otherwise this manuscript wouldn't be ready for publication.
 

Minor comments:

- Line 44: Please mention a reference for this statement "with an accuracy typically within 1 % of the person’s weight".
- Line 156: "A few short gaps ...", I would advise to be more specific about the number/frequency of gaps available in the dataset.
- The manuscript would benefit from a thorough language revision to improve clarity and readability.