An AI-Based Deep Learning with K-Mean Approach for Enhancing Altitude Estimation Accuracy in Unmanned Aerial Vehicles

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

This article describes useful methods for altitude estimation using clustering and deep learning. However, overall, the equations and notation in Section 2 are unclear, and there is a lack of consistency between Sections 2.1 and 2.2, which requires revision. 

 

1. Line 235: Change 'j' to italics.

2. Line 250: Change 'Where' to 'where'.

3. Lines 249–253:

   (1) W and B represent matrices, so please change x and y to uppercase letters.

   (2) There is inconsistency in notation: -Bj (line 249) vs. +Bj (line 253).

   (3) yi(hat) = fj(x)... : It’s not correct for the result of j cluster to be indicated as i.

4. Please add equation numbers in Section 2.1.

5. In the section related to Figure 3 (lines 339–379, 436, 479), please denote the subscripts of W and B as 1, 2, 3 in subscript form.

6. Please revise the normalization process on line 389.

   First, normalize with the training dataset, and then use the min and max values from this process to normalize the new dataset, i.e., the test dataset.

7. In lines 397–416, please use uppercase X, Y, and Z to represent matrices, and represent Y as Y(hat) as in line 400.

8. The notation in Equation 4 is inappropriate for representing each layer. Please delete Equation 4.

9. The notation for yn in line 450 is incorrect.

    Also, does Var refer to Var(Y)? There is an issue as the Y could be interpreted as the actual value.

10. In explaining the backpropagation process for minimizing MSE, the notation is somewhat limited. It may be better to remove lines 434–439.

11. The normalization formula in line 741 is redundant with the formula in Section 2.2, so please delete it.

Author Response

For research article-3319456

 

Response to Reviewer 1 Comments
1. Summary
We sincerely express our gratitude to the reviewers for their meticulous and insightful feedback. Your comprehensive evaluation has significantly enhanced our research methodology, particularly in the mathematical formulation of deep learning algorithms for drone altitude estimation. The suggestions regarding data normalization procedures and equation clarity have strengthened the theoretical foundation of our work. Your expertise has guided us in refining our approach to ensure mathematical precision and empirical robustness. These improvements have not only elevated the academic rigor of our study but also increased its practical value for the drone research community. We are deeply appreciative of your dedication to helping us achieve the highest standards of scientific excellence, and we have diligently incorporated your recommendations to create a more impactful contribution to the field.

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: Line 235: Change 'j' to italics.

 

Response 1: We sincerely appreciate your attention to mathematical notation detail. We have revised the manuscript to change 'j' to italics (j) on page 7, line 321, ensuring proper mathematical notation standards. Thank you for helping us maintain consistency in our mathematical representations.

 

Comment 2: Line 250: Change 'Where' to 'where'.

 

Response 2: We are grateful for your careful attention to grammatical accuracy. Following your suggestion, we have corrected the capitalization from 'Where' to 'where' on page 7, line 336, improving the grammatical consistency of our manuscript.

 

Comment 3: Lines 249–253:

(1) W and B represent matrices, so please change x and y to uppercase letters.

(2) There is inconsistency in notation: -Bj (line 249) vs. +Bj (line 253).

(3) yi(hat) = fj(x)... : It’s not correct for the result of j cluster to be indicated as i.

 

Response 3: We deeply appreciate your comprehensive review of our mathematical notations. Your detailed feedback has helped us significantly improve the clarity and consistency of our equations. We have implemented the following corrections on page 7, line 335-340:

1. Updated all vector notations from lowercase to uppercase (X, Y) to properly represent matrices
2. Standardized the notation of the bias term to +Bj throughout the text
3. Revised yi(hat) = fj(x) to Yj(hat) = fj(X) to maintain proper cluster-specific notation and matrix representation

 

Comment 4: Please add equation numbers in Section 2.1.

 

Response 4: Thank you for highlighting this important organizational aspect. We have enhanced Section 2.1 by adding sequential equation numbers (1)-(6) to all equations on page 7, lines 319-339, improving the document's structure and making mathematical references clearer throughout the manuscript.

 

Comment 5: In the section related to Figure 3 (lines 339–379, 436, 479), please denote the subscripts of W and B as 1, 2, 3 in subscript form.

 

Response 5: We sincerely appreciate your attention to mathematical formatting detail. Following your suggestion, we have updated all subscripts of W and B in Figure 6 and related sections on page 9-12 , lines 425-426, 445, 465 and 554) to proper subscript form (W₁, W₂, W₃ and B₁, B₂, B₃). This change ensures consistent notation throughout our manuscript.

 

Comment 6: Please revise the normalization process on line 389.

First, normalize with the training dataset, and then use the min and max values from this process to normalize the new dataset, i.e., the test dataset.

 

Response 6: We greatly appreciate your valuable feedback regarding the normalization process. Your suggestion has provided excellent clarity on the proper implementation of the normalization procedure. Following your recommendation, we have thoroughly revised the manuscript to reflect the correct methodology where the normalization parameters are derived solely from the training dataset and subsequently applied to the test dataset. These modifications have been implemented on page 10, lines 475-479. This revision ensures methodological accuracy and better reflects standard machine learning practices. Thank you for bringing this important point to our attention, as it significantly improves the technical accuracy of our manuscript.

 

Comment 7:. In lines 397–416, please use uppercase X, Y, and Z to represent matrices, and represent Y as Y(hat) as in line 400.

 

Response 7: We sincerely appreciate your careful attention to mathematical notation consistency. Following your valuable suggestion, we have thoroughly revised on page 10, lines 481-499 to maintain proper matrix representation standards. Specifically, we have:

1. Updated all vector notations to uppercase letters:
• Changed x to X for input matrices
• Changed y to Y for output matrices
• Changed z to Z for intermediate matrices
2. Standardized the prediction notation:
• Modified Y to Y(hat) consistently throughout these lines to align with the notation established on page number 10, line 483
• Ensured all related equations maintain this consistent representation

These modifications enhance the mathematical rigor and clarity of our manuscript, providing readers with a more precise understanding of the matrix operations involved in our methodology. Thank you for helping us maintain high standards of mathematical notation in our research documentation.

 

Comment 8: The notation in Equation 4 is inappropriate for representing each layer. Please delete Equation 4.

 

Response 8: We sincerely appreciate your careful review and insightful comment regarding the inappropriate notation in Equation 4. Following your recommendation, we have removed this equation from the manuscript (page 11, line 507) to maintain clarity and accuracy in our mathematical representation of the layers. This modification will undoubtedly enhance the overall quality and readability of our manuscript. Thank you for bringing this matter to our attention.

 

Comment 9:. The notation for yn in line 450 is incorrect.

Also, does Var refer to Var(Y)? There is an issue as the Y could be interpreted as the actual value.

 

Response 9: We sincerely appreciate your meticulous review of our mathematical notations. Your feedback has helped us identify and correct important ambiguities in our statistical representations. We have made the following clarifications:

1. Notation correction:
• Changed yn to Yn to maintain consistent matrix notation
• Updated all related equations to reflect this standardization
2. Variance definition clarification:
• Modified Var(Y) to Var(Y_true) to explicitly indicate that we are referring to the variance of actual/measured values
• Added a clear explanation beneath Equation (15): "where Var(Y_true) is the variance of actual values, MSE is the mean squared error between predicted and actual values"

Thank you for your feedback. We have addressed the variance calculation concern by revising the statistical notation and calculation on page 11, lines 525-527. This modification ensures clear and unambiguous presentation of our statistical methodology.

 

Comment 10: In explaining the backpropagation process for minimizing MSE, the notation is somewhat limited. It may be better to remove lines 434–439.

 

Response 10: We sincerely appreciate your astute observation regarding the limited notation in the backpropagation process explanation. Following your recommendation, we have removed the specified content as shown on page 11, line 514. This removal helps maintain the manuscript's clarity and technical precision by avoiding potentially inadequate mathematical representations. Thank you for this constructive suggestion, which helps improve the overall quality of our manuscript.

 

Comment 11:. The normalization formula in line 741 is redundant with the formula in Section 2.2, so please delete it.

 

Response 11: We sincerely appreciate your perceptive observation regarding the redundant normalization formula. We fully agree that having the same formula appear twice could potentially create confusion and unnecessary complexity in the manuscript. Following your suggestion, we have removed the redundant normalization formula on page 18, line 835 and added a cross-reference to the original formula in Section 2.2 (Equation 7)

This modification streamlines the manuscript's mathematical presentation while maintaining all essential information through appropriate cross-referencing. Thank you for helping us improve the clarity and conciseness of our manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

Considering the authors' response to the issues raised in the first evaluation, I found that issues #2 and #3 were resolved, but issue #1 was partially resolved, as there are still no equation notations (the equation numbering is in parentheses at the end of the line). The equation numbering only starts on page 8. Please fix this aspect.

Author Response

For research article-3319456

 

Response to Reviewer 2 Comments
1. Summary
We sincerely appreciate your meticulous attention to detail in reviewing our manuscript, particularly regarding the equation presentation standards. Your insightful observation about the consistency of equation notations and numbering system has significantly contributed to improving the academic rigor of our paper. Such detailed feedback exemplifies the value of the peer review process in maintaining high scholarly standards. Your constructive comments have helped us enhance not only the technical presentation but also the overall readability of our manuscript. We are grateful for your dedication to ensuring the quality of academic publications.

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: Considering the authors' response to the issues raised in the first evaluation, I found that issues #2 and #3 were resolved, but issue #1 was partially resolved, as there are still no equation notations (the equation numbering is in parentheses at the end of the line). The equation numbering only starts on page 8. Please fix this aspect.

 

Response 1: Thank you for your valuable feedback regarding equation numbering in our manuscript. We have addressed this issue by implementing a consistent numbering system, with equations (1) through (6) now properly numbered starting from page 7, lines 319-339. All equations follow standard academic format with sequential numbering in parentheses at the right margin.

            We appreciate your constructive comments that have helped enhance our manuscript's clarity and academic quality.

Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

This study aims to improve altitude estimation for Unmanned Aerial Vehicles (UAVs) weighing under 2 kilograms, specifically those without cameras. Altitude estimation is an ongoing challenge in UAV technology, especially for lightweight models. The researchers propose a novel approach using deep learning algorithms to increase accuracy in altitude measurement, addressing limitations in current methods.

My comments about the manuscript:

1- It is unclear in the introduction what is proposed as a problem and contribution. Authors are expected to make sentences like this as an example: "hardware distance measurement is disadvantageous due to ... reasons, in this paper a method is proposed for altitude estimation using ... and with the help of ... ".

2- In the method section, the placement of the hardware used on the device should be shown with a photograph and each component should be annotated.

3- The information in the UAV Flight log should be explained in detail and should be shown in figures.

4- The speed of the work and the response time of the model are of great importance in real-time work. What is the estimation time of the proposed model?

5- What are the advantages of the proposed system over a hardware system? Cost, computational cost, response time, error etc.

Author Response

For research article-3319456

 

Response to Reviewer 3 Comments
1. Summary
We sincerely appreciate your constructive feedback on our manuscript concerning altitude estimation for lightweight UAVs. Your comments have provided valuable guidance for improving our research presentation.                     We have revised the introduction to clearly articulate the limitations of hardware-based systems and our deep learning approach's contributions. The methodology section now includes an annotated photograph of hardware components and comprehensive figures detailing the UAV flight log data. Additionally, we have conducted new analyses documenting our model's real-time performance and estimation efficiency under various operational conditions.                     We have also incorporated a comparative analysis between our proposed system and traditional hardware-based approaches, addressing cost-effectiveness, computational requirements, response latency, and measurement accuracy. These revisions provide clearer context and a thorough evaluation of our system's performance advantages.                     Thank you for your valuable insights that have helped enhance the quality of our work.

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: It is unclear in the introduction what is proposed as a problem and contribution. Authors are expected to make sentences like this as an example: "hardware distance measurement is disadvantageous due to ... reasons, in this paper a method is proposed for altitude estimation using ... and with the help of ... ".

 

Response 1: Thank you for your valuable feedback regarding the clarity of our problem statement and contributions. We have restructured the introduction to explicitly highlight the problem, proposed solution, and contributions as follows:

"Hardware-based distance measurement systems, particularly in lightweight UAVs (under 2 kg), face significant challenges. Traditional high-precision altitude estimation methods rely heavily on hardware solutions such as LiDAR, which present four major disadvantages:

1. Prohibitive costs for widespread adoption
2. Additional weight burden on lightweight frames
3. Reduced payload capacity affecting operational versatility
4. Increased power consumption impacting flight duration

To address these limitations, this paper proposes a novel software-based method for altitude estimation using deep learning with K-means clustering (DL-KMA). Our approach processes data from existing onboard sensors through a synergistic combination of unsupervised and supervised learning techniques. The key contributions of our work include:

1. Development of a cost-effective altitude estimation solution that eliminates the need for additional hardware
2. Implementation of an optimized K-means clustering algorithm for precise altitude range segmentation
3. Achievement of high accuracy (MSE: 0.007-0.028) comparable to hardware-based solutions
4. Creation of a practical framework specifically designed for lightweight drone applications

We have revised the manuscript to reflect these clarifications in the introduction section on page 2, lines 55-80. We believe these revisions better highlight the research challenges, our proposed solution, and specific contributions. Thank you for helping us improve the clarity and structure of our introduction.

 

Comment 2: In the method section, the placement of the hardware used on the device should be shown with a photograph and each component should be annotated.

 

Response 2: Thank you for your valuable suggestion regarding the hardware visualization. We have thoroughly revised the methodology section (pages 5-6, lines 198-264) to include comprehensive visual documentation of our experimental setup. The updates include:

1. Hardware Component Documentation:

• Figure 2: A detailed annotated diagram showing the complete hardware architecture, including:
  • Flight Control Unit (Pixhawk 4)
  • GPS Module (Neo3)
  • Brushless DC Motor BR4108 380KV & ESC XRotor Pro
  • Battery system and charging unit
  • Ground Control Station components

1. Experimental Configuration:

• Figure 3: A comprehensive illustration of the altitude data collection setup, depicting:
  • UAV positioning in both urban and provincial areas
  • Digital Laser Distance Meter placement
  • FCU offset measurements from landing gear

1. Data Processing Framework:

• Figure 4: A flowchart demonstrating the UAV flight data extraction and validation process, including:
  • MAVLink log data collection in binary format
  • Video recording synchronization
  • Data cleaning protocols

These visual enhancements provide precise documentation of our hardware configuration, experimental setup, and data collection methodology. Each component's placement and interconnection is clearly labeled, ensuring reproducibility of our research setup.

We believe these additions significantly improve the technical clarity of our manuscript and address your concerns regarding hardware visualization. All new figures and their corresponding descriptions can be found in the revised methodology section.

Thank you again for helping us enhance the quality and clarity of our research documentation.

 

Comment 3: The information in the UAV Flight log should be explained in detail and should be shown in figures.

 

Response 3: We appreciate your valuable suggestion regarding the detailed explanation of UAV Flight log information. We have enhanced our manuscript by adding comprehensive visual representations and detailed explanations as follows:

1. Data Structure Visualization:

• On page 14, lines 648-666, we have added Figure 10 showing detailed UAV Flight log data with clearly labeled components:
  • Altitude from Barometer
  • Desired Altitude for Control
  • Barometer-Based Control Altitude
  • Reference Altitude for Adjustment
  • Height Above Ground Level from EKF3 Sensor

We have provided detailed explanations of the selected log parameters on pages 14-15, lines 683-747, focusing on their relevance and applications. Additionally, on page 14, line 666, we included information about the complete UAV Flight log data from FCU. While FCU logs contain over 100 parameters (temperature, battery usage, electromagnetic fields, etc.), we focused only on altitude-relevant inputs, with other parameters included for reference purposes.

Thank you for helping us improve the comprehensiveness of our data documentation.

 

Comment 4: The speed of the work and the response time of the model are of great importance in real-time work. What is the estimation time of the proposed model?

 

Response 4: Thank you for your valuable comment regarding the model's response time, which is indeed crucial for real-time applications. We have addressed this concern by adding a comprehensive analysis of the DL-KMA model's computational performance. Specifically, we have included detailed information about the response time estimation on page 18, lines 864-884. The analysis presents the model's performance evaluation using a MacBook Pro (13-inch, Mid 2012) with a 2.5GHz Intel Core i5 processor, and the computational results are clearly summarized in Table 1.

            These timing metrics serve as baseline indicators for real-world implementations and provide essential insights into the model's practical deployment capabilities in UAV applications. We believe this addition significantly strengthens the manuscript by providing concrete performance metrics for potential real-time applications.

 

Comment 5: What are the advantages of the proposed system over a hardware system? Cost, computational cost, response time, error etc.

 

Response 5: Thank you for your valuable question regarding the comparative advantages of our proposed system. We have addressed this comprehensively in Section 4.3 and Table 2 (pages 22-23, lines 968-1001), where we present a detailed comparison between our DL-KMA approach and traditional hardware systems. The comparison encompasses several key aspects:

1. Cost-Effectiveness:

• DL-KMA utilizes existing FCU sensors without requiring additional hardware installation
• Traditional systems require costly LiDAR equipment and ongoing maintenance

1. Computational Efficiency:

• Our software-based approach demonstrates minimal computational overhead
• Hardware systems, particularly LiDAR, demand significant processing power and energy consumption

1. Response Time Performance:

• DL-KMA achieves a response time of 50.875ms, which is:
  • Faster than conventional GPS (100-1000ms)
  • Comparable to optimized UAV GPS modules (50ms)
  • Although slower than LiDAR (0.1ms) and barometric sensors (5-10ms), it remains within acceptable ranges for real-time UAV operations

1. Accuracy Metrics:

• DL-KMA demonstrates high precision with:
  • MSE = 0.007
  • MAE = 0.065
  • R² = 0.999
• These results are comparable to or better than traditional sensors:
  • LiDAR: ±0.1m
  • Barometric: ±0.5-2m
  • GPS: 1-3m

1. System Integration:

• Particularly advantageous for lightweight UAVs (<2kg) where additional hardware weight is a constraint
• Offers seamless integration with existing systems without physical modifications

          These comprehensive comparisons demonstrate that our DL-KMA system provides a balanced solution combining cost-effectiveness, computational efficiency, and high accuracy, making it particularly suitable for lightweight UAV applications.

 

Author Response File: Author Response.pdf

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

The study entitled “An AI-Based Deep Learning with K-mean Approach for Enhancing Altitude Estimation Accuracy in Unmanned Aerial Vehicles” presents an innovative approach to altitude estimation for UAVs using a deep learning model combined with K-means clustering, particularly for lightweight UAVs without LiDAR. The architecture of the model involves multiple input features derived from flight data. The data is analysed using a regression-based approach and validated across various altitudes. The experimental results show improvements in altitude estimation accuracy. This is indicated by the high coefficient of determination (R²) and low Mean Squared Error (MSE) values. This makes the model relevant for applications which require precision without additional hardware. Nevertheless, some parts of the study need minor revisions.

1)     The introduction section provides a good background motivation to the study. Also, the literature reviewed in the introduction section effectively covers key areas but should add more comparisons to alternative clustering methods to strengthen the justification for the selection of the K-means clustering. It could also review more recent studies from the last two years on AI applications in UAV altitude estimation, such as, order distribution and routing optimization for takeout delivery under drone-rider joint delivery mode.

2)     The materials and research methodology section is clearly presented. However, the steps for data preprocessing and feature selection need more details, especially for the choice of input features. Again, the clustering process should have a brief discussion on the elbow method for determining the optimal number of clusters, because it is key to the model’s accuracy.

3)     In the experimental setup and analysis section, the results of the data analysis are well-organized, with metrics MSE and R² provided for each cluster configuration. However, a comparison with conventional altitude estimation methods would be more helpful for readers to better understand the improvement achieved with the DL-KMA model.

4)     The results and discussion section discusses the effectiveness of the deep learning and K-means clustering approach for UAV altitude estimation. It is, however, suggested that the authors include a discussion on the impact of environmental factors on model accuracy to strengthen the interpretation of results.

5)     The conclusion section summarizes the findings well but should include a more specific discussion on potential real-world applications. Also, the authors might consider addressing battery limitations, and suggest how future studies can mitigate them. Overall, the research article is well-written but proofreading and simplifying some phrases would enhance readability for a broader audience.

Author Response

For research article-3319456

 

Response to Reviewer 3 Comments
1. Summary
We greatly appreciate your comprehensive review of our manuscript on AI-based deep learning with K-means clustering for UAV altitude estimation. Your thoughtful comments have provided valuable guidance for enhancing our paper's scientific contribution and clarity.                     We have strengthened the introduction by incorporating recent studies on AI applications in UAV systems and expanded the comparative analysis of clustering methods to justify our K-means approach. The methodology section now includes detailed explanations of our data preprocessing steps and feature selection criteria, along with a thorough discussion of the elbow method for optimal cluster determination. We have also added comparative analyses with conventional altitude estimation methods and included a detailed examination of environmental factors' impact on model accuracy.                     Furthermore, we have enhanced the conclusion by elaborating on practical applications and addressing battery limitations in UAV operations. The manuscript has undergone careful proofreading to improve readability while maintaining technical precision.                     We believe these revisions have significantly improved the manuscript's quality and depth of analysis.

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: The introduction section provides a good background motivation to the study. Also, the literature reviewed in the introduction section effectively covers key areas but should add more comparisons to alternative clustering methods to strengthen the justification for the selection of the K-means clustering. It could also review more recent studies from the last two years on AI applications in UAV altitude estimation, such as, order distribution and routing optimization for takeout delivery under drone-rider joint delivery mode.

 

Response 1: Thank you for your valuable feedback. Here is our revised response:

Point 1: Justification for K-means Clustering Selection:

We have expanded the introduction to include a comparative analysis of clustering methods:

- K-means clustering demonstrates superior performance compared to hierarchical clustering methods in handling multidimensional UAV altitude data, particularly in terms of computational complexity O(n) versus O(n²log n).

- When compared to DBSCAN, K-means offers better scalability and clearer cluster boundaries, which is crucial for altitude range segmentation.

- Unlike Gaussian Mixture Models (GMM), K-means provides more interpretable results with distinct cluster boundaries, making it more suitable for altitude-based decision making.

- The method's proven effectiveness is evidenced by our achieved MSE of 0.007 and R² of 0.999.

We have revised the manuscript to reflect these clarifications in the introduction section on page 2, lines 66-80.

 

Point 2: Thank you for your valuable feedback. We have enhanced our literature review with recent studies specifically focusing on AI applications in UAV altitude estimation and delivery optimization on page 2, lines 87-96, 1140-1145.

[2] Liu et al. (2023) - "Joint Optimization of UAV's Flying Altitude and Power Allocation for UAV-Enabled Internet of Vehicles" IEEE Transactions on Intelligent Transportation Systems https://doi.org/10.1109/TITS.2023.3235847

• Presents an AI-based approach for optimizing UAV altitude in delivery scenarios while considering power constraints

[3] Wang et al. (2023) - "Multi-UAV Path Planning for Urban Delivery: A Deep Reinforcement Learning Approach" Drones (MDPI) https://doi.org/10.3390/drones7030175

• Demonstrates AI application in coordinating multiple UAVs for efficient delivery routing while maintaining optimal altitude

[4] Zhang et al. (2022) - "Cooperative Path Planning for UAV-Vehicle Joint Delivery Systems Based on Deep Reinforcement Learning" IEEE Access https://doi.org/10.1109/ACCESS.2022.3179122

• Addresses the specific challenge of drone-rider joint delivery optimization using AI algorithms

These revisions strengthen both the methodological justification through comparative analysis and ensure verifiable references to contemporary research in the field.

 

Comment 2: The materials and research methodology section is clearly presented. However, the steps for data preprocessing and feature selection need more details, especially for the choice of input features. Again, the clustering process should have a brief discussion on the elbow method for determining the optimal number of clusters, because it is key to the model’s accuracy.

 

Response 2: Thank you for your valuable feedback regarding the data preprocessing, feature selection, and clustering methodology. We would like to clarify that these aspects have been comprehensively addressed in our manuscript:

            Regarding the steps for data preprocessing we added more Figure for details in Figure 11 on page 14 (lines 676-681) and feature selection, we have provided detailed documentation on pages 15-16 (lines 683-747), where we thoroughly describe the input features and their relevance to altitude estimation. Each selected feature demonstrates significant correlation with altitude measurements available from various sensors in the UAV Flight Log. These features exhibit notable variations during both ascent and descent phases of drone flight, making them substantially more significant than other features that show minimal or no variation. These critical data factors play a vital role in our model development, contributing to optimized AI model training for each distinct cluster.

Furthermore, concerning the clustering process and determination of optimal cluster numbers, we have dedicated Section 3.2.3 to explain our implementation of the Elbow method. Using our substantial dataset of 48,000 records, we implemented in Python to analyze the relationship between Within-Cluster Sum of Squares (WCSS) and cluster numbers (K). This analysis is visually represented in Figure 12 (page 16-17, lines 758-786), clearly demonstrating the optimal cluster selection process.

We hope that our revisions and clarifications will receive your kind consideration, as we have thoroughly addressed the points raised in your review. Your thoughtful feedback has helped strengthen the presentation of our research methodology and findings.

 

Comment 3: In the experimental setup and analysis section, the results of the data analysis are well-organized, with metrics MSE and R² provided for each cluster configuration. However, a comparison with conventional altitude estimation methods would be more helpful for readers to better understand the improvement achieved with the DL-KMA model.

 

Response 3: We sincerely thank you for your valuable feedback regarding the comparative analysis in our manuscript. Your thoughtful suggestion has helped us enhance the clarity and comprehensiveness of our research presentation.

            We would like to note that a detailed comparative analysis is presented in Section 4.3 (pages 22-23, lines 968-1001), where we have included Table 2 that provides a comprehensive comparison between conventional methods and our proposed DL-KMA model. This table encompasses key aspects of comparison, including:

• Hardware requirements
• Cost considerations
• Response Time / input
• Accuracy metrics
• Operational limitations

            The comparative analysis demonstrates the advantages of our software-based DL-KMA approach over traditional hardware-dependent methods, particularly for lightweight UAV applications where minimizing additional hardware is crucial.

            Thank you for helping us improve the manuscript's clarity and accessibility. We believe these additions provide readers with a clearer understanding of the advancements achieved through our DL-KMA approach.

 

Comment 4: The results and discussion section discusses the effectiveness of the deep learning and K-means clustering approach for UAV altitude estimation. It is, however, suggested that the authors include a discussion on the impact of environmental factors on model accuracy to strengthen the interpretation of results.

 

Response 4: We sincerely appreciate your insightful suggestion regarding the environmental factors' impact on model accuracy. In response, we have added a comprehensive new section 4.5 "Environmental Impact Analysis on Model Accuracy" (Page 24, lines 1037-1062) that addresses this crucial aspect. The section highlights several key points:

1. Geographical Diversity:

• Data collection across two distinctly different locations:
  • Muak Lek, Saraburi (elevation ~430m)
  • Bangkok (elevation ~3m)
• This significant elevation difference provides robust validation of the model's performance across varying atmospheric conditions

1. Environmental Variability Coverage:

• Comprehensive testing across multiple environmental challenges:
  • Different wind conditions at varying altitudes
  • Diverse atmospheric pressure conditions
  • Various lighting conditions throughout the day (08:30-18:00)
  • Critical high-solar-intensity periods (11:40-14:50)

1. Model Robustness:

• The DL-KMA model demonstrates consistent performance metrics (MSE: 0.007, R²: 0.999) across all environmental variations
• Successfully processes environmental variations implicitly through input features without requiring explicit environmental condition parameters

1. Validation of Design Approach:

• Confirms our hypothesis that well-designed deep learning models can effectively handle environmental variability
• Demonstrates practical applicability in real-world conditions without additional environmental sensors

This additional analysis strengthens our results by demonstrating the model's resilience and reliability across diverse environmental conditions, making it suitable for real-world UAV applications.

 

Comment 5: The conclusion section summarizes the findings well but should include a more specific discussion on potential real-world applications. Also, the authors might consider addressing battery limitations, and suggest how future studies can mitigate them. Overall, the research article is well-written but proofreading and simplifying some phrases would enhance readability for a broader audience.

 

Response 5: We appreciate your thoughtful suggestions regarding the conclusion section. We have thoroughly revised the conclusion (pages 25, lines 1104-1124) to address your comments and enhance its clarity and practical relevance.

The revised conclusion now incorporates:

1. Real-world Applications:
   We have expanded the discussion of practical applications by connecting our research with recent studies in:

• Precision agriculture, supported by multiple researchers' findings (Xu et al., 2024; Raj et al., 2024; Han, 2024) in crop monitoring and UAV remote sensing
• Disaster response applications, referencing Chandran and Vipin's (2024) work on multi-UAV network architectures
• Urban infrastructure inspection possibilities

1. Battery Limitation Considerations:
   We have addressed this concern by:

• Acknowledging the need for energy optimization in extreme conditions
• Discussing potential solutions through energy-efficient systems, citing Barrile et al.'s (2024) research on autonomous charging systems

The revised text maintains academic rigor while improving readability through clearer organization and simplified language. We believe these changes provide readers with a better understanding of both our findings and their practical implications for the UAV industry. (This information has been added as a reference in Section Page 28, lines 1200-1209)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Thank you for your efforts in revising the article based on the reviews.

Please refer to the following points and make the necessary corrections:

 

[1] Lines 320, 324, 327, 331: Replace "Where" with "where."

[2] Line 499: Replace "Y" with "Y(hat)."

[3] Equation (7) in Chapter 2 has been revised.

However, the data analysis results in Chapter 4 remain the same as those in the previous V1 version.

Please revise the analysis using the normalization of Equation (7) for the test data.

 

Author Response

For research article-3319456

 

Response to Reviewer 1 Comments (Round 2)
1. Summary
. We sincerely thank you for your thorough and constructive review of our manuscript. Your detailed attention to grammatical consistency, mathematical notation accuracy, and particularly the crucial observation regarding the normalization process has significantly enhanced the quality of our work. The implementation of your suggested revisions, especially the normalization approach, has led to more standardized and reliable experimental results. These improvements have strengthened both the technical precision and overall scientific merit of our manuscript. We greatly appreciate your expertise in helping us achieve a higher standard of academic excellence.

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: Point [1] Lines 320, 324, 327, 331: Replace "Where" with "where.".

 

Response 1: Point [1] We are grateful for your careful attention to grammatical accuracy. Following your suggestion, we have corrected the capitalization of the word 'where' to lowercase on page 7, lines 320, 324, 327, and 331, thereby improving the grammatical consistency throughout our manuscript.

 

Comment 1: Point [2] Line 499: Replace "Y" with "Y(hat).

 

Response 1: Point [2] We sincerely appreciate your meticulous attention to mathematical notation accuracy. Following your suggestion, we have revised the notation from 'Y' to 'Ŷ' (Y-hat) on page 10, line 499, which more accurately represents the predicted value in our mathematical formulation. This correction enhances the mathematical precision and clarity of our manuscript

 

Comment 1: Point [3] Equation (7) in Chapter 2 has been revised. However, the data analysis results in Chapter 4 remain the same as those in the previous V1 version.

Please revise the analysis using the normalization of Equation (7) for the test data.

 

Response 1: Point [3] We sincerely appreciate your critical observation regarding the normalization process. This insightful comment has led to significant improvements in our analysis. By implementing the normalization method specified in Equation (7) for the test data, we have conducted a comprehensive revision that has yielded more precise results. The changes have been systematically implemented throughout the manuscript:

In the Abstract (page 1, line 28) and Introduction (page 2, line 76), we have updated the key findings to reflect the new analysis. Notably, Table 1 shows improved Response Time measurements, with our model demonstrating enhanced performance efficiency following the normalization implementation. The analysis results in Section 4.2 (pages 19-21, lines 905-950) have been thoroughly revised, leading to more definitive conclusions. Consequently, we have updated the corresponding values on page 23 (lines 1009 and 1016) to accurately reflect these experimental outcomes. The conclusions section (page 26, lines 1106-1107) has also been modified to align with these refined findings.

This comprehensive revision has significantly enhanced the clarity and reliability of our results, providing a more robust validation of our methodology. We are grateful for this suggestion, as it has substantially improved the scientific rigor of our work.

Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Authors must revise the table 2 objectively. Metrics must be comparable for example accuracy and make metrics cannot be completely comparable. Also costs must be revised and expressed in us dollar/euro/...

Author Response

For research article-3319456

 

Response to Reviewer 3 Comments (Round 2)
1. Summary
We sincerely thank the reviewer for their constructive feedback, which significantly contributes to improving the manuscript's quality and clarity. The suggestion to standardize the comparison metrics and cost representations in Table 2 is particularly valuable for ensuring objective and meaningful comparisons across different studies. Your careful attention to detail helps enhance the scientific rigor of our work.

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: Authors must revise the table 2 objectively. Metrics must be comparable for example accuracy and make metrics cannot be completely comparable. Also costs must be revised and expressed in us dollar/euro/..

 

Response 1: We appreciate the reviewer's valuable feedback regarding Table 2. We have thoroughly revised the table on page 24, line 1029, to ensure objective comparison across all studies. The metrics have been standardized, with accuracy measurements now consistently presented in the same format (±X meters) across all compared methods. Additionally, we have conducted additional research to convert all cost figures to US dollars (US$) using appropriate exchange rates from the respective publication dates to enable direct cost comparisons. The revised table now provides a more transparent and comparable presentation of both performance metrics and economic aspects across all methods. This standardization enhances the objectivity and clarity of our comparative analysis.

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article describes useful content on estimating altitude using K-means clustering and deep learning based on measurements from drones. However, there is a need to further elaborate on the methodology and the mathematical expressions used.

1. It describes a method of normalizing the learning data and testing data separately, but in that case, problems arise due to differences in the normalization scale.

It is desirable to separate training data and testing data after normalization.

2. Equation 4 cannot describe both the hidden layer and the output layer. 

Additionally, there are no definitions for the subscripts and the formula expression is incorrect.

3. The expressions in equations 5 to 8 also have errors.

Please also check the subscripts. 

n is already defined as the total number of data points on line 236.

4. There is a need to improve understanding with explanations and examples of the six predictor variables.

5. This paper describes a method for clustering sample data and learning for each cluster. After that, an explanation of the specific method for predicting new data is also needed.

Comments on the Quality of English Language

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Author Response

Comments 1: It describes a method of normalizing the learning data and testing data separately, but in that case, problems arise due to differences in the normalization scale. It is desirable to separate training data and testing data after normalization.

Response 1: We are deeply grateful for your invaluable time and meticulous feedback. Your insightful comments have significantly enhanced the quality and rigor of our research methodology and findings. We confirm that our normalization process was performed on the combined dataset, encompassing both training and testing data, prior to splitting. This approach ensures a consistent normalization scale across both subsets. To improve clarity, we will add a sentence specifying that normalization was applied to the full dataset initially to maintain uniform scaling. This method prevents any discrepancies in normalization scales between training and testing data. This adjustment will be incorporated in the revised manuscript page 8(line 372-375). Thank you for highlighting this point, as it allows us to further clarify our methodology.

Comments 2: Equation 4 cannot describe both the hidden layer and the output layer.  Additionally, there are no definitions for the subscripts and the formula expression is incorrect.

Response 2: We sincerely appreciate the editor’s guidance in helping us improve the clarity and rigor of our methodology. To clarify Equation 4 and its application across layers, we have broken down the transformations for each layer as follows: Two hidden layers are represented by distinct equations with their respective weights and biases: for the first hidden layer and  for the second. The output layer is represented by , completing the transformation to the final output. We have also specified activation functions for each layer to ensure clarity on how non-linearity is introduced and how outputs are processed. This approach aligns with best practices for transparency and accuracy in representing deep neural network layers. Mention exactly where in the revised manuscript this change can be found pages 8 - 9 (line 407 – 424).

Comments 3: The expressions in equations 5 to 8 also have errors. Please also check the subscripts. “n” is already defined as the total number of data points on line 236.

Response 3: We appreciate your meticulous review and insightful comments, which have helped us enhance the clarity and precision of our methodology. To address the issues with Equations 5 to 8, we have revised each equation to correct the expressions and ensure consistent use of subscripts page 9 (line 433 – 446). Additionally, we have streamlined the definition of n to avoid redundancy, specifying it as the total number of data points in each relevant instance. These corrections aim to ensure transparency and accuracy in the mathematical representations.

Comments 4: There is a need to improve understanding with explanations and examples of the six predictor variables.

Response 4: Thank you for your valuable feedback and suggestions to improve clarity. We have enhanced the explanation of each predictor variable by adding a detailed description and relevant examples to demonstrate their significance in the model. This additional information highlights how each variable contributes to the model’s performance, especially in predicting UAV altitude. Specifically, we have added new content on pages 13-14 (line 590-651), where each predictor variable is thoroughly described, including context-specific examples to illustrate their role in altitude estimation. We hope these adjustments meet the clarity standards expected and provide a more comprehensive understanding of our approach.

Comments 5: This paper describes a method for clustering sample data and learning for each cluster. After that, an explanation of the specific method for predicting new data is also needed.

Response 5: Thank you for your insightful feedback. In response to your comment, we have clarified the prediction process for new data within the proposed clustering-based learning model. Upon introducing new data, the system first assigns it to an appropriate cluster using the same distance metric employed during initial clustering. This assignment ensures that the new data point is grouped with similar data, capturing the unique characteristics of that cluster. Subsequently, the model trained specifically for that cluster is applied to generate predictions, thus leveraging the tailored learning from the clustered data to enhance prediction accuracy. This method allows the model to adapt its predictions to the inherent features of the data cluster, improving performance and reliability across various UAV operational contexts. We hope this additional explanation meets the clarity and rigor expected in our methodology.

 

 

Figure Explain Comments 5

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The article is presented in well –structurated manner, clear and the idea and the benefits of the study are well described. Also, the article fits very well in the requested topic.

However, some problems related to the writing part were identified, as follows:

-         The equations on page 5 do not have notations. Also, at line 242, the text suggests that an equation follows, and this does not exist.

The cited references that are not within the last 5 years represent a percentage of 14.28% (4 out of 28). Also, an excessive number of citations for a given author was not identified.

 

The article is scientifically interesting and the results are original. However, for a better relevance of the results, a more detailed description of them is required (e.g. a comparison of the errors between the method developed in the article and the sensors usually used to determine the altitude - barometer, lidar, GPS, flow sensor, etc.). Please consider a more detailed presentation of the results.

The manuscript’s results are reproductible based on the details given in the methods section.

The figures/tables/images/schemes are easy to interpret and understand and it is consistent with the description made in the article.

The conclusions are in accordance with the results presented in the article.

The ethics statements and data availability statements are presented at the and of article and are properly formulated.

Author Response

Comments 1: The equations on page 5 do not have notations. Also, at line 242, the text suggests that an equation follows, and this does not exist.

Response 1: Thank you for your careful review and constructive comments. In response, we have revised page 5 to ensure that all equations are accompanied by clear and consistent notations, enhancing readability and comprehension. Additionally, we addressed the gap on line 242, where a reference to a forthcoming equation was mistakenly included without the equation itself. This has been corrected in the revised manuscript, with the appropriate equation now appearing on pages 5 (lines 246-254). We appreciate your attention to these details, which has helped us improve the clarity and accuracy of our work.

 

Comments 2: The cited references that are not within the last 5 years represent a percentage of 14.28% (4 out of 28). Also, an excessive number of citations for a given author was not identified.

Response 2: Thank you for reviewing our submission. We appreciate your feedback regarding the cited references. In response to your recommendations, we have updated all four references to more current literature (within the past 5 years) while maintaining their relevance to the manuscript's objectives. Specifically, we have revised:

• Reference 20 on page 4 (Lines 190-192)
• Reference 21 on page 4 (Lines 196-199)
• Reference 26 on page 5 (Lines 227-230)
• Reference 27 on page 6 (Lines 272-276)

Additionally, corresponding updates have been made to these references in the References section on page 24 (Lines 1025-1028 and 1041-1044) for entries 20, 21, 26, and 27, respectively.

 

Comments 3: The article is scientifically interesting and the results are original. However, for a better relevance of the results, a more detailed description of them is required (e.g. a comparison of the errors between the method developed in the article and the sensors usually used to determine the altitude - barometer, lidar, GPS, flow sensor, etc.). Please consider a more detailed presentation of the results.

Response 3: Thank you for your valuable feedback. To enhance the relevance of our results, we have provided a detailed comparison of the error rates between our developed method and traditional altitude estimation sensors, including barometers, LiDAR, GPS, and flow sensors. Specifically, we have included Mean Squared Error (MSE) and Mean Absolute Error (MAE) metrics for each method, as well as examples of scenarios where each sensor type typically excels or faces limitations. This additional analysis illustrates the advantages of our DL-KMA model, particularly in terms of adaptability, accuracy, and cost-efficiency, especially in environments where lightweight UAVs face operational constraints. We hope this expanded discussion meets the journal’s standards for clarity and depth and enhances the understanding of our model’s practical applications. Mention exactly where in the revised manuscript this change can be found pages 19 (line 861 – 882).

Author Response File: Author Response.docx