Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study focuses on the development of Pedestrian Dead Reckoning (PDR) systems. This area of ​​research is relevant. Before publication in the journal Sensors, a more detailed description of the proposed methods and algorithms, the experiments conducted, and a comparison of the results with those of other studies are required.

Comments:

1) Introduction. The introduction contains very few references. References are needed to support the relevance of indoor navigation, and in particular the relevance of Pedestrian Dead Reckoning (PDR) (PDR).

2) Introduction. In the introduction, you need to more precisely formulate the problem solved in the manuscript.

2.1. It's necessary to clearly describe the type (or types) of indoor environment for which navigation and orientation are being addressed. For example, specify the minimum number (or density) of Wi-Fi devices in the space. Also, indicate the presence/absence of steps, elevators, etc.

2.2. It is also necessary to list (numerically) the requirements for solving the navigation problem. For example, specify the permissible maximum and average positioning errors. For example, specify the permissible maximum and average orientation (heading) errors.

3) Figure 1. The elements and graphs shown in the center (Core Algorithms) of the figure are difficult to see. Correct this.

4) Lines 39-40. The text "The accelerometer measures the force of movement..." is incorrect. "Accelerometers" measure acceleration. Force is measured by "force sensors."

5) Section 3. Materials and methods are not described in sufficient detail.

5.1.  The Step Counting Algorithm should be described in more detail. The choice of algorithm should be justified. For example, in Section 2, several algorithms (methods) were mentioned, but it was not noted which one was more suitable for this study and why.

5.2. A human can maneuver and turn while pathfinding in less than a second (i.e., the 0.1-10 Hz range is also important). You may be losing a significant portion of the useful signal. In section 3.2, you should provide more detailed justification for the choice of a sampling frequency = 100 Hz and a cutoff frequency = 0.1 Hz.

5.3. Lines 310-312. Clarification is needed on what exactly is rotating and how it is rotating. Is the rotation physical, virtual, or does it involve a coordinate system transformation?

5.4. There is a lack of mathematical description of the PDR proposed in the manuscript.

6) Section 4. It is necessary to provide the characteristics of the sensors of the smartphones used.

7) Section 4. It is necessary to compare in detail the results you obtained for solving the indoor navigation problem with those obtained by other research groups. For example, with [Zhao, H.; Zhang, L.; Qiu, S.; Wang, Z.; Yang, N.; Xu, J. Pedestrian dead reckoning using a pocket-worn smartphone. IEEE Access 2019, 7, 91063–91073.]

8) Section 4.2. What are the conditions (number of people, treadmill, etc.) of the experiment described in Section 4.2? Do they differ from the conditions of the previous experiment?

9) Section 4.2. The previous section considered fewer smartphone placement options. Why? This needs to be substantiated, or sections 4.1 and 4.2 need to be aligned.

10) Section 4.3. This section does not contain a description of the test group, gait dynamics (whether there were stops, whether the pedestrian avoided obstacles, etc.), or the number of experiments (how many experiments were in the “Pocket” and “Reading” modes).

11) The number of experiments is very small. The presented sample is unrepresentative in many respects. This reduces confidence in the authors' conclusions. This should be taken into account (discussed) in sections 5 and 6.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript focuses on the development of a smartphone-based, orientation-free pedestrian navigation (PDR) system. We propose a step-counting algorithm with IMU data split by axis, a dynamic HEAT-MAP axis mapping algorithm for azimuth estimation, and an adaptive scheme for fusing PDR with Wi-Fi fingerprints. This topic is relevant because PDR robustness to arbitrary smartphone orientation and error accumulation remains a key challenge in indoor navigation. While the paper includes experimental work, methodological limitations should be addressed. The following comments are included:
Major comments:
1. The authors demonstrate improvements over their own version of the magnitude-based approach (SGL), the commercial Sensor Logger app, and a "standard" particle filter. However, a quantitative comparison with published scientific papers is lacking. In particular, a comparison with modern direction estimation algorithms and a comparison with results from other PDR systems is missing.
2. The HEAT-MAP algorithm is presented without mathematical representations such as rotation matrices, coordinate transformation models, and magnetic field robustness analysis. This undermines the scientific validity of the key contribution of the study, which is the estimation of pedestrian direction.
3. In the Discussion section, the authors explicitly state that HEAT-MAP was tested only outdoors. This is a serious limitation, as the system is marketed as an indoor navigation system, the algorithm is based on a magnetometer, and indoor spaces are characterized by significant magnetic distortions (hard/soft iron effects). The lack of indoor testing significantly reduces the reliability of the results. A full-scale indoor testing of HEAT-MAP, taking into account the limitations described above, should be conducted and described.
4. True direction of travel was determined using a magnetic compass with a tolerance of ±10°. This method does not provide highly accurate reference measurements and can introduce significant error in the RMSE estimate.

Minor comments:
1. The text requires stylistic editing.
2. Smartphone models and IMU specifications are not specified.
3. An analysis of the computing load and power consumption is missing.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper addresses the accuracy degradation in smartphone-based Pedestrian Dead Reckoning (PDR) caused by varying device placement attitudes and low-cost IMU sensor drift, proposing a comprehensive solution that includes: (1) a robust step counting algorithm, (2) a novel heading estimation algorithm (HEAT-MAP), and (3) an adaptive fusion framework. However, the following issues require clarification:

1. The work appears to integrate the authors' previously published (References 2-4). It is necessary to more explicitly articulate the incremental contributions and improvements of this journal version compared to the published conference papers (e.g., IPIN 2024, 2025).
2. The algorithm design employs "three sensor datastreams at a time (i.e., ALG, ALM, LGM, MAG)", but its innovative aspects remain unclear. The authors should clarify the methodological advancements beyond merely using component data. Additionally, the rationale for threshold selection in step estimation should be explicitly justified.
3. In the Heading/Orientation Estimation section, the method determines gravity direction via accelerometer, but the precise heading estimation mechanism is not elaborated. The authors should address: when the phone operates in arbitrary motion modes, accelerometer measurements couple motion acceleration, making horizontal plane determination solely by gravity vector infeasible; moreover, magnetometer-based heading estimation is unreliable without calibration and in magnetically noisy environments. Clarification on how these challenges are resolved is essential.
4.  The integration of PDR with WiFi is presented; however, its novelty is not sufficiently demonstrated. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This study focuses on the development of Pedestrian Dead Reckoning (PDR) systems. This area of ​​research is relevant.  The authors took into account the reviewers' comments and remarks, which had a positive impact on the manuscript quality.

Author Response

Dear Reviewer,

We thank you for your careful evaluation of our manuscript and for the constructive comments provided. These suggestions have helped us improve the manuscript’s presentation, quality, and scientific robustness. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attachment.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

We thank you for your careful evaluation of our manuscript and for the constructive comments provided. These suggestions have helped us improve the manuscript’s presentation, quality, and scientific robustness. Below we respond to your comments point by point and indicate where changes were made in the revised manuscript in red colour.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for the response. However, my key concerns regarding methodological justification and novelty remain largely unaddressed.

 

1. The response is still descriptive. Please quantify the performance improvement of this integrated framework over your prior conference works in Section 1.2 (e.g., with a summary table of error metrics).

 

2. How to utilize the data of the 84 possibilities? This critical algorithm must be explicitly described. The threshold justification (one standard deviation) requires a stronger rationale for its robustness across all modes.

 

3. The 0.1 Hz cutoff frequency choice is arbitrary without a design rationale tied to human gait dynamics.

The solution primarily addresses relative heading drift. The fundamental challenge of ensuring absolute heading accuracy in magnetically noisy environments is not resolved.

4. The dynamic coefficient (α) is a known concept. The novelty hinges on its specific adaptation rule, which is undefined. The mathematical formulation for calculating α in real-time must be provided for the method to be reproducible and verifiable.

Author Response

Dear Reviewer,

We thank you for your careful evaluation of our manuscript and for the constructive comments provided. These suggestions have helped us improve the manuscript’s presentation, quality, and scientific robustness. Below we respond to your comments point by point and indicate where changes were made in the revised manuscript in blue colour.

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

I thank the authors for their careful revision of the manuscript and detailed responses to the reviewers' comments. The manuscript is significantly improved compared to previous versions. In particular, the authors expanded the discussion of the literature, added a mathematical refinement of the HEAT-MAP algorithm, and improved the description of the experimental setup.

The inclusion of a comparison with previously published work and an additional mathematical description of the orientation model strengthen the presentation of the proposed approach. Overall, the manuscript now provides a clearer explanation of the proposed system and its implementation.

However, some methodological limitations remain that should be explicitly stated in the manuscript:

First, the comparison with state-of-the-art methods is primarily based on interstudy comparisons rather than on experiments conducted under identical conditions. While this is understandable due to differences in hardware platforms and datasets, the manuscript should clearly highlight this limitation when discussing performance superiority.

Second, the HEAT-MAP heading estimation algorithm was primarily tested in controlled outdoor experiments, while the integrated PDR system was evaluated indoors. Since magnetometer measurements are known to be affected by indoor magnetic interference, it would be useful to explicitly state in the manuscript that specialized indoor heading verification remains an area for future research.

Third, the true heading values ​​were obtained using a compass. While this approach is acceptable for practical experiments, the manuscript should clearly note that the accuracy of the reference value can affect the reported RMSE values.

With these clarifications included in the discussion section, the manuscript makes a useful contribution to the development of smartphone-based PDR systems.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I  have no question.

Author Response

Dear Reviewer,

We thank you for your careful evaluation of our manuscript and for the constructive comments provided. These suggestions have helped us improve the manuscript’s presentation, quality, and scientific robustness.