An Exhaustive Method of TOA-Based Positioning in Mixed LOS/NLOS Environments

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors in the next paragraphs, my comments about your manuscript.

 

The article proposes an innovative EM method for positioning in mixed LOS/NLOS scenarios, one recognized as a limitation in literature. The method does not require any prior information on the NLOS state, amplitudes, or noise variances-especially important in a real setting. It is a very well-formulated mathematical framework with a clear development of the model (equations 1-21), which allows for further reproducibility by other researchers.

The error decomposition and the formation of the sets Φ (BS combinatorics) and Ω are clear and well-founded. In each simulation setting, four scenarios are modeled-typical for industrial and urban environments, with various numbers of BSs and NLOS paths. The comparison with reference algorithms (SDR, SOCR, CWLS, RSDP-New) strengthens the soundness of the results. Comparatively, the proposed method has execution times in the order of milliseconds (Table 1), which makes it suitable for applying in practice.

 

Points to Improve

1. The language contains a relatively large number of grammatical and spelling errors, which hinder both the readability nd presentational quality of the scientific article. Such errors include "exhautive," "appeld," "corrsponding," "numbder," and "perfor-". A proper technical English review is strongly recommended before publication.
2. While the use of deep learning for NLOS detection is mentioned, no comparison of the proposed method with these AI-based approaches, which serve as a growing option in this field, is attempted.
3. Making up a further stake in the validation of a localization method, this work rests wholly on simulations, with no validation with actual experimental data.
4. Figures 1 through 5 are presented with axes that offer very little in terms of information, with units and scales never being consistent.
5. The Figure captions are sorely deficient in details that allow for proper interpretation without referring to the text.
6. Although the writers state that the method may be applicable for other localization methods, procedures and practical adaptations to these modalities are neither presented nor discussed.
7. In equation 19, the residue-based selection strategy assumes distributions of a certain nature for the errors; however, it does not consider the effect of the variability of these distributions.
8. The method claims to be efficient, but the combinatorial complexity grows rapidly with N. An analysis of computational scalability with N > 10 BSs would be pertinent.

Author Response

Comments 1: The language contains a relatively large number of grammatical and spelling errors, which hinder both the readability nd presentational quality of the scientific article. Such errors include "exhautive," "appeld," "corrsponding," "numbder," and "perfor-". A proper technical English review is strongly recommended before publication.

Response 1: The spelling problems pointed out in Question 1 have all been corrected in the new manuscript.

Comments 2: While the use of deep learning for NLOS detection is mentioned, no comparison of the proposed method with these AI-based approaches, which serve as a growing option in this field, is attempted.

Response 2: Thank you for your valuable suggestion. We fully understand your recommendation regarding the comparison of this study with AI-based NLOS detection methods, which indeed represent an important direction of development in this field. In our current research, we selected four classical traditional methods as benchmarks primarily for the following reasons: this study aims to propose a lightweight solution that does not rely on specific environmental prior information or complex model training. The chosen baseline methods exhibit higher direct comparability with our approach in terms of problem nature and design philosophy, which allows for a clearer demonstration of the advantages of our method in computational efficiency and robustness. We certainly recognize the importance of AI-based methods as you highlighted. In our future work, we will incorporate comparative analyses with advanced AI techniques, such as deep learning, into our research plan to further validate the performance boundaries and application potential of our method across different scenarios. Once again, we appreciate your insightful comments, which have been greatly helpful in improving our study.

 

Comments 3: Making up a further stake in the validation of a localization method, this work rests wholly on simulations, with no validation with actual experimental data.

Response 3: Thank you for your valuable feedback. We fully understand your perspective on the importance of real experimental data for validating localization methods. At this current stage of our research, we have chosen to conduct validation through theoretical simulations primarily for the following reasons: simulation experiments can provide readers with a clear and reproducible performance evaluation framework, facilitating other researchers to directly reference and verify the performance of our method. We designed four simulation experiments under different scenarios to systematically evaluate the proposed method in terms of accuracy, robustness, computational efficiency, among other aspects. These experiments effectively validate the core performance of our method. We fully recognize the importance of real-world experimental validation, and it remains an essential part of our future research plans. In the next phase of our work, we will proceed with testing and validation in practical environments to further improve the practicality and applicability of our method. Once again, we appreciate your valuable suggestion, which provides important guidance for refining our research.

 

Comments 4: Figures 1 through 5 are presented with axes that offer very little in terms of information, with units and scales never being consistent.

Response 4: In the experimental simulation result figures, the X-axis adopts noise variance while the Y-axis uses the logarithm of the root mean square error (log(RMSE)), both maintaining uniformity. In the new advanced manuscript, the font type and size are now consistent throughout.

 

Comments 5: The Figure captions are sorely deficient in details that allow for proper interpretation without referring to the text.

Response 5: Thank you for your important feedback regarding the figure captions. We fully understand your suggestion on enhancing the self-contained nature of the figures for interpretation.In the current manuscript, we have included key parameters such as comparative methods, number of base stations, and noise levels in the figure captions. Although the current captions are somewhat lengthy, they are intended to provide essential experimental conditions to facilitate interpretation alongside the main text. We fully recognize the importance of making figures self-explanatory and will strive to optimize the presentation in future research to achieve a better balance between informativeness and conciseness. We greatly appreciate your valuable comments, which are significant for improving the quality of our paper.

 

Comments 6: Although the writers state that the method may be applicable for other localization methods, procedures and practical adaptations to these modalities are neither presented nor discussed.

Response 6: While each method possesses broad applicability, the approach proposed in this study can also be extended to other types of positioning sensors. For the sake of conciseness and readability, however, the detailed steps for such extensions are not explicitly elaborated in the paper. We hope that the reviewers can appreciate this consideration and acknowledge the generalizability of our method beyond the presented context.

 

Comments 7: In equation 19, the residue-based selection strategy assumes distributions of a certain nature for the errors; however, it does not consider the effect of the variability of these distributions.

Response 7: We appreciate your insightful comments. Regarding the derivation of Equation 19, we adopted the assumption that NLOS errors are consistently positive and significantly larger than noise errors—a modeling approach consistent with studies such as references [14] and [16]. We fully recognize the importance of considering the variability of error distributions, as you rightly emphasized. In the current study, our focus has been on algorithm development building upon this widely used assumption, and we acknowledge that the impact of distribution variability has not been thoroughly explored. We kindly request your understanding regarding the rationality of the current assumptions made in this paper.

 

Comments 8: The method claims to be efficient, but the combinatorial complexity grows rapidly with N. An analysis of computational scalability with N > 10 BSs would be pertinent.

Response 8: Thank you for your valuable feedback. As you rightly pointed out, in many industrial application scenarios, the relatively high cost of UWB base station equipment often leads to a limited number of effective UWB base stations that positioning terminals can access in practical systems, due to cost-control considerations in deployment. Given this practical context, scenarios with N > 10 are indeed uncommon in real-world applications. Therefore, this study primarily focuses on analyzing typical base station configurations that are more universally applicable and practical, while not extending the investigation to setups with larger numbers of base stations. We kindly request your understanding regarding this research perspective grounded in practical considerations and would greatly appreciate your support.

Reviewer 2 Report

Comments and Suggestions for Authors

This author's team proposes and evaluates an exhaustive method for TOA-based positioning, which identifies and uses only line-of-sight base stations in mixed LOS/NLOS environments to improve accuracy and computation speed without requiring prior NLOS information.

The introduction gives a clear background on TOA-based positioning in mixed LOS/NLOS environments, referencing a good range of foundational and recent works. However, a few more citations on alternative recent machine learning approaches could further strengthen it.

The research design is sound and well-structured. It focuses on simulation-based comparative evaluation with relevant baselines and clear performance metrics.

The methods are described in considerable mathematical and procedural detail, making them reproducible, although a flow diagram or pseudocode could improve clarity for readers unfamiliar with the notation-heavy approach.

The results are clearly presented through figures and tables, with thoughtful comparisons to competing methods across multiple scenarios, though axis labels in figures could be more descriptive.

The conclusions are well-aligned with the presented results, appropriately acknowledging both strengths and limitations, particularly the constraint of needing at least three LOS-BSs.

The English is generally clear, though there are occasional minor grammatical errors and typographical issues (“corrsponding,” “numbder,” “reducation”) that should be corrected.

From the formal point of view, the manuscript is well written, readable with ordinary effort and self-explanatory. The authors have followed the MDPI template and structure, including the standard sections and declarations, although figure captions could be expanded per MDPI style guidelines.

There are several self-citations, but they appear relevant to the research rather than gratuitous. The references are technically relevant and up to date, covering both foundational literature and state-of-the-art developments.

Suggestions:

1. The mathematical formulation is thorough, but adding a concise algorithm flowchart or step-by-step pseudocode would help readers quickly grasp the procedure without navigating all the equations. This would also make the approach more accessible to practitioners from related fields.

2. Correct minor typographical and grammatical errors (“corrsponding,” “numbder,” “reducation”, etc.), ensure consistent tense usage, and expand figure captions to fully describe the experimental settings and key findings in each plot. This will improve professionalism and compliance with MDPI style.

3. The manuscript briefly notes the need for at least three LOS-BSs, but a fuller discussion of how the method might perform with fewer LOS-BSs, in real-world noisy datasets, or with hardware constraints would give the reader a more balanced view and strengthen the paper’s impact.

Comments on the Quality of English Language

Generally, the English is fine, but needs polishing. Also, please correct minor typographical and grammatical errors (“corrsponding,” “numbder,” “reducation”, “arrang”, “Ther efore”...).

Author Response

Comments 1: The mathematical formulation is thorough, but adding a concise algorithm flowchart or step-by-step pseudocode would help readers quickly grasp the procedure without navigating all the equations. This would also make the approach more accessible to practitioners from related fields.

Response 1: Given that the mathematical formulations in our paper are not overly complex and are presented in a clear manner, we opted not to include a dedicated algorithm flowchart. We hope the reviewer finds our presentation sufficient and supports our decision.

 

Comments 2: Correct minor typographical and grammatical errors (“corrsponding,” “numbder,” “reducation”, etc.), ensure consistent tense usage, and expand figure captions to fully describe the experimental settings and key findings in each plot. This will improve professionalism and compliance with MDPI style.

Response 2: In the revised manuscript, we have corrected several spelling errors. Additionally, we have provided more detailed explanations for each figure to facilitate quicker comprehension of the paper.

 

Comments 3: The manuscript briefly notes the need for at least three LOS-BSs, but a fuller discussion of how the method might perform with fewer LOS-BSs, in real-world noisy datasets, or with hardware constraints would give the reader a more balanced view and strengthen the paper’s impact.

Response 3: Thank you for your valuable suggestions. We fully understand your insight regarding the need to further explore the potential performance of the method in scenarios with fewer LOS base stations, real-world noisy datasets, or under hardware constraints. This is indeed highly valuable for enhancing the comprehensiveness and impact of the paper.

      In this study, we primarily focused on validating the performance of the proposed method in scenarios with three LOS base stations, which represents the most applicable and typical condition for our approach. We acknowledge the limitations you pointed out—for instance, the method's performance may be constrained in environments with fewer LOS base stations or in NLOS-dominated settings. This limitation has also helped identify important directions for our future research. As you are aware, every study has its specific scope of application and inherent constraints, along with respective strengths and weaknesses. Our research aims to provide an effective solution for typical application scenarios, rather than attempting to cover all possible environments. We will further investigate adaptive improvements for more complex scenarios in follow-up studies and look forward to sharing relevant progress with you in the future.

      Once again, we appreciate your insightful comments, which have helped us better understand the limitations of our work and identify directions for future improvements.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have proposed an exhaustive method (EM)-based positioning technique for mobile stations (MS) in wireless sensor networks (WSN) environment under mixed LOS and NLOS conditions. The approach utilizes the time of arrival (TOA) metric to estimate the distance of an MS from observed and predicted received signals. However, the following concerns should be addressed to improve the manuscript:

1. The abstract should be rewritten to clearly describe the conceptual framework of the proposed method, explicitly mentioning the techniques used in the positioning system. Additionally, it should summarize the overall performance of the method, including the achieved positioning (paths distance and direction) errors.
2. Abbreviations should be used consistently throughout the manuscript. For instance, in the Introduction (Page 1), “wireless sensor network” should be introduced as “wireless sensor network (WSN)” and WSN should be used thereafter. Similarly, TOA would be written in full-form upon first appearance.
3. Numerous typographical errors need correction. For example, “There fore” on Page 1 should be corrected to “Therefore.”
4. The term “residual” is critical in localization and would be defined clearly at the beginning before being used repeatedly.
5. Equation numbers should be referenced explicitly in the text when discussing them.
6. Several methods, such as the least squares (LS) approach, are mentioned without adequate discussion. The notation used in equations, such as Equation 4, should also be clearly defined.
7. The network topology, including base stations (BSs), MS, and obstacles, should be illustrated in figures. Additionally, a table summarizing all simulation parameters and their values should be added in Section 3.
8. In mixed LOS/NLOS environments, directional accuracy alongside path distance is crucial. Therefore, the directional error of the MS should be included in the performance evaluation.
9. Overall, the writing needs substantial improvement. Currently, the explanation of the proposed methods is insufficient, which hinders comprehension of the work.

Author Response

Comments 1: The abstract should be rewritten to clearly describe the conceptual framework of the proposed method, explicitly mentioning the techniques used in the positioning system. Additionally, it should summarize the overall performance of the method, including the achieved positioning (paths distance and direction) errors.

Response 1: We fully acknowledge that positioning accuracy is susceptible to specific experimental conditions, such as base station layout, and the distribution and severity of NLOS errors. A single numerical value may not adequately reflect the generalization capability of the method across diverse environments. Therefore, in the abstract, we have focused on elaborating the core concept of our approach and the overall performance improvement trend, rather than listing specific positioning accuracy value, to avoid potential misunderstandings when applied in different settings. We understand that the reviewer may be concerned about detailed quantitative results. To this end, in the experimental section of the paper, we have provided comprehensive accuracy data and analyses under various scenarios, along with derivations of formulae to explain the reasons for performance variations. We believe that by combining the methodological overview in the abstract and the complete experiments in the main text, readers can obtain an accurate and comprehensive understanding of our work. We sincerely hope that the reviewer can appreciate our rationale for this presentational choice and value any further comments on the research content of this paper.

Comments 2: Abbreviations should be used consistently throughout the manuscript. For instance, in the Introduction (Page 1), “wireless sensor network” should be introduced as “wireless sensor network (WSN)” and WSN should be used thereafter. Similarly, TOA would be written in full-form upon first appearance.

Response 2: We have already provided the full forms of both WSN and TOA in the abstract. Therefore, we believe it is unnecessary to reintroduce them in the main text. We kindly request the reviewer's understanding regarding this matter.

Comments 3: Numerous typographical errors need correction. For example, “There fore” on Page 1 should be corrected to “Therefore.”

Response 3: In the revised manuscript, we have corrected multiple spelling errors.

Comments 4: The term “residual” is critical in localization and would be defined clearly at the beginning before being used repeatedly.

Response 4: In the revised manuscript, the residual is defined as the difference between the estimated distance and the observed distance, where the estimated distance refers to the Euclidean distance between the positioning coordinates and the base station.

Comments 5: Equation numbers should be referenced explicitly in the text when discussing them.

Response 5: Formula (3) is simplified to obtain formula (4), and the parameters in formula(4) have been explained in detail in the paper. The expressions in the formulas are clearly presented, and we kindly request the reviewer's understanding.

Comments 6: Several methods, such as the least squares (LS) approach, are mentioned without adequate discussion. The notation used in equations, such as Equation 4, should also be clearly defined.

Response 6: The symbols in Formula (4) can be understood through Formulas (5) to (7), and the specific meanings of the latter three formulas have been previously explained.

Comments 7: The network topology, including base stations (BSs), MS, and obstacles, should be illustrated in figures. Additionally, a table summarizing all simulation parameters and their values should be added in Section 3.

Response 7: The new version of the manuscript includes two additional figures illustrating the distribution of base station coordinates.

Comments 8: In mixed LOS/NLOS environments, directional accuracy alongside path distance is crucial. Therefore, the directional error of the MS should be included in the performance evaluation.

Response 8: The authors have extensively reviewed relevant literature. In the field of TOA-based positioning, since terminal locations are typically simulated, directional error is rarely addressed in most published papers. The majority of evaluation methods still employ the root mean square error (RMSE) as the primary metric. Therefore, this paper adopts conventional evaluation indicators, which can effectively demonstrate the performance of the proposed method.

Comments 9: Overall, the writing needs substantial improvement. Currently, the explanation of the proposed methods is insufficient, which hinders comprehension of the work.

Response 9: We thank the reviewer for the comments. The manuscript has undergone comprehensive review and revision in the new version to meet the publication standards.

 

             In scientific research, it is quite normal for the same paper to be reviewed by different reviewers who hold different viewpoints. This often helps to promote academic exchanges and in-depth discussions. 1. We sincerely appreciate all the valuable suggestions you have provided. Your advice has played an important role in improving our paper. We have made multiple revisions to the manuscript based on your suggestions and have made adjustments in areas where consensus could be reached. For a few parts that have not yet been fully revised due to differences in academic viewpoints, we have conducted in-depth discussions and made careful references. We highly respect your review opinions and sincerely hope to receive your understanding and support. We look forward to the successful publication of this research.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors include and explain all my comments.

Author Response

We would like to express our sincere gratitude to the reviewers for their thorough and constructive feedback. We greatly appreciate that all of your comments and suggestions directly addressed the initial questions and concerns raised, providing us with valuable guidance for improving our manuscript. Your insightful input has been instrumental in enhancing the quality and clarity of this work.

Thank you once again for your time and effort in reviewing our submission.

Reviewer 3 Report

Comments and Suggestions for Authors

The following issues should be addressed in future revisions of the manuscript:

1. Several reasonable comments provided earlier have not been incorporated in the revised version.
2. The authors should include the angle of arrival along with the distance metric in the performance evaluation. Relying solely on distance measurement in indoor localization provides limited significance.

Author Response

First and foremost, we sincerely appreciate the valuable comments provided by the reviewers. In our initial response, we have provided detailed replies and corresponding revisions to six of the nine points raised. Regarding the three aspects that have not been fully addressed—namely, the inclusion of accuracy data in the abstract, the addition of direction error analysis, and further improvement in English writing quality—we would like to take this opportunity to further explain our considerations.

Since this study focuses on TOA-based positioning technology and objective experiments, we believe that including specific accuracy data in the abstract may not facilitate readers’ overall comparative understanding. Meanwhile, direction error is rarely applied in the field of TOA positioning, and therefore it was not incorporated into the performance evaluation metrics in this study. Furthermore, the manuscript has undergone professional language editing, and no other reviewers raised concerns regarding the English writing quality. That said, we highly value your feedback and remain willing to further refine the language details if necessary.

We genuinely hope that the above explanations are satisfactory. Should any further revisions be required, we are more than willing to continue improving the manuscript. Once again, we thank you for your time and guidance.

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

Although AoA is relatively rare in indoor environments due to hardware cost and multipath effects, advancements in modern MIMO technologies (Wi-Fi 6, 5G, UWB) are making AoA more feasible. However, the authors should address the following issue during the final submission:

1. The figures (Figure 1 and Figure 6) should include the locations of the MS and obstacles, particularly in NLOS scenarios, to provide a clearer representation of the network topology.

Author Response

Thank you for your valuable suggestion. We fully understand the importance of clearly indicating the locations of the MS and obstacles in the figures to represent the network topology in NLOS scenarios. In our experimental design, to comprehensively evaluate the generalizability of the algorithm, NLOS paths were randomly assigned to different base stations, while the position of the mobile station (MS) was also randomly generated within the area enclosed by the base stations. This randomness is a core aspect of our research methodology, aimed at simulating the uncertainties of real-world environments. As a result, it is indeed challenging to fixedly depict a specific topological state in the figures. We hope this explanation helps clarify our modeling approach, and we kindly seek your understanding and support. We believe that the methods and results presented in the paper still possess significant scientific value.